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1 25 mL of an aqueous solution of KCl was found to require 20 mL of 1 M AgNO3 solution when titrated

using a K 2CrO4 as indicator The freezing point of KCl solution will be

[ 1f K 20 mol kgminus= deg and molarity = molality]

(A) 16minus deg C (B) 32deg C (C) 16deg C (D) 32minus deg C

2 If there were three possible values1 1

02 2

minus +

for spin magnetic quantum number Which of the

following statement(s) isare correct regarding a hypothetical periodic table based on these conditions

assuming all other laws remain same

(A) First period would have only 2 elements (B) Second period would have 12 elements

(C) Periodic table would contain 27 groups (D) Helium will become paramagnetic

3 Statement 1 Edeg for 3 2Mn Mn+ + is more positive than for 3 2Cr Cr + +

Statement 2 The third ionization energy of Mn is larger than that of Cr

(A) Statement-1 is True Statement-2 is True and Statement-2 is a correct explanation for

Statement-1

(B) Statement-1 is True Statement-2 is True and Statement-2 is NOT a correct explanation for

Statement-1

(C) Statement-1 is True Statement-2 is False

(D) Statement-1 is False Statement-2 is True

4 Which of the following has dsp2 hybridisation and is diamagnetic in nature

I [Ni(DMG)2] II3

4[Ag(SCN) ] minus III 4[AuBr ]minus

(A) I III (B) I II III (C) I II (D) None of these

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5 The pH at which in presence of a given indicator a titration is ended is sometimes known as titration

exponent and is denoted by pT For methyl orange pT value is 40 Calculate the indicator (methyl

orange) error (in multiple of210minus

) if 01 N HCl is titrated by 01 N NaOH [Hint Visualise error in

terms of H+ added versus H

+ left]

(A) 10 (B) 20 (C) 30 (D) 40

6 A CCP structure has the formula AB2C4 where C atoms are cubic closed packed B atoms occupy half of

the octahedral voids A atoms are present in 18th of the tetrahedral voids The packing fraction if A B

atoms are in contact with C

(A) 062 (B) 077 (C) 070 (D) 059

7 X 2 4K CrO rarr Yellow ppt 3 NH

soln rarr No change

Y 2 4K CrO rarr Red ppt 3 NH

soln rarr black ppt

Z 2 4K CrO rarr Red ppt 3 NH

soln rarr ppt dissolves

X Y and Z are

(A) 222Pb Hg Ag++ + (B) 2 2

2Ag Hg Pb++ +

(C) 22

2Hg Ag Pb+ + + (D) 222Pb Ag Hg ++ +

8 Which of the following is INCORRECT

(A) Slowest step is the Rate determining step

(B) A reaction mechanism may have more than one intermediate complex

(C) For an exothermic reaction Energy of products is more than that of reactants

(D) Order of a reaction may be fractional

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9 The structure of a poly peptide formed from Alanine Glycine amp Phenylalanine will be

(A) 2 2

6 5 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H CH C H

minus minus minus minus minus minus minus minus

(B) 2 2

6 5 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H C H

minus minus minus minus minus minus minus minus

(C) 2 2

3 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

CH CH C H

minus minus minus minus minus minus minus minus

(D) 2 2 3

3 2 6 5

O O O|| || ||

H N CH C NH CH C NH C CH CH

| |CH CH C H

minus minus minus minus minus minus minus minus minus

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Sodium fusion extract obtained from nitrogen containing organic compounds on treatment with iron (II)

sulphate and H2SO4 in presence of air gives a Prussian blue precipitate

10 The blue colour is due to the formation of

(A) Fe4[Fe(CN)6]3 (B) Fe3[Fe(CN)6]2 (C) Fe4[Fe(CN)6]2 (D) Fe3[Fe(CN)6]3

11 In which of the following compound the sodium fusion extract of nitrogen containing compound on

treatment with iron(II) sulphate and H2SO4 in presence of air will not gives a Prussian blue precipitate

(A) H2 NCO NHNH2HCl (B) NH2 NH2

HCl

(C) NH2CONH2 (D) C6H5 NH NH2HCl

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The Organic compounds undergo various types of reaction Such as Electrophilic addition Nucleophilic

substitution Electrophilic substitution etc The characteristic reaction of an organic compound depends on nature

of functional group stability of intermediate and reaction conditions

12 The major product in the following reaction is

CH3 mdashC = CHmdash HBr

CH3

Major Product mdashNO2

CH3 mdashCHmdashCHmdash

CH3

mdashNO2

Br

(A)

CH3 mdashCmdash CH2 mdash

CH3

mdashNO2

Br

(B)

CH3 mdashCHmdashCHmdash

Br

mdashNO2(C)

CH3

CH3 mdashCHmdashCH2 mdash

CH3

(D) mdashNO2

Br

13 The rate of the reaction

Rmdash mdashCH2 mdashBr + N Rmdash mdashCH2 mdashN oplus

Br

is influenced by the hyper conjugation effect of group R If R sequentially is

(P) CH3 mdash (Q) CH3 ndashCH2 mdash CH3 mdashCHmdash

CH3

(R)

The decreasing order of speed of the above reaction is

(A) S gt R gt Q gt P (B) P gt Q gt R gt S (C) P gt S gt R gt Q (D) R gt Q gt P gt S

14 During FC alkylation in the given structure electrophile will go at position (A) 1 and 2 both

(B) 1 only

(C) 2 only

(D) No substitution possible

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CH3 mdashCmdash

CH3

(S)

CH3

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15 The correct statement(s) among the following is(are)

(A) NCl5 does not exist while PCl5 does

(B) Lead prefers to form tetravalent compounds

(C) The three CmdashO bonds are identical in the carbonate ion

(D) Both 2O+ and NO are paramagnetic

16

(A) Ring I is pyranose with α -glycosidic link

(B) Ring II is pyranose with β -glycosidic link

(C) The above given disaccharide is non-reducing

(D) The above given disaccharide is lactose

17 Which of the following is(are) TRUE

(A) A mixture of Toluene and aniline can be separated by reacting with hydrochloric acid

(B) (C2H5)2 NH amp C3H7OH can be separated by adding hot conc H2SO4 followed by steam

distillation(C) Adding ceric ammonium nitrate to an aqueous solution of para-cresol given reddish brown

precipitate

(D) HCHO and CH3CHO can be distinguished by the action of ammoniacal AgNO3

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18 Which of the following is(are) CORRECT statement(s) about the compound NO[BF4]

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B Fminus bond length in this compound is longer than that in BF3

19 K 2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration

Correct statement(s) regarding the above change are

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20 The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is

I 2 4-Dinitrophenyl hydrazine II Lucas reagent

III Iodoform Test IV Tollensrsquo reagent

The correct option is

(A) I II (B) II III (C) III IV (D) I III IV

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 8 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1119

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1219

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

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58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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9831269831179831072013 2 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113 (983107983112983109983117983113983123983124983122983129) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

1 25 mL of an aqueous solution of KCl was found to require 20 mL of 1 M AgNO3 solution when titrated

using a K 2CrO4 as indicator The freezing point of KCl solution will be

[ 1f K 20 mol kgminus= deg and molarity = molality]

(A) 16minus deg C (B) 32deg C (C) 16deg C (D) 32minus deg C

2 If there were three possible values1 1

02 2

minus +

for spin magnetic quantum number Which of the

following statement(s) isare correct regarding a hypothetical periodic table based on these conditions

assuming all other laws remain same

(A) First period would have only 2 elements (B) Second period would have 12 elements

(C) Periodic table would contain 27 groups (D) Helium will become paramagnetic

3 Statement 1 Edeg for 3 2Mn Mn+ + is more positive than for 3 2Cr Cr + +

Statement 2 The third ionization energy of Mn is larger than that of Cr

(A) Statement-1 is True Statement-2 is True and Statement-2 is a correct explanation for

Statement-1

(B) Statement-1 is True Statement-2 is True and Statement-2 is NOT a correct explanation for

Statement-1

(C) Statement-1 is True Statement-2 is False

(D) Statement-1 is False Statement-2 is True

4 Which of the following has dsp2 hybridisation and is diamagnetic in nature

I [Ni(DMG)2] II3

4[Ag(SCN) ] minus III 4[AuBr ]minus

(A) I III (B) I II III (C) I II (D) None of these

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5 The pH at which in presence of a given indicator a titration is ended is sometimes known as titration

exponent and is denoted by pT For methyl orange pT value is 40 Calculate the indicator (methyl

orange) error (in multiple of210minus

) if 01 N HCl is titrated by 01 N NaOH [Hint Visualise error in

terms of H+ added versus H

+ left]

(A) 10 (B) 20 (C) 30 (D) 40

6 A CCP structure has the formula AB2C4 where C atoms are cubic closed packed B atoms occupy half of

the octahedral voids A atoms are present in 18th of the tetrahedral voids The packing fraction if A B

atoms are in contact with C

(A) 062 (B) 077 (C) 070 (D) 059

7 X 2 4K CrO rarr Yellow ppt 3 NH

soln rarr No change

Y 2 4K CrO rarr Red ppt 3 NH

soln rarr black ppt

Z 2 4K CrO rarr Red ppt 3 NH

soln rarr ppt dissolves

X Y and Z are

(A) 222Pb Hg Ag++ + (B) 2 2

2Ag Hg Pb++ +

(C) 22

2Hg Ag Pb+ + + (D) 222Pb Ag Hg ++ +

8 Which of the following is INCORRECT

(A) Slowest step is the Rate determining step

(B) A reaction mechanism may have more than one intermediate complex

(C) For an exothermic reaction Energy of products is more than that of reactants

(D) Order of a reaction may be fractional

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9831269831179831072013 4 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

9 The structure of a poly peptide formed from Alanine Glycine amp Phenylalanine will be

(A) 2 2

6 5 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H CH C H

minus minus minus minus minus minus minus minus

(B) 2 2

6 5 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H C H

minus minus minus minus minus minus minus minus

(C) 2 2

3 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

CH CH C H

minus minus minus minus minus minus minus minus

(D) 2 2 3

3 2 6 5

O O O|| || ||

H N CH C NH CH C NH C CH CH

| |CH CH C H

minus minus minus minus minus minus minus minus minus

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 10 983085 11

Sodium fusion extract obtained from nitrogen containing organic compounds on treatment with iron (II)

sulphate and H2SO4 in presence of air gives a Prussian blue precipitate

10 The blue colour is due to the formation of

(A) Fe4[Fe(CN)6]3 (B) Fe3[Fe(CN)6]2 (C) Fe4[Fe(CN)6]2 (D) Fe3[Fe(CN)6]3

11 In which of the following compound the sodium fusion extract of nitrogen containing compound on

treatment with iron(II) sulphate and H2SO4 in presence of air will not gives a Prussian blue precipitate

(A) H2 NCO NHNH2HCl (B) NH2 NH2

HCl

(C) NH2CONH2 (D) C6H5 NH NH2HCl

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9831269831179831072013 5 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

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The Organic compounds undergo various types of reaction Such as Electrophilic addition Nucleophilic

substitution Electrophilic substitution etc The characteristic reaction of an organic compound depends on nature

of functional group stability of intermediate and reaction conditions

12 The major product in the following reaction is

CH3 mdashC = CHmdash HBr

CH3

Major Product mdashNO2

CH3 mdashCHmdashCHmdash

CH3

mdashNO2

Br

(A)

CH3 mdashCmdash CH2 mdash

CH3

mdashNO2

Br

(B)

CH3 mdashCHmdashCHmdash

Br

mdashNO2(C)

CH3

CH3 mdashCHmdashCH2 mdash

CH3

(D) mdashNO2

Br

13 The rate of the reaction

Rmdash mdashCH2 mdashBr + N Rmdash mdashCH2 mdashN oplus

Br

is influenced by the hyper conjugation effect of group R If R sequentially is

(P) CH3 mdash (Q) CH3 ndashCH2 mdash CH3 mdashCHmdash

CH3

(R)

The decreasing order of speed of the above reaction is

(A) S gt R gt Q gt P (B) P gt Q gt R gt S (C) P gt S gt R gt Q (D) R gt Q gt P gt S

14 During FC alkylation in the given structure electrophile will go at position (A) 1 and 2 both

(B) 1 only

(C) 2 only

(D) No substitution possible

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

CH3 mdashCmdash

CH3

(S)

CH3

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9831269831179831072013 6 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

15 The correct statement(s) among the following is(are)

(A) NCl5 does not exist while PCl5 does

(B) Lead prefers to form tetravalent compounds

(C) The three CmdashO bonds are identical in the carbonate ion

(D) Both 2O+ and NO are paramagnetic

16

(A) Ring I is pyranose with α -glycosidic link

(B) Ring II is pyranose with β -glycosidic link

(C) The above given disaccharide is non-reducing

(D) The above given disaccharide is lactose

17 Which of the following is(are) TRUE

(A) A mixture of Toluene and aniline can be separated by reacting with hydrochloric acid

(B) (C2H5)2 NH amp C3H7OH can be separated by adding hot conc H2SO4 followed by steam

distillation(C) Adding ceric ammonium nitrate to an aqueous solution of para-cresol given reddish brown

precipitate

(D) HCHO and CH3CHO can be distinguished by the action of ammoniacal AgNO3

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18 Which of the following is(are) CORRECT statement(s) about the compound NO[BF4]

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B Fminus bond length in this compound is longer than that in BF3

19 K 2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration

Correct statement(s) regarding the above change are

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20 The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is

I 2 4-Dinitrophenyl hydrazine II Lucas reagent

III Iodoform Test IV Tollensrsquo reagent

The correct option is

(A) I II (B) II III (C) III IV (D) I III IV

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9831269831179831072013 8 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

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9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

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9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

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9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

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38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

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983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

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9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

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9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

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9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

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9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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9831269831179831072013 3 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

5 The pH at which in presence of a given indicator a titration is ended is sometimes known as titration

exponent and is denoted by pT For methyl orange pT value is 40 Calculate the indicator (methyl

orange) error (in multiple of210minus

) if 01 N HCl is titrated by 01 N NaOH [Hint Visualise error in

terms of H+ added versus H

+ left]

(A) 10 (B) 20 (C) 30 (D) 40

6 A CCP structure has the formula AB2C4 where C atoms are cubic closed packed B atoms occupy half of

the octahedral voids A atoms are present in 18th of the tetrahedral voids The packing fraction if A B

atoms are in contact with C

(A) 062 (B) 077 (C) 070 (D) 059

7 X 2 4K CrO rarr Yellow ppt 3 NH

soln rarr No change

Y 2 4K CrO rarr Red ppt 3 NH

soln rarr black ppt

Z 2 4K CrO rarr Red ppt 3 NH

soln rarr ppt dissolves

X Y and Z are

(A) 222Pb Hg Ag++ + (B) 2 2

2Ag Hg Pb++ +

(C) 22

2Hg Ag Pb+ + + (D) 222Pb Ag Hg ++ +

8 Which of the following is INCORRECT

(A) Slowest step is the Rate determining step

(B) A reaction mechanism may have more than one intermediate complex

(C) For an exothermic reaction Energy of products is more than that of reactants

(D) Order of a reaction may be fractional

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 4 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

9 The structure of a poly peptide formed from Alanine Glycine amp Phenylalanine will be

(A) 2 2

6 5 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H CH C H

minus minus minus minus minus minus minus minus

(B) 2 2

6 5 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H C H

minus minus minus minus minus minus minus minus

(C) 2 2

3 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

CH CH C H

minus minus minus minus minus minus minus minus

(D) 2 2 3

3 2 6 5

O O O|| || ||

H N CH C NH CH C NH C CH CH

| |CH CH C H

minus minus minus minus minus minus minus minus minus

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 10 983085 11

Sodium fusion extract obtained from nitrogen containing organic compounds on treatment with iron (II)

sulphate and H2SO4 in presence of air gives a Prussian blue precipitate

10 The blue colour is due to the formation of

(A) Fe4[Fe(CN)6]3 (B) Fe3[Fe(CN)6]2 (C) Fe4[Fe(CN)6]2 (D) Fe3[Fe(CN)6]3

11 In which of the following compound the sodium fusion extract of nitrogen containing compound on

treatment with iron(II) sulphate and H2SO4 in presence of air will not gives a Prussian blue precipitate

(A) H2 NCO NHNH2HCl (B) NH2 NH2

HCl

(C) NH2CONH2 (D) C6H5 NH NH2HCl

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9831269831179831072013 5 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 12 983085 14

The Organic compounds undergo various types of reaction Such as Electrophilic addition Nucleophilic

substitution Electrophilic substitution etc The characteristic reaction of an organic compound depends on nature

of functional group stability of intermediate and reaction conditions

12 The major product in the following reaction is

CH3 mdashC = CHmdash HBr

CH3

Major Product mdashNO2

CH3 mdashCHmdashCHmdash

CH3

mdashNO2

Br

(A)

CH3 mdashCmdash CH2 mdash

CH3

mdashNO2

Br

(B)

CH3 mdashCHmdashCHmdash

Br

mdashNO2(C)

CH3

CH3 mdashCHmdashCH2 mdash

CH3

(D) mdashNO2

Br

13 The rate of the reaction

Rmdash mdashCH2 mdashBr + N Rmdash mdashCH2 mdashN oplus

Br

is influenced by the hyper conjugation effect of group R If R sequentially is

(P) CH3 mdash (Q) CH3 ndashCH2 mdash CH3 mdashCHmdash

CH3

(R)

The decreasing order of speed of the above reaction is

(A) S gt R gt Q gt P (B) P gt Q gt R gt S (C) P gt S gt R gt Q (D) R gt Q gt P gt S

14 During FC alkylation in the given structure electrophile will go at position (A) 1 and 2 both

(B) 1 only

(C) 2 only

(D) No substitution possible

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

CH3 mdashCmdash

CH3

(S)

CH3

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9831269831179831072013 6 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

15 The correct statement(s) among the following is(are)

(A) NCl5 does not exist while PCl5 does

(B) Lead prefers to form tetravalent compounds

(C) The three CmdashO bonds are identical in the carbonate ion

(D) Both 2O+ and NO are paramagnetic

16

(A) Ring I is pyranose with α -glycosidic link

(B) Ring II is pyranose with β -glycosidic link

(C) The above given disaccharide is non-reducing

(D) The above given disaccharide is lactose

17 Which of the following is(are) TRUE

(A) A mixture of Toluene and aniline can be separated by reacting with hydrochloric acid

(B) (C2H5)2 NH amp C3H7OH can be separated by adding hot conc H2SO4 followed by steam

distillation(C) Adding ceric ammonium nitrate to an aqueous solution of para-cresol given reddish brown

precipitate

(D) HCHO and CH3CHO can be distinguished by the action of ammoniacal AgNO3

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 7 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

18 Which of the following is(are) CORRECT statement(s) about the compound NO[BF4]

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B Fminus bond length in this compound is longer than that in BF3

19 K 2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration

Correct statement(s) regarding the above change are

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20 The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is

I 2 4-Dinitrophenyl hydrazine II Lucas reagent

III Iodoform Test IV Tollensrsquo reagent

The correct option is

(A) I II (B) II III (C) III IV (D) I III IV

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 8 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

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9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

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52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

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983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

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58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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9 The structure of a poly peptide formed from Alanine Glycine amp Phenylalanine will be

(A) 2 2

6 5 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H CH C H

minus minus minus minus minus minus minus minus

(B) 2 2

6 5 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

C H C H

minus minus minus minus minus minus minus minus

(C) 2 2

3 2 6 5

O O|| ||

H N CH C NH CH C NH CH COOH| |

CH CH C H

minus minus minus minus minus minus minus minus

(D) 2 2 3

3 2 6 5

O O O|| || ||

H N CH C NH CH C NH C CH CH

| |CH CH C H

minus minus minus minus minus minus minus minus minus

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 10 983085 11

Sodium fusion extract obtained from nitrogen containing organic compounds on treatment with iron (II)

sulphate and H2SO4 in presence of air gives a Prussian blue precipitate

10 The blue colour is due to the formation of

(A) Fe4[Fe(CN)6]3 (B) Fe3[Fe(CN)6]2 (C) Fe4[Fe(CN)6]2 (D) Fe3[Fe(CN)6]3

11 In which of the following compound the sodium fusion extract of nitrogen containing compound on

treatment with iron(II) sulphate and H2SO4 in presence of air will not gives a Prussian blue precipitate

(A) H2 NCO NHNH2HCl (B) NH2 NH2

HCl

(C) NH2CONH2 (D) C6H5 NH NH2HCl

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The Organic compounds undergo various types of reaction Such as Electrophilic addition Nucleophilic

substitution Electrophilic substitution etc The characteristic reaction of an organic compound depends on nature

of functional group stability of intermediate and reaction conditions

12 The major product in the following reaction is

CH3 mdashC = CHmdash HBr

CH3

Major Product mdashNO2

CH3 mdashCHmdashCHmdash

CH3

mdashNO2

Br

(A)

CH3 mdashCmdash CH2 mdash

CH3

mdashNO2

Br

(B)

CH3 mdashCHmdashCHmdash

Br

mdashNO2(C)

CH3

CH3 mdashCHmdashCH2 mdash

CH3

(D) mdashNO2

Br

13 The rate of the reaction

Rmdash mdashCH2 mdashBr + N Rmdash mdashCH2 mdashN oplus

Br

is influenced by the hyper conjugation effect of group R If R sequentially is

(P) CH3 mdash (Q) CH3 ndashCH2 mdash CH3 mdashCHmdash

CH3

(R)

The decreasing order of speed of the above reaction is

(A) S gt R gt Q gt P (B) P gt Q gt R gt S (C) P gt S gt R gt Q (D) R gt Q gt P gt S

14 During FC alkylation in the given structure electrophile will go at position (A) 1 and 2 both

(B) 1 only

(C) 2 only

(D) No substitution possible

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

CH3 mdashCmdash

CH3

(S)

CH3

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983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

15 The correct statement(s) among the following is(are)

(A) NCl5 does not exist while PCl5 does

(B) Lead prefers to form tetravalent compounds

(C) The three CmdashO bonds are identical in the carbonate ion

(D) Both 2O+ and NO are paramagnetic

16

(A) Ring I is pyranose with α -glycosidic link

(B) Ring II is pyranose with β -glycosidic link

(C) The above given disaccharide is non-reducing

(D) The above given disaccharide is lactose

17 Which of the following is(are) TRUE

(A) A mixture of Toluene and aniline can be separated by reacting with hydrochloric acid

(B) (C2H5)2 NH amp C3H7OH can be separated by adding hot conc H2SO4 followed by steam

distillation(C) Adding ceric ammonium nitrate to an aqueous solution of para-cresol given reddish brown

precipitate

(D) HCHO and CH3CHO can be distinguished by the action of ammoniacal AgNO3

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18 Which of the following is(are) CORRECT statement(s) about the compound NO[BF4]

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B Fminus bond length in this compound is longer than that in BF3

19 K 2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration

Correct statement(s) regarding the above change are

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20 The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is

I 2 4-Dinitrophenyl hydrazine II Lucas reagent

III Iodoform Test IV Tollensrsquo reagent

The correct option is

(A) I II (B) II III (C) III IV (D) I III IV

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9831269831179831072013 8 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

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28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

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9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

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In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

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983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

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38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

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983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

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9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

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49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

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9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

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9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

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9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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9831269831179831072013 5 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 12 983085 14

The Organic compounds undergo various types of reaction Such as Electrophilic addition Nucleophilic

substitution Electrophilic substitution etc The characteristic reaction of an organic compound depends on nature

of functional group stability of intermediate and reaction conditions

12 The major product in the following reaction is

CH3 mdashC = CHmdash HBr

CH3

Major Product mdashNO2

CH3 mdashCHmdashCHmdash

CH3

mdashNO2

Br

(A)

CH3 mdashCmdash CH2 mdash

CH3

mdashNO2

Br

(B)

CH3 mdashCHmdashCHmdash

Br

mdashNO2(C)

CH3

CH3 mdashCHmdashCH2 mdash

CH3

(D) mdashNO2

Br

13 The rate of the reaction

Rmdash mdashCH2 mdashBr + N Rmdash mdashCH2 mdashN oplus

Br

is influenced by the hyper conjugation effect of group R If R sequentially is

(P) CH3 mdash (Q) CH3 ndashCH2 mdash CH3 mdashCHmdash

CH3

(R)

The decreasing order of speed of the above reaction is

(A) S gt R gt Q gt P (B) P gt Q gt R gt S (C) P gt S gt R gt Q (D) R gt Q gt P gt S

14 During FC alkylation in the given structure electrophile will go at position (A) 1 and 2 both

(B) 1 only

(C) 2 only

(D) No substitution possible

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

CH3 mdashCmdash

CH3

(S)

CH3

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9831269831179831072013 6 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

15 The correct statement(s) among the following is(are)

(A) NCl5 does not exist while PCl5 does

(B) Lead prefers to form tetravalent compounds

(C) The three CmdashO bonds are identical in the carbonate ion

(D) Both 2O+ and NO are paramagnetic

16

(A) Ring I is pyranose with α -glycosidic link

(B) Ring II is pyranose with β -glycosidic link

(C) The above given disaccharide is non-reducing

(D) The above given disaccharide is lactose

17 Which of the following is(are) TRUE

(A) A mixture of Toluene and aniline can be separated by reacting with hydrochloric acid

(B) (C2H5)2 NH amp C3H7OH can be separated by adding hot conc H2SO4 followed by steam

distillation(C) Adding ceric ammonium nitrate to an aqueous solution of para-cresol given reddish brown

precipitate

(D) HCHO and CH3CHO can be distinguished by the action of ammoniacal AgNO3

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18 Which of the following is(are) CORRECT statement(s) about the compound NO[BF4]

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B Fminus bond length in this compound is longer than that in BF3

19 K 2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration

Correct statement(s) regarding the above change are

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20 The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is

I 2 4-Dinitrophenyl hydrazine II Lucas reagent

III Iodoform Test IV Tollensrsquo reagent

The correct option is

(A) I II (B) II III (C) III IV (D) I III IV

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983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

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9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

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58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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9831269831179831072013 6 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

15 The correct statement(s) among the following is(are)

(A) NCl5 does not exist while PCl5 does

(B) Lead prefers to form tetravalent compounds

(C) The three CmdashO bonds are identical in the carbonate ion

(D) Both 2O+ and NO are paramagnetic

16

(A) Ring I is pyranose with α -glycosidic link

(B) Ring II is pyranose with β -glycosidic link

(C) The above given disaccharide is non-reducing

(D) The above given disaccharide is lactose

17 Which of the following is(are) TRUE

(A) A mixture of Toluene and aniline can be separated by reacting with hydrochloric acid

(B) (C2H5)2 NH amp C3H7OH can be separated by adding hot conc H2SO4 followed by steam

distillation(C) Adding ceric ammonium nitrate to an aqueous solution of para-cresol given reddish brown

precipitate

(D) HCHO and CH3CHO can be distinguished by the action of ammoniacal AgNO3

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9831269831179831072013 7 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

18 Which of the following is(are) CORRECT statement(s) about the compound NO[BF4]

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B Fminus bond length in this compound is longer than that in BF3

19 K 2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration

Correct statement(s) regarding the above change are

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20 The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is

I 2 4-Dinitrophenyl hydrazine II Lucas reagent

III Iodoform Test IV Tollensrsquo reagent

The correct option is

(A) I II (B) II III (C) III IV (D) I III IV

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 8 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

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9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

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9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

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49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

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9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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9831269831179831072013 7 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

18 Which of the following is(are) CORRECT statement(s) about the compound NO[BF4]

(A) It has 5 and 2 bondσ π

(B) Nitrogen-oxygen bond length is higher than nitric oxide (NO)

(C) It is a diamagnetic species

(D) B Fminus bond length in this compound is longer than that in BF3

19 K 2MnO4 in unstable in solution and the green solution obtained is changed into purple colouration

Correct statement(s) regarding the above change are

(A) It is a disproportionation reaction

(B) It produces blackish-brown precipitate of MnO2

(C) Purple colour is due to formation of KMnO4 which forms purple (almost black) crystals on

crystallization

(D) Crystals of KMnO4 if heated will dissociate to give off oxygen

20 The reagent that can be used to distinguish between the products obtained by the acid hydrolysis of (A)

and (B) given below is

I 2 4-Dinitrophenyl hydrazine II Lucas reagent

III Iodoform Test IV Tollensrsquo reagent

The correct option is

(A) I II (B) II III (C) III IV (D) I III IV

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 8 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

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7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1519

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9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

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49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

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httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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httpslidepdfcomreaderfulljee-advance-mock-test-paper2 819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 8 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113 (983120983112983129983123983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

21 An insect of negligible mass is sitting on a block of mass M tied with a

spring of force constant k The block performs simple harmonic motion

with amplitude A in front of a plane mirror placed as shown

The maximum speed of insect relative to its image will be

(A)k

A (B)3

2

A k

(C) 3 k

A (D) 2 M

Ak

22 A particle revolves in clockwise direction (as seen from point A) in a

circle C of radius 1 cm and completes one revolution in 2 sec The axis

of the circle (coincides with) principal axis of the mirror and radius of

curvature of the mirror is 20 cm Then the direction of revolution

(as seen from A) of the image of the particle and its speed is

(A) Clockwise 11 57 cmsminus (B) Clockwise 314 1cmsminus

(C) Anticlockwise 157 1cmsminus (D) Anticlockwise 314 1cmsminus

23 The region between two concentric spheres of radii a and b(gta) contains volume charge

density ( ) C

r r ρ = where C is a constant and r is the radial distance as shown in

figure A point charge q is placed at the origin r = 0 Find the value of C for which the

electric field in the region between the spheres is constant (ie r independent)

(A) 2

q

aπ (B)

( )2 2

q

a bπ + (C)

22

q

aπ (D)

22

q

bπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

qra

b

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9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

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9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

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9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

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38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

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983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 9 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

24 Two ends A and B of a smooth chain of mass m and length l are situated as

shown in fig If an external agent pulls A till it comes to same level of B

work done by external agent is

(A) 36

mgl (B)

15

mgl

(C) 9

mgl (D) None of these

25 In the figure shown the instantaneous speed of end A of the rod is v to the

left The angular velocity of the rod of length L must be

(A)2

v

L (B)

v

L

(C) 3

2

v

L (D) None of these

26 Figure shows a crude type of atomizer When bulb A is compressed air flowsswiftly through tube BC causing a reduced pressure in the particles of the

vertical tube Liquid rises in the tube enters BC and is sprayed out If the

pressure in the bulb is P a + P where P is the gauge pressure and P a is the

atmospheric pressure v is the speed of air in BC find how large would v

need to be to cause the liquid to rise to BC Density of air = 13 Kg m3

(A) 0 65

P gh

ρ + (B)

0 65

P gh

minus ρ

(C)

0 65

P h g

ρ +

(D)

0 65

P gh

ρ minus

27 Two particles of medium disturbed by the wave propagation are at x1 = 0 and x2 = 1 cm The respective

displacements (in cm) of the particles can be given by the equations

( )1 22 3 2 3 8 y sin t y sin t π π π = = minus

The wave velocity is

(A) 16 cm s (B) 24 cm s (C) 12 cm s (D) 8 cm s

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

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9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

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9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1419

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

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983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1519

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1619

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1019

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 10 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

28 A tennis ball with (small) mass m2 rests on the top of a basketball of mass m1 which

is at a height h above the ground and the bottom of the tennis ball is at height

(h + d ) above the ground The balls are dropped To what height does the tennis ball

bounce with respect to ground (Assume all collisions to be elastic and 1 2m m )

(A) 7h + d (B) 7h (C) 9h (D) 9h + d

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 29 983085 30

In a modified YDSE the region between the screen and slits is

immersed in liquid whose refractive index varies with time as

micro1 = (52) ndash (T 4) until it reaches a steady state value of 54

A glass plate of thickness 36 mmicro and refractive index = 32 is

introduced in front of one of the slits

29 Find the time when central maxima is at point O

located symmetrically on the x-axis

(A) 2 s (B) 4 s (C) 6 s (D) 8 s

30 What is the speed of the central maxima when it is at O

(A) 3 13 10 msminus minustimes (B) 3 14 10 msminus minustimes (C) 3 110 10 msminus minustimes (C) 3 11 10 msminus minustimes

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1119

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1219

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1319

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1419

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1519

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1619

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1119

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 11 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120983137983154983137983143983154983137983152983144 983142983151983154 983121983157983141983155983156983145983151983150 31 983085 32

In the circuit shown in fig the capacitor has capacitance 20C mF = and is initially charged to 100 V with the

polarity shown The resistor R0 has resistance 10Ω At time t = 0 the switch is closed The smaller circuit is not

connected in any way to the larger one The wire of the smaller circuit has a

resistance of 11 0Ω mminus and contains 25 loops and its dimensions are a = 100 cm

and b = 200 cm The distance c is 50 cm (The figure is not drawn to scale) Both

circuits are held stationary in the same plane Assume that only the wire nearest to

the smaller circuit produces an appreciable magnetic field through it and length of

that wire is much larger than the smaller circuit (ln2 = 00693 and ln3 = 1010)

31 The current in the larger circuit 200 ms after closing S is

(A) 5

Ae

(B) 2

Ae

(C) 15

Ae

(D) 10

Ae

32 The current in the smaller circuit 200 ms after closing S is

(A) 0 54 Amicro B) 0 10 Amicro (C) 0 15 Amicro (D) 0 36 Amicro

33 A tube of uniform cross section is used to siphon water

from a vessel V as shown in the figure The pressure over

the open end of water in the vessel is atmospheric

pressure ( )50 1 10 P Pa= times The heights of the tube above

and below the water level in the vessel are h1 and h2

respectively If h2 = 30 m the maximum value of h1 for

which the siphon will work is ( g = 10 m s2)

(A) 30 m (B) 60 m (C) 7 m (D) 48 m

34 A uniform magnetic field of induction B is confined to a cylindrical region of radius R The magnetic

field is increasing at a constant rate of 1dB dt Tsminus An electron placed at the point P on the periphery of

the field experiences an acceleration of

(A) towards left2

eR dB

m dt (B) towards right

2

eR dB

m dt

(C) towards lefteR dB

m dt (D) zero

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1319

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1419

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1519

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1619

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 12 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

35 A parallel-plate air capacitor has initial capacitance C If plate separation is slowly increased from d 1 to

d 2 then mark the correct statement(s) [Take potential of the capacitor to be constant ie throughout the

process it remains connected to battery]

(A) Work done by electric force = minus work done by external agent

(B) Work done by external force F dx= minusint

where F

the electric force of attraction between the

plates at plate separation x

(C) Work done by electric force ne minus ve of work done by external agent

(D) Work done by battery = twice the change in electric potential energy stored in capacitor

36 Figure shows a cylindrical vessel of height 90 cm

filled up to the brim There are four holes in the vessel

as shown The liquid falling at maximum horizontal

distance from the vessel would come from

(A) hole 1 (B) hole 2

(C) hole 3 (D) hole 4

37 A plank with a uniform sphere placed on it rests on a smooth horizontal plane The plank is pulled to the

right by a constant force F If the sphere does not slip over the plank then

(A) Both have the same acceleration

(B) Acceleration of the centre of sphere is less than that of the plank

(C) Work done by friction acting on the sphere is equal to its total kinetic energy

(D) Total kinetic energy of the system is equal to work done by the force F

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1319

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

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983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 13 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

38 In the potentiometer experiment shown in figure the null point length is l

Choose the correct options given below

(A) If jockey J is shifted towards right l will increase

(B) If value of E 1 is increased l is decreased

(C) If value of E 2 is increased l is increased

(D) If switch S is closed l will decrease

39 In the figure if F = 4 N m = 2 kg M = 4 kg then

(A) The acceleration of m wrt ground is22

3msminus

(B) The acceleration of m wrt ground is 21 2 msminus

(C) Acceleration of M wrt ground is 20 4 msminus

(D) Acceleration of m wrt M is22

ms3

40 Two different coils have self-inductance L1 = 8 mH L2 = 2mH The current in one coil is increased at a

constant rate The current in the second coil is also increased at the same rate At a certain instant of time

the power given to the two coils is same At that time the current the induced voltage and the energy

stored in the first coil are i1 V 1 and W 1 respectively Corresponding values for the second coil at the same

instant are i2 V 2 and W 2 respectively Then

(A) 1

2

1

4

i

i= (B) 1

2

48i

i= (C) 2

1

4W

W = (D) 2

1

1

4

V

V =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

G

E1

E2

J

S

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1419

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1519

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1619

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1419

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 14 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983120A983122983124 983085 983113983113983113 (983117A983124983112983109983117A983124983113983107983123) 66 983117A983122983115983123

983123983109983107983124983113983119983118 983085 983113

983123983124983122A983113983111983112983124 983119983106983114983109983107983124983113983126983109 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 14 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144

983119983150983148983161 983119983150983141 983145983155 983107983151983154983154983141983139983156

41 If a gt1 and the value of[ ]

1

1

2

a

alog x e

xa dxminus minus

=int where [ ] denotes greatest integer xle then the

value of a is

(A) 2

e (B) eminus (C)

2

e (D) e

42 The plane lx + my = 0 is rotated about its line of intersection with the XOY plane through an angle α then the equation of plane is lx + my + nz = 0 where n is

(A) 2 2l m cosplusmn + α (B) 2 2l m sinplusmn + α

(C) 2 2l m tanplusmn + α (D)

2 2l m cot plusmn + α

43434343 Let f ( x) = x3 + x2 + 100 x + 7 sinx then equation1 2 3

0(1) (2) (3) y f y f y f

+ + =minus minus minus

has

(A) No real root (B) One real root (B) Two real roots (D) More than two real root

44 The maximum number of points into which 4 circles and 4 straight lines interest is

(A) 26 (B) 50 (C) 56 (D) 72

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1519

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1619

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1519

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 15 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

45 If the system of equations 2 x ndash y + z = 0 x ndash 2 y + z = 0 tx ndash y + 2 z = 0 has infinitely many solutions and

f ( x) be a continuous function such that f ( x + 5) + f ( x) = 2 then ( )2

0

t

f x dx

minus

int is equal to

(A) 0 (B) ndash2t (C) 5 (D) t

46 The set of points on the axis of the parabola y2 = 4 x + 8 from which the 3 normals to the parabola are allreal and distinct is

(A) (K 0) K le ndash2 (B) (K 0) K gt ndash2

(C) (0 K) K gt ndash2 (D) (K 0) K gt 0

47 With usual notations if in a ∆ ABC11 12 13

b c c a a b+ + += = then cosA cosB cosC equals

(A) 7 19 25 (B) 19 7 25 (C) 12 14 20 (D) 19 25 20

48 If a b

are orthogonal unit vectors then for a vector r

non-coplanar with a

and b

the vector r atimes

is

equal to

(A) ( )r a b b r b b a + sdot times

(B) ( ) +

r a b a b

(C) ( )r a b a r a a b + sdot times

(D) None of these

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1619

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1619

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 16 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

49 Let ( )( )

1

1

nn

n f x x

n

+=

minus The value of ( )

1

01

n

n

f x dxinfin

=

sumint is

(A) e (B) 0 (C) 2e (D) None of these

50 The value of ( )4 1 4 1 2

0

n

n n n j

j

C C + + minus=

+sum is

(A)4 4 12 n n

nC ++ (B) 4 12 n+ (C)4 1 4 12 n n

nC + ++ (D) 42 n

51 Let f and g are two functions such that f ( x) and g ( x) are continuous in [a b] and differentiable in (a b)

Then at least one ( )c a bisin such that ( ) ( ) ( ) f b f a

f cb a

minusprime =

minus

I If ( ) ( ) f x f b= then ( ) 0 f cprime = (RMVT)

II ( ) ( ) f a f bne and a bne (LMVT)

III If ( ) 0 g xprime ne then( ) ( )

( ) ( )

( )

( )

f b f a f c

g b g a g c

primeminus= primeminus (cauchy theorem)

Let 02

π α θ β lt lt lt lt then

sin sin

cos cos

α β

α β

minus

minus is equal to

(A) tanθ (B) tanθ minus (C) cot θ (D) cot θ minus

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1719

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 17 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

52 If ( ) ( ) ( )

( )

1 11

f a x

x

f a

e f x I x g x x dx

eminus

= = sdot minus+ int and ( )

( )

( )

2 1

f a

f a

I g x x dx

minus

= minusint then the value of 2

1

I

I is

(A) 2 (B) 3minus (C) 1minus (D) 1

53 S 1 Radius of great circle of section of a plane with a sphere is equal to the radius of the sphere S 2 Points ( )1 1 1 x y z and ( )2 2 2 x y z lies on the same side of the plane 0ax by cz d + + + =

if ( ) ( )1 1 1 2 2 2 0ax by cz d ax by cz d + + + + + + ge

S 3 Point ( )1 1 1 x y z lies inside of the sphere 2 2 2 2 2 2 0 x y z ux vy wz d + + minus minus minus + =

If 2 2 21 1 1 1 1 12 2 2 x y z ux uy wz d + + lt + + minus

S 3 Shortest distance between the planes 3 6 2 11 0 x y z + minus minus = and 3 6 2 3 0 x y z + minus + = is 2 units

(A) TFTT (B) FFTT (C) TTFF (D) FTFT

54 Area bounded by the curve 1 y nx tan xminus= + and x-axis from x = 1 to x = 2 is

(A) 15 12 5 2 2 12 2 3

minusminus + minus minus n n tan π (B) 15 12 5 2 2 12 2 4

minusminus + minus + n n tan π

(C) 15 1

2 5 2 2 12 2 4

minusminus + + minus n n tanπ

(D) 15 1

2 5 2 2 12 2 4

minusminus + minus minus n n tanπ

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 18 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

983123983109983107983124983113983119983118 983085 983113983113

983117983125983116983124983113983120983116983109 983107983119983122983122983109983107983124 A983118983123983127983109983122983123 983124983129983120983109

983124983144983145983155 983123983141983139983156983145983151983150 983139983151983150983156983137983145983150983155 6 983117983157983148983156983145983152983148983141 983107983144983151983145983139983141 983121983157983141983155983156983145983151983150983155 983109983137983139983144 983121983157983141983155983156983145983151983150 983144983137983155 4 983139983144983151983145983139983141983155 A 983106 983107 amp 983108 983151983157983156 983151983142 983159983144983145983139983144 983151983150983141

983151983154 983117983151983154983141 983107983144983151983145983139983141983155 983149983137983161 983138983141 983107983151983154983154983141983139983156

55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

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9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

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7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1819

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55 A and B are two independent events such that ( )2

15 P A Bprime cap = and ( )

1

6 P A Bprimecap = Then P ( B) is equal

to

(A)4

5 (B)

1

6 (C)

1

5 (D)

5

6

56 A plane parallel to 3 x y z + + = and at distance4

3 from it has the equation

(A) 2 0 x y z minus minus = (B) 1 0 x y z + + + =

(C) 3 3 4

23

x y z +

minus minus = (D) 7 x y z + + =

57 In the ABC ∆ b c = 2 1 and ( ) 35

sin B C minus = Then

(A) ABC ∆ is right-angled (B) ABC ∆ is obtuse-angled

(C) a c = 3 1 (D) 5 1a c =

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

983126983145983140983161983137983149983137983150983140983145983154 983107983148983137983155983155983141983155

9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115

7172019 jee advance mock test paper2

httpslidepdfcomreaderfulljee-advance-mock-test-paper2 1919

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9831269831179831072013 19 983117983151983139983147 983113983113983124 A983140983158983137983150983139983141983140 98312498314198315598315698308529831209831379831529831419831549830852

58 Let c a b a bλ micro γ = + + times

where a

and b

are unit vectors such that 0a bsdot =

Then

(A) b cmicro = sdot

(B) a cλ = times

(C) a b cγ =

(D) ( )a b a b cλ micro γ + + = + + times sdot

59 The area bounded by the curves 2 1 0 y x y sinx x= minus minus = = and x = 2 is

(A)21 2 1cos+ (B)

22 1+ sin (C) 2 + cos 2 (D) 1 2log +

60 The sum of first lsquonrsquo terms of the series1 3 7 15

2 4 8 16 + + + + is f (n) then

(A) ( )9

110 8

2 f = + (B) ( )

10

110 9

2 f = +

(C) ( )20

120 19

2= + f (D) ( )

30

130 31

2 f = +

983123983120A983107983109 983110983119983122 983122983119983125983111983112 983127983119983122983115