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Test Type : FULL SYLLABUS Test Pattern : JEE-Main
TEST DATE : 23 - 03 - 2017
Paper Code : 1001CT102116065Form Number :
CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)E
NG
LIS
H
Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005
+91-744-5156100 [email protected] www.allen.ac.in
Your Target is to secure Good Rank in JEE (Main) 2017
Important Instructions
Do not open this Test Booklet until you are asked to do so.
1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball PointPen. Use of pencil is strictly prohibited.
2. The candidates should not write their Form Number anywhere else (except in the specified space)on the Test Booklet/Answer Sheet.
3. The test is of 3 hours duration.
4. The Test Booklet consists of 90 questions. The maximum marks are 360.
5. There are three parts in the question paper A,B,C consisting of Physics, Chemistry andMathematics having 30 questions in each part of equal weightage. Each question is allotted 4(four) marks for correct response.
6. One Fourth mark will be deducted for indicated incorrect response of each question. No deduction
from the total score will be made if no response is indicated for an item in the Answer Sheet.
7. Use Blue/Black Ball Point Pen only for writting particulars/marking responses on Side–1 andSide–2 of the Answer Sheet. Use of pencil is strictly prohibited.
8. No candidate is allowed to carry any textual material, printed or written, bits of papers, mobile
phone any electronic device etc, except the Identity Card inside the examination hall/room.
9. Rough work is to be done on the space provided for this purpose in the Test Booklet only.
10. On completion of the test, the candidate must hand over the Answer Sheet to the invigilator on dutyin the Room/Hall. However, the candidate are allowed to take away this Test Booklet withthem.
11. Do not fold or make any stray marks on the Answer Sheet.
JEE (Main + Advanced)
LEADER COURSE (SCORE-I) & ENTHUSIAST COURSE (SCORE-II)
E-1/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
PART A - PHYSICS
BEWARE OF NEGATIVE MARKING
HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS
1. An optical fibre communication system works on a
wavelength of 1.3 m. The number of subscribers it
can feed if a channel requires 20 kHz are
(1) 2.3 1010 (2) 1.15 1010
(3) 1 105 (4) None of these
2. Velocity-displacement graph of a particle moving in
a straight line is as shown in figure:
S
V
(1) magnitude of acceleration of particle is constant.
(2) magnitude of acceleration of particle is increasing
(3) acceleration versus displacement graph is straight
line
(4) acceleration versus displacement graph is parabola
3. Velocity of a particle moving in a curvilinear path in
a horizontal X Y plane varies with time as2ˆv (2t i t j)
m/s. Here, t is in second. At t = 1 s.
(1) acceleration of particle is 8 m/s2
(2) tangential acceleration of particle is 4
5 m/s2
(3) radial acceleration of particle is 6
5m/s2
(4) radius of curvature to the path is 5 5
2m
4. A block of mass m slides down on a wedge of mass
M as shown in figure. Let 1a
be the acceleration of
the wedge and 2a
the acceleration of block w.r.t.
ground. N1 is the normal reaction between block and
wedge and N2 the normal reaction between wedge
and ground. Friction is absent everywhere. Select the
incorrect alternative
M
m
(1) N2< (M + m)g
(2) N1 = m(g cos – | 1a
|sin)
(3) N1 sin = M| 1a
|
(4) m 2a
= – M 1a
1001CT102116065E-2/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
5. In the adjoining figure if acceleration of M with respect
to ground is a, then:
mM
a
(1) acceleration of m with respect to M is 2a
(2) acceleration of m with respect to ground is
2a sin (/2)
(3) acceleration of m with respect to ground is a
(4) acceleration of m with respect to ground is a tan
6. Which of the following statement is incorrect for a
spherical body rolling without slipping on a rough
horizontal ground at rest?
(1) The acceleration of a point in contact with ground
is zero
(2) The acceleration of C.O.M. of the sphere may or
may not be zero.
(3) Friction force may or may not be zero .
(4) Work done by friction w.r.t. ground on the body is
zero .
7. The end B of the rod AB which makes angle with
the floor is being pulled with, a constant velocity v0
as shown. The length of the rod is l. At the instant
when = 37° theny
A
v0
BO x
(1) velocity of end A is 5
3 v0 downwards
(2) angular velocity of rod is 05 v
3 (3) angular velocity of rod is constant
(4) velocity of end A is constant
8. A solid sphere of radius R is rolled by a force F acting
at the top of the sphere as shown in the figure. The
sphere rolls without slipping on rough stationary
surface.Initially sphere is in the rest position then:
Rough
F
(1) work done by friction when the centre of mass
moves a distance S is 2FS.
(2) speed of the CM when CM moves a distance S
is 20 FS
7 M(3) work done by the force F when Centre of Mass
moves a distance S is FS
(4) speed of the CM when CM moves a distance S
is 4RS
M
E-3/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
9. A disc of mass M and radius R moves in the x-y plane
as shown in the figure. The angular momentum of
the disc at the instant shown is:
(1) 5
2mR2 along- z axis about O
(2) 5
2mR2 along + z axis about O
(3) zero about point A
(4) 4 mR2 along +Z axis about A
10. The figure shows a process AB undergone by 2 moles
of an ideal diatomic gas. The process AB is in such a
way that VT= constant. T1 = 300 K and T2 = 500 K.
(R = gas constant)
V
T
A
B
T1 T2
(1) The molar heat capacity of gas in the process
A B is R
52
J/mol–K
(2) The molar heat capacity of gas in the process
A B is R J/mol–K
(3) The work done by the gas is –400R J
(4) The work done by the gas is –200R J.
11. An ideal gas undergoes cyclic process as shown indensity pressure graph. During the process AB the
work done ABW = 70 J. During the process BC, thegas absorbs 150 J of heat. During the process CA,gas undergoes expansion and does 210 J of work.
P (pressure)
(kg/m3)
de
nsity
A
B 20
0
P0 2P0 4P0
C
N/m2
(1) The efficiency of cyclic process is 33 %(2) The efficiency of cyclic process is 66%(3)The process CA is adiabatic .(4) The process BC is isothermal .
12. Assuming all pulleys, springs and string massless.Consider all surface smooth. Choose the correctstatement(s).
K
m
K
K
(1) The angular frequency for small oscillation of
the system is K
3m(2) The angular frequency for small oscillation of
the system is 4K
33m(3) The elastic potential energy of system at
equilibrium is 2 233m g
4K(4) The elastic potential energy of system at
equilibrium is 2 23m g
2K
1001CT102116065E-4/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
13. A small sphere of mass m = 0.5 kg carrying a
positive charge q = 110 C is connected with a light,
flexible and inextensible string of length r = 60 cm
and whirled in a vertical circle. If a vertically upwards
electric field of strength E = 105 NC–1 exists in the
space, The minimum velocity of sphere required at
highest point so that it may just complete the circle.
(g = 10 ms–2)
(1) 8 m/s
(2) 7m/s
(3) 6m/s
(4) 9 m/s
14. A particle of mass m having negative charge q move
along an ellipse around a fixed positive charge Q so
that its maximum and minimum distances from fixed
charge are equal to r1 and r2 respectively.
The angular momentum L of this particle is
(1) 1 2
0 1 2
mr r Qq
(r r ) (2)
1 2
0 1 2
mr r Qq
2 (r r )
(3) 1 2
0 1 2
mr r Qq
3 (r r ) (4)
1 2
0 1 2
mr r Qq
4 (r r )
15. Switch S of circuit shown in figure is in position 1 for
a long time. At instant t = 0, it is thrown from
position 1 to 2. The thermal power P1(t) generated in
resistance R1.
S
+ –
R 1
R 2
1
2
E
C
(1)
2 2
22t /(R R )C1
2
1 2
E R.e
(R R )
(2)
2 2
2t /(R R )C1
2
1 2
E R.e
(R R )
(3)
2 2
2t / 2(R R )C1
2
1 2
E R.e
(R R )
(4)
2 2
2t /(R R )C1
21 2
E R.e
2(R R )
E-5/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
16. In the figure the potentiometer wire of length
l =100 cm and resistance 9is joined to a cell of emf
E1 = 10V and internal resistance r1 = 1. Another
cell of emf E2 = 5 V and internal resistance r2 = 2 is
connected as shown. The galvanometer G will show
no deflection when the length AC is:
G
A BC
E = 10Vr = 1
1
1
E = 5Vr = 2
2
2
(1) 50 cm (2) 55.55 cm
(3) 52.67 cm (4) 54.33 cm
17. A cubical room is formed with 6 plane mirrors. An
insect moves along the diagonal of the floor with
uniform speed. The speed of its image in two adjacent
walls parallel to the walls is 202 cm/s. Then the speed
of the image formed on the roof with respect to ground
is :
(1) 20 cm/s (2) 40 cm/s
(3) 20 2 cm/s (4) 10 2 cm/s
18. A prism of refractive index 2 refracting angle A
produces minimum deviation Dm of a ray on one face
at an angle of incidence 45. The values of
A and Dm are respectively.
(1) 45, 45 (2) 45, 60
(3) 60, 30 (4) 60, 45
19. In young’s double slit experiment, the intensity of light
at a point on the screen where the path difference is
is k units; being the wavelength of light used. The
intensity at a point where the path difference is /4
will be
(1) k/4 (2) k/2
(3) k (4) zero
20. In the ideal double-slit experiment, when a glass-plate
(refractive index 1.5) of thickness t is introduced in the
path of one of the interfering beams (wave-length ),
the intensity at the position where the central
maximum occurred previously remains unchanged.
The minimum thickness of the glass-plate is
(1) 2 (2) 2/3
(3) /3 (4)
21. In Young’s double slit experiment the two slits act as
coherent sources of equal amplitude A and of
wavelength . In another experiment with same set
up the two slits are sources of equal amplitude A and
wavelength , but are incoherent. The ratio of intensity
of light at the mid point of the screen in the first case
to that in the second case is
(1) 1 : 1 (2) 1 : 2
(3) 2 : 1 (4) 4 : 1
1001CT102116065E-6/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
22. A certain radioactive material can undergo three
different types of decay, each with a different decay
constant 1, 2 and 3. Then the effective decay
constant is
(1) 1 2 3
eff3
(2) eff 1 2 3
1 1 1 1
(3) eff 1 2 3
(4) eff 1 2 3
1 1 1 1 1
3
23. The wavelength of K line for an element of atomic
number 29is . Then the wavelength of K line for an
element of atomic no 15 is (Take mosley‘s
constant b = 1 for both elements)
(1)29
15 (2)
28
15
(3) 4 (4) 2
24 . In the given circuit, the current through 5mH indicator
in steady state is
(1) 4/3 Amp (2) 8/3 AMP
(3) 4 Amp (4) 2/3 Amp
25. In the circuit shown, the key (k) is closed at t = 0,
the current through the key at the instant
t = 10–3ln 2 sec. is
(1) 1.5 Amp (2) 2.5 Amp
(3) 4 Amp (4) 2/3 Amp
26. Two long parallel horizontal rails, a distance aparttand each has a resistance per unit length are joinedat one end by a resistance R. A perfectly conductingrod MN of mass m is free to slide along the rails withoutfriction. There is a uniform magnetic field of inductionB normal to the plane of paper and directed into thepaper. A variable force F is applied to the rod MNsuch that, as the rod moves, a constant current i flowsthrough P.
M
N
x x x x x
x x x x x
x x x x x
i
x
F
B
The applied force F as function of distance x of the
rod from R is
(1) 2
2 2
2m ii B (R 2 x)
B
(2) 2
2 2
4m ii B (R 2 x)
B
(3) 2
2 2
2m ii B (R 2 x)
B
(4) none of these
E-7/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
27. A small conducting loop of radius o and resistance r
is pulled with velocity v perpendicular to a long straight
conductor carrying a current i0. If a constant power P
is dissipated in the loop. The variation of velocity of
the loop as a function of x.Given that x >> 0.
a v
x
i0
(1)
2
2
0 0
2xPr
i a(2)
2
2
0 0
4xPr
i a
(3)
2
2
0 0
6xPr
i a(4) none of these
28. Two coaxial solenoids are made by winding thin
insulated wire over a pipe of cross-sectional area
A = 10 cm2 and length = 20 cm. If one of the
solenoids has 300 turns and the other 400 turns, their
mutual inductance is (0 = 4 × 10–7 T mA–1)
(1) 2.4 × 10–5 H (2) 4.8 × 10–4 H
(3) 4.8 × 10–5 H (4) 2.4 × 10–4 H
29. In the adjacent circuit, A and B represent two inputs
and C represents the output,
C
R2
A
B
The circuit represents
(1) NOR gate (2) AND gate
(3) NAND gate (4) OR gate
30. In the given circuit, a voltmeter ‘V’ is connected across
a bulb ‘B’. If the resistor ‘R’ is increased in value ?
VB
6V
R
(1) The voltmeter shows a lower voltage
(2) The voltmeter shows a higher voltage
(3) The voltmeter shows a same voltage
(4) The glow of bulb will increase
1001CT102116065E-8/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
PART B - CHEMISTRY31. The electronic spectrum of [Ti(H2O)6]
3+ gives a single
broad peak with a maxima at 20300 cm–1. The crystal
field stabilization energy is equal to
(1) 97 kJ mol–1 (2) 243 kJ mol–1
(3) 297 kJ mol–1 (4) None of these
32. Phenol condenses with phthalic anhydride in
presence of conc. H2SO4 to form
(1) methyl orange (2) phenolphthalein
(3) phenyl red (4) salicylic acid
33. At 298 K the equivalent conductivity of aniline
hydrochloride of 0.01 M solution is 122.5 but in
presence of sufficient excess of aniline to prevent of
hydrolysis it is 106.5. The equivalent conductivity of
HCl at infinite dilution is 426.0. The hydrolysis
constant of aniline is
(1) 0.05 (2) 2.63 × 10–5
(3) 4.86 × 10–5 (4) 2.18 × 10–8
34. Which of the following is not concentrated by
electromagnetic separation ?
(1) Copper pyrites (2) Pyrolusite
(3) Chromite (4) Cassiterite
35 The two substances A and B are in equilibrium with
C and D as
2A B 3C 2D
if the initial pressure of A and B in the ratio of 4 : 1
and at equilibrium partial pressure of A and D are
equal. Find the correct relation.
(1) pP 10 K (2) pP 0.4 K
(3) P = 0.4 Kp (4) P = 0.4 (Kp)2
36. Select the option containing correct order of the given
parameter.
(1) C > Si > Pb > Ge (Order of reactivity with alkali)
(2) C > Pb > Ge > Si (Order of reactivity with alkali)
(3) [CoCl3(NH3)3] > [CoCl(NH3)5]Cl2 >
[Co(NH3)6]Cl3 > [CoCl2(NH3)4]Cl
(order of electrical conductivity.)
(4) [Co(NH3)6]Cl3 > [CoCl(NH3)5]Cl2 >
[CoCl2(NH3)4]Cl > [CoCl3(NH3)3]
(order of electrical conductivity.)
37.H
O
4 3LiAlH CH MgBr
35ºC ExcessA B
Identify B in the reaction :-
(1) H
O
(2) OH
(3) OH
(4) CH4
38. The wavelength of the electron emitted by a metal
sheet of work function 4 eV when photons from EMR
of wavelength 124 nm strike the metal plate.
(1) 10 nm
(2) 206.67 nm
(3) 50 nm
(4) 0.5 nm
E-9/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
39. Which of the following is paramagnetic ?
(1) O2[AsF6] (2) Al2O3
(3) C2 (4) Be2
40. Which of the following amino acids does not contain
asymmetric carbon ?
(1) Histidine (2) Glycine
(3) –Alanine (4) Threonine
41. Identify the correct option.
(I) AgCl is not soluble in H2O but soluble in KCN.
(II) Zn when reacts with cold v.v. dil HNO3 gives
NH4NO3.
(III) CuSO4 reacts with KI to form Cu2I2 + K2SO4.
(IV) 1000ºC4 2CuSO .5H O The gases liberated
are SO2 and O2.
(1) All statements are correct
(2) I, II and IV are correct
(3) II and III are incorrect statements
(4) Only I is incorrect.
42. Identify the correct option regarding surfacephenomenon.
(1) Colloidal solution of As2S3 can be prepared byPeptization.
(2) Out of KCl, BaCl2, AlCl3, Na3PO4 ; BaCl2 is most
effective in coagulation of sulphur sol.
(3) C H COOCH —C—CH OH15 31 2 2
CH OH2
CH OH2
is non–ionic
detergent.(4) On increasing concentration of
C2H5 SO3Na electrical conductance
will always increase
43. Which of the following is correct for the equilibrium ?
2CH3 C
O
O H H3C C
O
O H
H O
OC CH3
(Equilibrium constants for the reaction in water and
benzene are KWater KBenzene)
(1) KWater > KBenzene (2) KWater < KBenzene
(3) KWater = KBenzene (4) None of these
44. Which of the following options is incorrect ?
(1) Tailing of mercury can be used as test for Ozone.
(2) Carbon suboxide is amphoteric in nature and
carbon monoxide is neutral.
(3) Both Ni3B and FeB have no B–B bond.
(4) Both V3B2 and NaB15 have B–B bond.
45. 2 2 4H O / H SOA
Identify ‘A’ in the reaction.
(1)
OH
(2)
OH
(3)
OH
(4)
OH
1001CT102116065E-10/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
46. Which of the following statements is incorrect ?
(1) The specific heat capacity of substance is greater
in the solid state than in liquid state.
(2) The specific heat capacity of a substance is greater
in gaseous state than in the liquid state.
(3) The latent heat of vaporization of a substance is
greater than that of fusion.
(4) The internal energy of an ideal gas is a function of
its temperature.
47. The anode mud in the refining of silver
(1) Zn, Cu, Ag, Au
(2) Zn, Au
(3) Cu, Ag, Au
(4) Au
48. Identify the incorrect order of the given parameter.
(1) V > Ni > Mn (order of melting point)
(2) Co > Ni > Cu > Zn (order of melting point)
(3) Na2S > ZnS > CuS
(order of solubility in aqueous medium)
(4) CuS > ZnS > Na2S
(order of solubility in aqueous medium)
49.
CHO OHC
CHO OHC
2
(i)NaOH(excess)
(ii)H / 2H O,0ºC
(1)
HO
OH HO
OH
(2)
HO
OH
O–
O
O–
O
(3)
O
O
O
O
(4)
COOH
O
OH HO
OOH
E-11/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
50. 5 milli-moles of a solid A was dissolved in 5 moles ofH2O. On adding to the solvent, A starts polymerisinginto another insoluble solid following zero orderkinetics. On adding 6 milli-moles of another solidsolute C (after 20 minute) the polymerisationcompletely stops. The insoluble solid polymer isremoved and the resulting solution was cooled to atemperature less than - 0.186°C (melting point ofsolution) to cause solidification of some liquidwater. Calculate the value of ‘X’ if rate constantfor polymerisation reaction is represented as10–X moles/minute. [Kf(H2O) = 1.86 K –Kg mole–1]
(1) 1 (2) 4 (3) 3 (4) 5
51. Silver has an atomic radius of 144 pm and the
density of silver is 10.6 g cm–3. Based on this
information identify the correct statement.
(1) It has FCC crystal lattice.
(2) It has BCC crystal lattice.
(3) Approximately 0.24 fraction of edge is not
covered by atoms.
(4) None of the statement is true.
52. Which of the following is least biodegradable ?
(1) C17H35COONa
(2) CH3(CH2)11SO3Na
(3) SO3NaCH(CH2)9
CH3
H3C
(4) CH3—CH—(CH2—CH)2—CH2—CH—CH3
CH3 CH3
SO3Na
53. + 3 4H PO3 2CH CH CH A
2 2 4O dil.H SO
heatB C D
A, C and D are
(1)
CH2CH2CH3
,
OH
, CH3COCH3
(2)
CHH3C CH3
,
OH
, CH3COCH3
(3)
CHH3C CH3
,
COCH3
, CH3COCH3
(4)
CHH3C CH3
,
OH
, CH3—CH—CH3
OH
54. How many moles of H2O (per mole of Cl2 evolved)
will be formed when KMnO4 is added to HCl solution?
(1) 5/4 (2) 4/5
(3) 5/8 (4) 8/5
1001CT102116065E-12/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
55. The densities of air at 25ºC and 100ºC are 1.2 gL–1
and 0.9 g L–1 respectively. Assuming that the air obey’s
Charle’s law, the value of absolute zero of
temperature in degree Celsius is
(1) –273ºC (2) 200ºC
(3) –200ºC (4) 0ºC
56. Which of the following order is correct w.r.t.
magnitude of enthalpies of formation for alkali metal
halides ?
(1) Iodide > Bromide > Chloride > Fluoride
(of same metal)
(2) CsCl > RbCl > NaCl > LiCl
(3) NaF > CsF > RbF > KF
(4) LiI > NaI > RbI > CsI
57. For the reaction : N2 (g) + 3H2(g) 2NH3(g),
H = –24 Kcal at 427ºC and 200 atm. Calculate
magnitude of internal energy change (in Kcal U), if
168 gm N2 gas and 30 gm H2 gas are allowed to
react completely (100 % reaction yield) to form NH3
gas at 427ºC and 200 atm.
(1) –106 Kcal
(2) –24 Kcal
(3) –21.2 Kcal
(4) – 120 kcal
58.
NH2
2 2NaNO HCl H O
0 5ºC boilA B
2 2Br / H O Zn
dustC D
Compound ‘D’ is
(1)
OH
Br
BrBr
(2)
OH
(3)
Br
BrBr
(4)
OH
HO OH
59. Calculate solubility (in moles/litre) of a saturated
aqueous solution of Ag3PO4 if the vapour pressure of
the solution becomes 750 torr at 373 K.
(1) 2
15(2)
1
30(3)
10
54(4)
20
27
60. It is found that for every 10º rise in temperature, the
rate of the reaction doubles itself. This is mainly
because
(1) The speed of the reactants doubles for every 10º
rise in temperature.
(2) The fraction of the molecules forming the
activated complex doubles itself.
(3) The concentration doubles itself.
(4) The collision frequency doubles itself.
E-13/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
PART C - MATHEMATICS
61. If the lines ax + y + 1 = 0, x + by + 1 = 0 andx + y + c = 0 (where a, b & c are distinct anddifferent from 1) are concurrent, then the value of
1 1 1
1 a 1 b 1 c
(1) –1 (2) 1 (3) 0 (4) 2
62. Domain of the function
x
1f x
x 1 e 1 x 4 x 5 x 6
(1) , 5 1, 4 6,
(2) , 5 1, 0 0, 4 6,
(3) 5, 1 0, 4 6,
(4) , 5 1, 4 6,
63. 1 2
2 2
0 0
1 sinx ax bx c dx 1 sin x ax bx c dx .
So, location of the roots of 2ax bx c 0 is
(1) At least one real root between (1, 2)
(2) At least one real root between (0, 1)
(3) At most one real root between (0, 2)
(4) Can’t say exactly about the roots
64. If the sum of first n terms of an A.P. is cn(n – 1), wherec 0, then sum of the squares of these terms is
(1) 22 2c n n 1
(2) 22c n n 1 2n 1
3
(3) 22c n n 1 2n 1
3
(4) 2 2
2c nn 1
3
65. The maximum value of sin cos(tanx) is
(1) 3
2(2) sin1
(3) 1 (4) sin (cos1)
66. The interval of the values of ‘a’ for which the line
x y 0 bisect 2 distinct chords drawn from a
point 1 2a 1 2a
, 2 2
to the circle
2 22x 2y 1 2a x 1 2a y 0
(1) a , 0 2,
(2) a , 0 0,
(3) a 2,
(4) a , 2 2,
67. The vector ˆ ˆ ˆxi yj zk makes with the plane of the
two vectors (2, 3, –1) and (1, –1, 2) an acute
angle 1cot 2 . Then,
(1) y x z zx (2) z x y xy
(3) x y z yz (4) x y z xyz
68. If from a point P (a, b, c) perpendiculars PA, PB aredrawn to yz and zx plane, then the equation of theplane OAB (where O is origin) is:(1) bcx + cay + abz = 0(2) bcx + cay – abz = 0(3) bcx – cay + abz = 0(4) –bcx + cay + abz = 0
69. If sin 2sin 3sin 0 and
cos 2cos 3cos 0 , then the value of
cos 3 8 cos3 27cos 3 (1) cos (3 + 3 + 3) (2) 18 cos ( + + )(3) 6 cos ( + + ) (4) 36 cos ( + + )
1001CT102116065E-14/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
70. If , are the roots of the equation 2x 2x 4 0 ,
then the value of n n is :
(1) n n2 cos
3
(2) n 1 n
2 cos3
(3) n n
2 sin3
(4)
n 1 n2 sin
3
71. If n 2 n 1
1 1 1s 1 .......
2 2 2 , then the least
integral value of n such that n
12 s
100 is
(1) 7 (2) 9
(3) 8 (4) 6
72. Statement-1: Any function f (x) is even function,when f (– x) = f (x) over its specified domain.
Statement-2: 2
2
1 x x 1f x
41 x
,
where [.] is greatest integer function. Function f(x) is
even function.
(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanation
for statement-2
(2) Statement-1 is true, statement-2 is false
(3) Statement-1 is false, statement-2 is true
(4) Both statements are true, and statement-1 is the
true explanation of statement-2
73. Statement-1: If two tangents are drawn to an
ellipse from a single point and if they are perpendicu-
lar to each other, then locus of that point is always a
circle.
Statement-2: For an ellipse 2 2
2 2
x y1
a b , locus of
that point from which two perpendicular tangents
are drawn, is 22 2x y a b .
(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanation
for statement-2
(2) Statement-1 is true, statement-2 is false
(3) Statement-1 is false, statement-2 is true
(4) Both statements are true, and statement-1 is the
true explanation of statement-2
74. Consider a system of equations ax + by = 0,
cx + dy = 0, where a, b, c, d, {0, 1}.
Statement-1: The probability that system of
equations has a solution is 1.
Statement-2: The probability that the system of
equations has a unique solution is 3
8.
(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanation
for statement-2
(2) Statement-1 is true, statement-2 is false
(3) Statement-1 is false, statement-2 is true
(4) Both statements are true, and statement-1 is the
true explanation of statement-2
E-15/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
75. In a ABC, if two sides b & c and an angle B aregiven.Statement-1: Let b = 5 cm, c = 3 cm andB = 60o. Total number of possible triangles are 2.Statement-2: If c sin B < b < c and B is an acuteangle, then there are two possible values of C.(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanationfor statement-2
(2) Statement-1 is true, statement-2 is false(3) Statement-1 is false, statement-2 is true(4) Both statements are true, and statement-1 is the
true explanation of statement-276. For a series S = 1 – 2 + 3 – 4 … n terms,
Statement-1: Sum of series always dependent onthe value of n, i.e. whether it is even or odd.
Statement-2: Sum of series is n
2 when value of
n is any even integer.(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanationfor statement-2
(2) Statement-1 is true, statement-2 is false(3) Statement-1 is false, statement-2 is true(4) Both statements are true, and statement-1 is the
true explanation of statement-2
77. 2 2 2 2 2 2n
n 1 n 2 n 3 1lim ........
nn 1 n 2 n 3
(1) ln 24
(2) ln 2
4
(3) 1
ln24 2
(4)
1ln2
4 2
78. The area bounded by the curve x1y e
2
is
(1) 2 1 ln2 (2) 1
1 ln 22
(3) 2 ln2 1 (4) 1
1 ln 22
79. If 0
A1 1
and 1 0
B5 1
, then the value of
for which 2A B is
(1) 1 (2) –1
(3) 4 (4) No real values
80. If n 2 3 n0 1 2 3 n1 x c c x c x c x ....... c x ,
then the value of
n0 1 2 nc 3c 5c ........ 1 2n 1 c is :
(1) nn 1 .2 (2) 0
(3) n 11 2n .2 (4) n1 n .2
81. For what value of k to the following system ofequations possess a non-trivial solution ?
x ky 3z 0
3x ky 2z 0
2x 3y 4z 0
(1) 11
14(2)
33
2 (3)
33
20(4)
33
2
82. The mean and variance of a binomial variable X are2 and 1 respectively. Then, the probability that X takesvalues greater than 1 is
(1) 15
16(2)
11
16(3)
5
16(4)
1
16
83. The curve for which the intercept cut off by anytangent on y-axis is proportional to the square of theordinate of the point of tangency is
(1) 2
1
cc x 1
y (2)
12
cc y 1
x
(3) 1 2c c
1x y (4) 2 3
1 2c y c x y
(where c1 and c
2 are arbitrary constants)
1001CT102116065E-16/17
SPACE FOR ROUGH WORK
Target : JEE (Main + Advanced) 2017/23-03-2017
84. Evaluate x
dxx
(1) 2
(2)
2
(3) 2
(4)
2
85. The angle between the lines joining the origin to the
points of intersection of the straight line y 3x 2
with the curve 2 2x 2xy 3y 4x 8y 11 0 is
(1) 1tan 2 (2) 1 2
tan3
(3) 1 4
tan3
(4)
1 2 2tan
3
86. The tangents to the parabola y2 = 4ax makes angle
1 and
2 with the positive x-axis. Then, the locus of
their point of intersection if cot 1 + cot
2 = c is
(1) y = ac (2) x = ac
(3) xy = ac2 (4) xy = a
c
87. If two points P and Q on the hyperbola2 2
2 2
x y1
a b , whose centre is C, are such that CP
is perpendicular to CQ, ( a b ), then value of
2 2
1 1
CP CQ
(1) 1
ab(2) 2 2
1 1
a b
(3) 2 2
1 1
a b (4) 2 2
1
a b
88. Tangent is drawn to ellipse 2
2xy 1
27 at
3 3 cos , sin (where 0, 2
). Then, the
value of such that sum of intercepts on the axes
made by this tangent is minimum, is
(1) 3
(2)
6
(3) 8
(4)
4
89. Solution of the equation
x 3 4 x 1 x 8 6 x 1 1 is
(1) x 4, 9 (2) x 3, 8
(3) x 5, 10 (4) x 4, 7
90. Let 2A : 2cos sin 2 and
3B :
2 2
, then A B is
(1) 3
: , 2
(2) 7
: , 2 6
(3) : , 2 6
(4) 5 3
: , , 2 6 2
E-17/171001CT102116065
SPACE FOR ROUGH WORK
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
SPACE FOR ROUGH WORK
Paper Code : 1001CT102116065Form Number :
CLASSROOM CONTACT PROGRAMME(Academic Session : 2016 - 2017)
HIN
DI
Corporate Office : CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan)-324005
+91-744-5156100 [email protected] www.allen.ac.in
Your Target is to secure Good Rank in JEE (Main) 2017
Important Instructions
Do not open this Test Booklet until you are asked to do so.
1. Immediately fill in the form number on this page of the
Test Booklet with Blue/Black Ball Point Pen. Use of pencil
is strictly prohibited.
2. The candidates should not write their Form Number
anywhere else (except in the specified space) on the Test
Booklet/Answer Sheet.
3. The test is of 3 hours duration.
4. The Test Booklet consists of 90 questions. The maximum
marks are 360.
5. There are three parts in the question paper A,B,C
consisting of Physics, Chemistry and Mathematics
having 30 questions in each part of equal weightage.
Each question is allotted 4 (four) marks for correct
response.
6. One Fourth mark will be deducted for indicated incorrect
response of each question. No deduction from the total
score will be made if no response is indicated for an item
in the Answer Sheet.
7. Use Blue/Black Ball Point Pen only for writting
particulars/marking responses on Side–1 and Side 2 of
the Answer Sheet.
Use of pencil is strictly prohibited.
8. No candidate is allowed to carry any textual material,
printed or written, bits of papers, mobile phone any
electronic device etc, except the Identity Card inside the
examination hall/room.
9. Rough work is to be done on the space provided for this
purpose in the Test Booklet only.
10. On completion of the test, the candidate must hand over
the Answer Sheet to the invigilator on duty in the Room/
Hall. However, the candidate are allowed to take away
this Test Booklet with them.
11. Do not fold or make any stray marks on the Answer
Sheet.
1.
2.
3. 3 4. 90360
5. A, B, C 30 4
6.
7.
8.
9.
10.
11.
Test Type : FULL SYLLABUS Test Pattern : JEE-Main
TEST DATE : 23 - 03 - 2017
JEE (Main + Advanced)
LEADER COURSE (SCORE-I) & ENTHUSIAST COURSE (SCORE-II)
H-1/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
PART A - PHYSICS
BEWARE OF NEGATIVE MARKING
HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS
1. 1.3 m 20 kHz
(1) 2.3 1010 (2) 1.15 1010
(3) 1 105 (4)
2.
S
V
(1)
(2)
(3)
(4)
1. An optical fibre communication system works on a
wavelength of 1.3 m. The number of subscribers it
can feed if a channel requires 20 kHz are
(1) 2.3 1010 (2) 1.15 1010
(3) 1 105 (4) None of these
2. Velocity-displacement graph of a particle moving in
a straight line is as shown in figure:
S
V
(1) magnitude of acceleration of particle is constant.
(2) magnitude of acceleration of particle is increasing
(3) acceleration versus displacement graph is straight
line
(4) acceleration versus displacement graph is parabola
1001CT102116065H-2/33
Target : JEE (Main + Advanced) 2017/23-03-2017
3. Velocity of a particle moving in a curvilinear path in
a horizontal X Y plane varies with time as2ˆv (2t i t j)
m/s. Here, t is in second. At t = 1 s.
(1) acceleration of particle is 8 m/s2
(2) tangential acceleration of particle is 4
5 m/s2
(3) radial acceleration of particle is 6
5m/s2
(4) radius of curvature to the path is 5 5
2m
4. A block of mass m slides down on a wedge of mass
M as shown in figure. Let 1a
be the acceleration of
the wedge and 2a
the acceleration of block w.r.t.
ground. N1 is the normal reaction between block and
wedge and N2 the normal reaction between wedge
and ground. Friction is absent everywhere. Select the
incorrect alternative
M
m
(1) N2< (M + m)g
(2) N1 = m(g cos – | 1a
|sin)
(3) N1 sin = M| 1a
|
(4) m 2a
= – M 1a
3. X-Y
2ˆv (2t i t j)
m/s
t t = 1s
(1) 8 m/s2
(2) 4
5 m/s2
(3) 6
5m/s2
(4) 5 5
2m
4. M M
1a
2a
N1 N2
M
m
(1) N2< (M + m)g
(2) N1 = m(g cos – | 1a
|sin)
(3) N1 sin = M| 1a
|
(4) m 2a
= – M 1a
H-3/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
5. In the adjoining figure if acceleration of M with respect
to ground is a, then:
mM
a
(1) acceleration of m with respect to M is 2a
(2) acceleration of m with respect to ground is
2a sin (/2)
(3) acceleration of m with respect to ground is a
(4) acceleration of m with respect to ground is a tan
6. Which of the following statement is incorrect for a
spherical body rolling without slipping on a rough
horizontal ground at rest?
(1) The acceleration of a point in contact with ground
is zero
(2) The acceleration of C.O.M. of the sphere may or
may not be zero.
(3) Friction force may or may not be zero .
(4) Work done by friction w.r.t. ground on the body is
zero .
5. M a
mM
a
(1) M m 2a
(2) m 2a sin (/2)
(3) m a
(4) m a tan
6.
(1)
(2)
(3)
(4)
1001CT102116065H-4/33
Target : JEE (Main + Advanced) 2017/23-03-2017
7. The end B of the rod AB which makes angle with
the floor is being pulled with, a constant velocity v0
as shown. The length of the rod is l. At the instant
when = 37° theny
A
v0
BO x
(1) velocity of end A is 5
3 v0 downwards
(2) angular velocity of rod is 05 v
3 (3) angular velocity of rod is constant
(4) velocity of end A is constant
8. A solid sphere of radius R is rolled by a force F acting
at the top of the sphere as shown in the figure. The
sphere rolls without slipping on rough stationary
surface.Initially sphere is in the rest position then:
Rough
F
(1) work done by friction when the centre of mass
moves a distance S is 2FS.
(2) speed of the CM when CM moves a distance S
is 20 FS
7 M(3) work done by the force F when Centre of Mass
moves a distance S is FS
(4) speed of the CM when CM moves a distance S
is 4RS
M
7. AB B v0 l = 37°
y
A
v0
BO x
(1) A 5
3v0
(2) 05 v
3
(3) (4) A
8. R F
Rough
F
(1) S 2FS
(2) S
20 FS
7 M
(3) S F FS
(4) S
4RS
M
H-5/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
9. A disc of mass M and radius R moves in the x-y plane
as shown in the figure. The angular momentum of
the disc at the instant shown is:
(1) 5
2mR2 along- z axis about O
(2) 5
2mR2 along + z axis about O
(3) zero about point A
(4) 4 mR2 along +Z axis about A
10. The figure shows a process AB undergone by 2 moles
of an ideal diatomic gas. The process AB is in such a
way that VT= constant. T1 = 300 K and T2 = 500 K.
(R = gas constant)
V
T
A
B
T1 T2
(1) The molar heat capacity of gas in the process
A B is R
52
J/mol–K
(2) The molar heat capacity of gas in the processA B is R J/mol–K
(3) The work done by the gas is –400R J
(4) The work done by the gas is –200R J.
9. M R x-y
(1) O –z 5
2mR2
(2) O +z 5
2mR2
(3) A
(4) A +Z 4 mR2
10. AB AB VT= T1 = 300 K T2 = 500 K. (R = )
V
T
A
B
T1 T2
(1) A B R
52
J/mol–K
(2) A B R J/mol–K
(3) –400R J (4) –200R J
1001CT102116065H-6/33
Target : JEE (Main + Advanced) 2017/23-03-2017
11. An ideal gas undergoes cyclic process as shown indensity pressure graph. During the process AB the
work done ABW = 70 J. During the process BC, thegas absorbs 150 J of heat. During the process CA,gas undergoes expansion and does 210 J of work.
P (pressure)
(kg/m3)
de
nsity
A
B 20
0
P0 2P0 4P0
C
N/m2
(1) The efficiency of cyclic process is 33 %
(2) The efficiency of cyclic process is 66%
(3)The process CA is adiabatic.
(4) The process BC is isothermal.12. Assuming all pulleys, springs and string massless.
Consider all surface smooth. Choose the correctstatement(s).
K
m
K
K
(1) The angular frequency for small oscillation of
the system is K
3m(2) The angular frequency for small oscillation of
the system is 4K
33m(3) The elastic potential energy of system at
equilibrium is 2 233m g
4K(4) The elastic potential energy of system at
equilibrium is 2 23m g
2K
11. AB
ABW = 70 J BC 150 J CA 210 J
P (pressure)
(kg/m3)
de
nsity
A
B 20
0
P0 2P0 4P0
C
N/m2
(1) 33 % (2) 66% (3) CA (4) BC
12.
K
m
K
K
(1) K
3m
(2) 4K
33m
(3) 2 233m g
4K
(4) 2 23m g
2K
H-7/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
13. A small sphere of mass m = 0.5 kg carrying a
positive charge q = 110 C is connected with a light,
flexible and inextensible string of length r = 60 cm
and whirled in a vertical circle. If a vertically upwards
electric field of strength E = 105 NC–1 exists in the
space, The minimum velocity of sphere required at
highest point so that it may just complete the
circle. (g = 10 ms–2)
(1) 8 m/s
(2) 7m/s
(3) 6m/s
(4) 9 m/s
14. A particle of mass m having negative charge q move
along an ellipse around a fixed positive charge Q so
that its maximum and minimum distances from fixed
charge are equal to r1 and r2 respectively.
The angular momentum L of this particle is
(1) 1 2
0 1 2
mr r Qq
(r r ) (2)
1 2
0 1 2
mr r Qq
2 (r r )
(3) 1 2
0 1 2
mr r Qq
3 (r r ) (4)
1 2
0 1 2
mr r Qq
4 (r r )
13. r = 60 cm
m = 0.5 kg q = 110 C
E = 105 NC–1
( g = 10 ms–2)
(1) 8 m/s
(2) 7m/s
(3) 6m/s
(4) 9 m/s
14. q m
Q
r1 r2
L
(1) 1 2
0 1 2
mr r Qq
(r r ) (2)
1 2
0 1 2
mr r Qq
2 (r r )
(3) 1 2
0 1 2
mr r Qq
3 (r r ) (4)
1 2
0 1 2
mr r Qq
4 (r r )
1001CT102116065H-8/33
Target : JEE (Main + Advanced) 2017/23-03-2017
15. Switch S of circuit shown in figure is in position 1 for
a long time. At instant t = 0, it is thrown from
position 1 to 2. The thermal power P1(t) generated in
resistance R1.
S
+ –
R 1
R 2
1
2
E
C
(1)
2 2
22t /(R R )C1
2
1 2
E R.e
(R R )
(2)
2 2
2t /(R R )C1
21 2
E R.e
(R R )
(3)
2 2
2t / 2(R R )C1
2
1 2
E R.e
(R R )
(4)
2 2
2t /(R R )C1
21 2
E R.e
2(R R )
15. S
1 t = 0, 1 2
R1 P1(t)
S
+ –
R 1
R 2
1
2
E
C
(1)
2 2
22t /(R R )C1
2
1 2
E R.e
(R R )
(2)
2 2
2t /(R R )C1
21 2
E R.e
(R R )
(3)
2 2
2t / 2(R R )C1
21 2
E R.e
(R R )
(4)
2 2
2t /(R R )C1
21 2
E R.e
2(R R )
H-9/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
16. In the figure the potentiometer wire of length
l =100 cm and resistance 9is joined to a cell of emf
E1 = 10V and internal resistance r1 = 1. Another
cell of emf E2 = 5 V and internal resistance r2 = 2 is
connected as shown. The galvanometer G will show
no deflection when the length AC is:
G
A BC
E = 10Vr = 1
1
1
E = 5Vr = 2
2
2
(1) 50 cm (2) 55.55 cm
(3) 52.67 cm (4) 54.33 cm
17. A cubical room is formed with 6 plane mirrors.
An insect moves along the diagonal of the floor with
uniform speed. The speed of its image in two adjacent
walls parallel to the walls is 202 cm/s. Then the
speed of the image formed on the roof with respect
to ground is :
(1) 20 cm/s (2) 40 cm/s
(3) 20 2 cm/s (4) 10 2 cm/s
16. =100 cm 9 E1 = 10V r1 = 1 E2 = 5 V r2 = 2 G AC
G
A BC
E = 10Vr = 1
1
1
E = 5Vr = 2
2
2
(1) 50 cm (2) 55.55 cm
(3) 52.67 cm (4) 54.33 cm
17. 6
202 cm/s
(1) 20 cm/s (2) 40 cm/s
(3) 20 2 cm/s (4) 10 2 cm/s
1001CT102116065H-10/33
Target : JEE (Main + Advanced) 2017/23-03-2017
18. A prism of refractive index 2 refracting angle A
produces minimum deviation Dm of a ray on one face
at an angle of incidence 45. The values of
A and Dm are respectively.
(1) 45, 45 (2) 45, 60
(3) 60, 30 (4) 60, 45
19. In young’s double slit experiment, the intensity of light
at a point on the screen where the path difference is
is k units; being the wavelength of light used. The
intensity at a point where the path difference is /4
will be
(1) k/4 (2) k/2
(3) k (4) zero
20. In the ideal double-slit experiment , when a
glass-plate (refractive index 1.5) of thickness t is
introduced in the path of one of the interfering beams
(wave-length ), the intensity at the position where
the central maximum occurred previously remains
unchanged. The minimum thickness of the glass-plate
is
(1) 2 (2) 2/3
(3) /3 (4)
21. In Young’s double slit experiment the two slits act as
coherent sources of equal amplitude A and of
wavelength . In another experiment with same set
up the two slits are sources of equal amplitude A and
wavelength , but are incoherent. The ratio of intensity
of light at the mid point of the screen in the first case
to that in the second case is
(1) 1 : 1 (2) 1 : 2
(3) 2 : 1 (4) 4 : 1
18. 2 A 45° Dm A Dm (1) 45, 45 (2) 45, 60(3) 60, 30 (4) 60, 45
19.
k ;
/4
(1) k/4 (2) k/2
(3) k (4) zero
20. t
1.5
(1) 2 (2) 2/3
(3) /3 (4)
21. A A (1) 1 : 1 (2) 1 : 2
(3) 2 : 1 (4) 4 : 1
H-11/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
22. A certain radioactive material can undergo three
different types of decay, each with a different decay
constant 1, 2 and 3. Then the effective decay
constant is
(1) 1 2 3
eff3
(2) eff 1 2 3
1 1 1 1
(3) eff 1 2 3
(4) eff 1 2 3
1 1 1 1 1
3
23. The wavelength of K line for an element of atomic
number 29is . Then the wavelength of K line for
an element of atomic no 15 is (Take mosley‘s constant
b = 1 for both elements)
(1)29
15 (2)
28
15
(3) 4 (4) 2
24 . In the given circuit, the current through 5mH indicator
in steady state is
(1) 4/3 Amp (2) 8/3 AMP
(3) 4 Amp (4) 2/3 Amp
22. 1, 2 3
(1) 1 2 3
eff3
(2) eff 1 2 3
1 1 1 1
(3) eff 1 2 3
(4) eff 1 2 3
1 1 1 1 1
3
23. 29 K 15 K b = 1
(1)29
15 (2)
28
15
(3) 4 (4) 2
24. 5mH
(1) 4/3 Amp (2) 8/3 AMP
(3) 4 Amp (4) 2/3 Amp
1001CT102116065H-12/33
Target : JEE (Main + Advanced) 2017/23-03-2017
25. In the circuit shown, the key (k) is closed at t = 0,
the current through the key at the instant
t = 10–3ln 2 sec. is
(1) 1.5 Amp (2) 2.5 Amp
(3) 4 Amp (4) 2/3 Amp
26. Two long parallel horizontal rails, a distance aparttand each has a resistance per unit length are joinedat one end by a resistance R. A perfectly conductingrod MN of mass m is free to slide along the rails withoutfriction. There is a uniform magnetic field of inductionB normal to the plane of paper and directed into thepaper. A variable force F is applied to the rod MNsuch that, as the rod moves, a constant current i flowsthrough P.
M
N
x x x x x
x x x x x
x x x x x
i
x
F
B
The applied force F as function of distance x of the
rod from R is
(1) 2
2 2
2m ii B (R 2 x)
B
(2) 2
2 2
4m ii B (R 2 x)
B
(3) 2
2 2
2m ii B (R 2 x)
B
(4) none of these
25. t = 0 (k) t = 10–3n 2 sec
(1) 1.5 Amp (2) 2.5 Amp
(3) 4 Amp (4) 2/3 Amp
26. R m MN
B F MN P i R x F
M
N
x x x x x
x x x x x
x x x x x
i
x
F
B
(1) 2
2 2
2m ii B (R 2 x)
B
(2) 2
2 2
4m ii B (R 2 x)
B
(3) 2
2 2
2m ii B (R 2 x)
B
(4)
H-13/331001CT102116065
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27. A small conducting loop of radius o and resistance r
is pulled with velocity v perpendicular to a long straight
conductor carrying a current i0. If a constant power P
is dissipated in the loop. The variation of velocity of
the loop as a function of x.Given that x >> 0.
a v
x
i0
(1) 2
2
0 0
2xPr
i a(2)
2
2
0 0
4xPr
i a
(3) 2
2
0 0
6xPr
i a(4) none of these
28. Two coaxial solenoids are made by winding thin
insulated wire over a pipe of cross-sectional area
A = 10 cm2 and length = 20 cm. If one of the
solenoids has 300 turns and the other 400 turns, their
mutual inductance is (0 = 4 × 10–7 T mA–1)
(1) 2.4 × 10–5 H
(2) 4.8 × 10–4 H
(3) 4.8 × 10–5 H
(4) 2.4 × 10–4 H
27. a r I0 v P x x >> 0.
a v
x
i0
(1) 2
2
0 0
2xPr
i a(2)
2
2
0 0
4xPr
i a
(3) 2
2
0 0
6xPr
i a(4)
28. A = 10 cm2
= 20 cm
300 400
(0 = 4 × 10–7 T mA–1)
(1) 2.4 × 10–5 H
(2) 4.8 × 10–4 H
(3) 4.8 × 10–5 H
(4) 2.4 × 10–4 H
1001CT102116065H-14/33
Target : JEE (Main + Advanced) 2017/23-03-2017
29. In the adjacent circuit, A and B represent two inputs
and C represents the output,
C
R2
A
B
The circuit represents
(1) NOR gate (2) AND gate
(3) NAND gate (4) OR gate
30. In the given circuit, a voltmeter ‘V’ is connected across
a bulb ‘B’. If the resistor ‘R’ is increased in value ?
VB
6V
R
(1) The voltmeter shows a lower voltage
(2) The voltmeter shows a higher voltage
(3) The voltmeter shows a same voltage
(4) The glow of bulb will increase
29. A B C
C
R2
A
B
(1) NOR (2) AND
(3) NAND (4) OR
30. ‘V’ ‘B’‘R’
VB
6V
R
(1)
(2)
(3)
(4)
H-15/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
PART B - CHEMISTRY31. [Ti(H2O)6]
3+ 20300 cm–1 (1) 97 kJ mol–1 (2) 243 kJ mol–1
(3) 297 kJ mol–1 (4)
32. H2SO4 (1) (2) (3) (4)
33. 298 K 0.01 M 122.5 106.5 HCl 426.0
(1) 0.05 (2) 2.63 × 10–5
(3) 4.86 × 10–5 (4) 2.18 × 10–8
34. (1) (2) (3) (4)
35 A B, C D 2A B 3C 2D
A B 4 : 1
A D
(1) pP 10 K (2) pP 0.4 K
(3) P = 0.4 Kp (4) P = 0.4 (Kp)2
31. The electronic spectrum of [Ti(H2O)6]3+ gives a single
broad peak with a maxima at 20300 cm–1.
The crystal field stabilization energy is equal to
(1) 97 kJ mol–1 (2) 243 kJ mol–1
(3) 297 kJ mol–1 (4) None of these
32. Phenol condenses with phthalic anhydride in
presence of conc. H2SO4 to form
(1) methyl orange (2) phenolphthalein
(3) phenyl red (4) salicylic acid
33. At 298 K the equivalent conductivity of aniline
hydrochloride of 0.01 M solution is 122.5 but in
presence of sufficient excess of aniline to prevent of
hydrolysis it is 106.5. The equivalent conductivity of
HCl at infinite dilution is 426.0. The hydrolysis
constant of aniline is
(1) 0.05 (2) 2.63 × 10–5
(3) 4.86 × 10–5 (4) 2.18 × 10–8
34. Which of the following is not concentrated by
electromagnetic separation ?
(1) Copper pyrites (2) Pyrolusite
(3) Chromite (4) Cassiterite
35 The two substances A and B are in equilibrium with
C and D as
2A B 3C 2D
if the initial pressure of A and B in the ratio of 4 : 1
and at equilibrium partial pressure of A and D are
equal. Find the correct relation.
(1) pP 10 K (2) pP 0.4 K
(3) P = 0.4 Kp (4) P = 0.4 (Kp)2
1001CT102116065H-16/33
Target : JEE (Main + Advanced) 2017/23-03-2017
36. Select the option containing correct order of the given
parameter.
(1) C > Si > Pb > Ge (Order of reactivity with alkali)
(2) C > Pb > Ge > Si
(Order of reactivity with alkali)
(3) [CoCl3(NH3)3] > [CoCl(NH3)5]Cl2 >
[Co(NH3)6]Cl3 > [CoCl2(NH3)4]Cl
(order of electrical conductivity.)
(4) [Co(NH3)6]Cl3 > [CoCl(NH3)5]Cl2 >
[CoCl2(NH3)4]Cl > [CoCl3(NH3)3]
(order of electrical conductivity.)
37.H
O
4 3LiAlH CH MgBr
35ºC ExcessA B
Identify B in the reaction
(1) H
O
(2) OH
(3) OH
(4) CH4
38. The wavelength of the electron emitted by a metal
sheet of work function 4 eV when photons from EMR
of wavelength 124 nm strike the metal plate.
(1) 10 nm (2) 206.67 nm
(3) 50 nm (4) 0.5 nm
36. (1) C > Si > Pb > Ge ()(2) C > Pb > Ge > Si ()(3) [CoCl3(NH3)3] > [CoCl(NH3)5]Cl2 >
[Co(NH3)6]Cl3> [CoCl2(NH3)4]Cl
()
(4) [Co(NH3)6]Cl3 > [CoCl(NH3)5]Cl2 >
[CoCl2(NH3)4]Cl > [CoCl3(NH3)3]
()
37.H
O
4 3LiAlH CH MgBr
35ºC ExcessA B
B
(1) H
O
(2) OH
(3) OH
(4) CH4
38. EMR124 nm
4 eV
(1) 10 nm (2) 206.67 nm
(3) 50 nm (4) 0.5 nm
H-17/331001CT102116065
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39. Which of the following is paramagnetic ?
(1) O2[AsF6] (2) Al2O3
(3) C2 (4) Be2
40. Which of the following amino acids does not containasymmetric carbon ?(1) Histidine (2) Glycine(3) –Alanine (4) Threonine
41. Identify the correct option.
(I) AgCl is not soluble in H2O but soluble in KCN.
(II) Zn when reacts with cold v.v. dil HNO3 givesNH4NO3.
(III) CuSO4 reacts with KI to form Cu2I2 + K2SO4.
(IV) 1000ºC4 2CuSO .5H O The gases liberated
are SO2 and O2.
(1) All statements are correct
(2) I, II and IV are correct
(3) II and III are incorrect statements
(4) Only I is incorrect.
42. Identify the correct option regarding surfacephenomenon.
(1) Colloidal solution of As2S3 can be prepared by
Peptization.
(2) Out of KCl, BaCl2, AlCl3, Na3PO4 ; BaCl2 is most
effective in coagulation of sulphur sol.
(3) C H COOCH —C—CH OH15 31 2 2
CH OH2
CH OH2
is non–ionic
detergent.(4) On increasing concentration of
C2H5 SO3Na electrical conductance
will always increase
39. (1) O2[AsF6] (2) Al2O3
(3) C2 (4) Be2
40. (1) (2) (3) – (4)
41. (I) AgCl, H2O KCN (II) HNO3 Zn, NH4NO3 (III) CuSO4, KI Cu2I2 + K2SO4 (IV) 1000ºC
4 2CuSO .5H O SO2
O2 (1) (2) I, II IV (3) II III (4) I
42. (1) As2S3
(2) KCl, BaCl2, AlCl3, Na3PO4 BaCl2
(3) C H COOCH —C—CH OH15 31 2 2
CH OH2
CH OH2
(4) C2H5 SO3Na
1001CT102116065H-18/33
Target : JEE (Main + Advanced) 2017/23-03-2017
43. Which of the following is correct for the equilibrium ?
2CH3 C
O
O H H3C C
O
O H
H O
OC CH3
(Equilibrium constants for the reaction in water and
benzene are KWater KBenzene)
(1) KWater > KBenzene (2) KWater < KBenzene
(3) KWater = KBenzene (4) None of these
44. Which of the following options is incorrect ?
(1) Tailing of mercury can be used as test for Ozone.
(2) Carbon suboxide is amphoteric in nature and
carbon monoxide is neutral.
(3) Both Ni3B and FeB have no B–B bond.
(4) Both V3B2 and NaB15 have B–B bond.
45. 2 2 4H O / H SOA
Identify ‘A’ in the reaction.
(1)
OH
(2)
OH
(3)
OH
(4)
OH
43.
2CH3 C
O
O H H3C C
O
O H
H O
OC CH3
( KWater KBenzene )
(1) KWater > KBenzene (2) KWater < KBenzene
(3) KWater = KBenzene (4) None of these
44. (1) Tailing of mercury
(2)
(3) Ni3B FeB B–B (4) V3B2 NaB15 B–B
45. 2 2 4H O / H SOA
‘A’
(1)
OH
(2)
OH
(3)
OH
(4)
OH
H-19/331001CT102116065
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46. Which of the following statements is incorrect ?
(1) The specific heat capacity of substance is greater
in the solid state than in liquid state.
(2) The specific heat capacity of a substance is greater
in gaseous state than in the liquid state.
(3) The latent heat of vaporization of a substance is
greater than that of fusion.
(4) The internal energy of an ideal gas is a function of
its temperature.
47. The anode mud in the refining of silver
(1) Zn, Cu, Ag, Au
(2) Zn, Au
(3) Cu, Ag, Au
(4) Au
48. Identify the incorrect order of the given parameter.
(1) V > Ni > Mn (order of melting point)
(2) Co > Ni > Cu > Zn (order of melting point)
(3) Na2S > ZnS > CuS
(order of solubility in aqueous medium)
(4) CuS > ZnS > Na2S
(order of solubility in aqueous medium)
46.
(1)
(2)
(3)
(4)
47.
(1) Zn, Cu, Ag, Au
(2) Zn, Au
(3) Cu, Ag, Au
(4) Au
48.
(1) V > Ni > Mn ()
(2) Co > Ni > Cu > Zn ()
(3) Na2S > ZnS > CuS
()
(4) CuS > ZnS > Na2S
()
1001CT102116065H-20/33
Target : JEE (Main + Advanced) 2017/23-03-2017
49.
CHO OHC
CHO OHC
2
(i)NaOH(excess)
(ii)H / 2H O,0ºC
(1)
HO
OH HO
OH
(2)
HO
OH
O–
O
O–
O
(3)
O
O
O
O
(4)
COOH
O
OH HO
OOH
49.
CHO OHC
CHO OHC
2
(i)NaOH(excess)
(ii)H / 2H O,0ºC
(1)
HO
OH HO
OH
(2)
HO
OH
O–
O
O–
O
(3)
O
O
O
O
(4)
COOH
O
OH HO
OOH
H-21/331001CT102116065
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50. 5 milli-moles of a solid A was dissolved in 5 moles ofH2O. On adding to the solvent, A starts polymerisinginto another insoluble solid following zero orderkinetics. On adding 6 milli-moles of another solidsolute C (after 20 minute) the polymerisationcompletely stops. The insoluble solid polymer isremoved and the resulting solution was cooled to atemperature less than - 0.186°C (melting point ofsolution) to cause solidification of some liquidwater. Calculate the value of ‘X’ if rate constantfor polymerisation reaction is represented as10–X moles/minute. [Kf(H2O) = 1.86 K –Kg mole–1]
(1) 1 (2) 4 (3) 3 (4) 5
51. Silver has an atomic radius of 144 pm and the density
of silver is 10.6 g cm–3. Based on this information
identify the correct statement.
(1) It has FCC crystal lattice.
(2) It has BCC crystal lattice.
(3) Approximately 0.24 fraction of edge is not
covered by atoms.
(4) None of the statement is true.
52. Which of the following is least biodegradable ?
(1) C17H35COONa
(2) CH3(CH2)11SO3Na
(3) SO3NaCH(CH2)9
CH3
H3C
(4) CH3—CH—(CH2—CH)2—CH2—CH—CH3
CH3 CH3
SO3Na
50. A 5 5 A (20 ) C 6 – 0.186°C () 10–X x [Kf(H2O)=1.86K –Kg mole–1]
(1) 1 (2) 4 (3) 3 (4) 5
51. 144 pm 10.6 g cm–3 (1) FCC (2) BCC (3) 0.24 fraction covered
(4)
52. (1) C17H35COONa
(2) CH3(CH2)11SO3Na
(3) SO3NaCH(CH2)9
CH3
H3C
(4) CH3—CH—(CH2—CH)2—CH2—CH—CH3
CH3 CH3
SO3Na
1001CT102116065H-22/33
Target : JEE (Main + Advanced) 2017/23-03-2017
53. + 3 4H PO3 2CH CH CH A
2 2 4O dil.H SO
heatB C D
A, C and D are
(1)
CH2CH2CH3
,
OH
, CH3COCH3
(2)
CHH3C CH3
,
OH
, CH3COCH3
(3)
CHH3C CH3
,
COCH3
, CH3COCH3
(4)
CHH3C CH3
,
OH
, CH3—CH—CH3
OH
54. How many moles of H2O (per mole of Cl2 evolved)
will be formed when KMnO4 is added to HCl solution?
(1) 5/4 (2) 4/5
(3) 5/8 (4) 8/5
53. + 3 4H PO3 2CH CH CH A
2 2 4O dil.H SO
heatB C D
A, C D
(1)
CH2CH2CH3
,
OH
, CH3COCH3
(2)
CHH3C CH3
,
OH
, CH3COCH3
(3)
CHH3C CH3
,
COCH3
, CH3COCH3
(4)
CHH3C CH3
,
OH
, CH3—CH—CH3
OH
54. KMnO4 HCl H2O
(Cl2 )
(1) 5/4 (2) 4/5
(3) 5/8 (4) 8/5
H-23/331001CT102116065
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55. The densities of air at 25ºC and 100ºC are 1.2 gL–1
and 0.9 g L–1 respectively. Assuming that the air obey’s
Charle’s law, the value of absolute zero of
temperature in degree Celsius is
(1) –273ºC (2) 200ºC
(3) –200ºC (4) 0ºC
56. Which of the following order is correct w.r.t.
magnitude of enthalpies of formation for alkali metal
halides ?
(1) Iodide > Bromide > Chloride > Fluoride
(of same metal)
(2) CsCl > RbCl > NaCl > LiCl
(3) NaF > CsF > RbF > KF
(4) LiI > NaI > RbI > CsI
57. For the reaction : N2 (g) + 3H2(g) 2NH3(g),
H = –24 Kcal at 427ºC and 200 atm. Calculate
magnitude of internal energy change (in Kcal U), if
168 gm N2 gas and 30 gm H2 gas are allowed to
react completely (100 % reaction yield) to form NH3
gas at 427ºC and 200 atm.
(1) –106 Kcal
(2) –24 Kcal
(3) –21.2 Kcal
(4) – 120 kcal
55. 25ºC 100ºC 1.2 gL–1
0.9 g L–1
(1) –273ºC (2) 200ºC
(3) –200ºC (4) 0ºC
56.
(1) Iodide > Bromide > Chloride > Fluoride
(of same metal)
(2) CsCl > RbCl > NaCl > LiCl
(3) NaF > CsF > RbF > KF
(4) LiI > NaI > RbI > CsI
57. N2 (g) + 3H2(g) 2NH3(g) 427ºC
200 atm H = –24 Kcal
U (Kcal ) ,
427ºC 200 atm 168 gm N2 30 gm
H2
NH3
(1) –106 Kcal
(2) –24 Kcal
(3) –21.2 Kcal
(4) – 120 kcal
1001CT102116065H-24/33
Target : JEE (Main + Advanced) 2017/23-03-2017
58.
NH2
2 2NaNO HCl H O
0 5ºC boilA B
2 2Br / H O Zn
dustC D
Compound ‘D’ is
(1)
OH
Br
BrBr
(2)
OH
(3)
Br
BrBr
(4)
OH
HO OH
59. Calculate solubility (in moles/litre) of a saturated
aqueous solution of Ag3PO4 if the vapour pressure of
the solution becomes 750 torr at 373 K.
(1) 2
15(2)
1
30(3)
10
54(4)
20
27
60. It is found that for every 10º rise in temperature, the
rate of the reaction doubles itself. This is mainly
because
(1) The speed of the reactants doubles for every 10º
rise in temperature.
(2) The fraction of the molecules forming the
activated complex doubles itself.
(3) The concentration doubles itself.
(4) The collision frequency doubles itself.
58.
NH2
2 2NaNO HCl H O
0 5ºC boilA B
2 2Br / H O Zn
dustC D
‘D’
(1)
OH
Br
BrBr
(2)
OH
(3)
Br
BrBr
(4)
OH
HO OH
59. Ag3PO4 373 K 750 torr
(1) 2
15(2)
1
30(3)
10
54(4)
20
27
60. 10º
(1) 10º
(2) fraction
(3)
(4)
H-25/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
PART C - MATHEMATICS
61. ax + y + 1 = 0, x + by + 1 = 0 x + y + c = 0 ( a, b & c
1 1 1
1 a 1 b 1 c
(1) –1 (2) 1 (3) 0 (4) 2
62. x
1f x
x 1 e 1 x 4 x 5 x 6
(1) , 5 1, 4 6,
(2) , 5 1, 0 0, 4 6,
(3) 5, 1 0, 4 6,
(4) , 5 1, 4 6,
63. 1 2
2 2
0 0
1 sinx ax bx c dx 1 sin x ax bx c dx .
2ax bx c 0 (1) (1, 2) (2) (0, 1) (3) (0, 2) (4)
64. A.P. n cn(n – 1) ,c 0, (1) 22 2c n n 1
(2) 22c n n 1 2n 1
3
(3) 22c n n 1 2n 1
3
(4) 2 2
2c nn 1
3
61. If the lines ax + y + 1 = 0, x + by + 1 = 0 andx + y + c = 0 (where a, b & c are distinct anddifferent from 1) are concurrent, then the value of
1 1 1
1 a 1 b 1 c
(1) –1 (2) 1 (3) 0 (4) 2
62. Domain of the function
x
1f x
x 1 e 1 x 4 x 5 x 6
(1) , 5 1, 4 6,
(2) , 5 1, 0 0, 4 6,
(3) 5, 1 0, 4 6,
(4) , 5 1, 4 6,
63. 1 2
2 2
0 0
1 sinx ax bx c dx 1 sin x ax bx c dx .
So, location of the roots of 2ax bx c 0 is
(1) At least one real root between (1, 2)
(2) At least one real root between (0, 1)
(3) At most one real root between (0, 2)
(4) Can’t say exactly about the roots
64. If the sum of first n terms of an A.P. is cn(n – 1), wherec 0, then sum of the squares of these terms is
(1) 22 2c n n 1
(2) 22c n n 1 2n 1
3
(3) 22c n n 1 2n 1
3
(4) 2 2
2c nn 1
3
1001CT102116065H-26/33
Target : JEE (Main + Advanced) 2017/23-03-2017
65. The maximum value of sin cos(tanx) is
(1) 3
2(2) sin1
(3) 1 (4) sin (cos1)
66. The interval of the values of ‘a’ for which the line
x y 0 bisect 2 distinct chords drawn from a
point 1 2a 1 2a
, 2 2
to the circle
2 22x 2y 1 2a x 1 2a y 0
(1) a , 0 2,
(2) a , 0 0,
(3) a 2,
(4) a , 2 2,
67. The vector ˆ ˆ ˆxi yj zk makes with the plane of the
two vectors (2, 3, –1) and (1, –1, 2) an acute
angle 1cot 2 . Then,
(1) y x z zx (2) z x y xy
(3) x y z yz (4) x y z xyz
68. If from a point P (a, b, c) perpendiculars PA, PB aredrawn to yz and zx plane, then the equation of theplane OAB (where O is origin) is :
(1) bcx + cay + abz = 0
(2) bcx + cay – abz = 0
(3) bcx – cay + abz = 0
(4) –bcx + cay + abz = 0
69. If sin 2sin 3sin 0 and
cos 2cos 3cos 0 , then the value of
cos 3 8 cos3 27cos 3
(1) cos (3 + 3 + 3) (2) 18 cos ( + + )
(3) 6 cos ( + + ) (4) 36 cos ( + + )
65. sin cos(tanx)
(1) 3
2(2) sin1
(3) 1 (4) sin (cos1)
66. ‘a’ x y 0
2 22x 2y 1 2a x 1 2a y 0
1 2a 1 2a
, 2 2
(1) a , 0 2,
(2) a , 0 0,
(3) a 2,
(4) a , 2 2,
67. ˆ ˆ ˆxi yj zk , (2, 3, –1) (1, –1, 2)
1cot 2
(1) y x z zx (2) z x y xy
(3) x y z yz (4) x y z xyz
68. P (a, b, c) yz zx PA, PB OAB O ) (1) bcx + cay + abz = 0(2) bcx + cay – abz = 0(3) bcx – cay + abz = 0(4) –bcx + cay + abz = 0
69. sin 2sin 3sin 0 cos 2cos 3cos 0 cos 3 8 cos3 27cos 3 (1) cos (3 + 3 + 3) (2) 18 cos ( + + )(3) 6 cos ( + + ) (4) 36 cos ( + + )
H-27/331001CT102116065
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70. If , are the roots of the equation 2x 2x 4 0 ,
then the value of n n is :
(1) n n2 cos
3
(2) n 1 n
2 cos3
(3) n n
2 sin3
(4)
n 1 n2 sin
3
71. If n 2 n 1
1 1 1s 1 .......
2 2 2 , then the least
integral value of n such that n
12 s
100 is
(1) 7 (2) 9
(3) 8 (4) 6
72. Statement-1: Any function f (x) is even function,when f (– x) = f (x) over its specified domain.
Statement-2: 2
2
1 x x 1f x
41 x
,
where [.] is greatest integer function. Function f(x) is
even function.
(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanation
for statement-2
(2) Statement-1 is true, statement-2 is false
(3) Statement-1 is false, statement-2 is true
(4) Both statements are true, and statement-1 is the
true explanation of statement-2
70. , 2x 2x 4 0 n n
(1) n n2 cos
3
(2) n 1 n
2 cos3
(3) n n
2 sin3
(4)
n 1 n2 sin
3
71. n 2 n 1
1 1 1s 1 .......
2 2 2 , n
n
12 s
100
(1) 7 (2) 9
(3) 8 (4) 6
72. -1: f (x) f (– x) = f (x)
-2: 2
2
1 x x 1f x
41 x
,
[.] f (x)
(1) -1 -2 ; -2-1
(2) - 1 - 2
(3) - 1 - 2
(4) -1 -2 -2-1
1001CT102116065H-28/33
Target : JEE (Main + Advanced) 2017/23-03-2017
73. Statement-1: If two tangents are drawn to an
ellipse from a single point and if they are perpendicular
to each other, then locus of that point is always a
circle.
Statement-2: For an ellipse 2 2
2 2
x y1
a b , locus of
that point from which two perpendicular tangents
are drawn, is 22 2x y a b .
(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanation
for statement-2
(2) Statement-1 is true, statement-2 is false
(3) Statement-1 is false, statement-2 is true
(4) Both statements are true, and statement-1 is the
true explanation of statement-2
74. Consider a system of equations ax + by = 0,
cx + dy = 0, where a, b, c, d, {0, 1}.
Statement-1: The probability that system of
equations has a solution is 1.
Statement-2: The probability that the system of
equations has a unique solution is 3
8.
(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanation
for statement-2
(2) Statement-1 is true, statement-2 is false
(3) Statement-1 is false, statement-2 is true
(4) Both statements are true, and statement-1 is the
true explanation of statement-2
73. -1:
-2: 2 2
2 2
x y1
a b
22 2x y a b
(1) -1 -2 ; -2-1
(2) - 1 - 2
(3) - 1 - 2
(4) -1 -2 -2-1
74. ax + by = 0, cx + dy = 0 a, b, c, d, {0, 1}.
-1:
-2: 3
8
(1) -1 -2 ; -2-1
(2) - 1 - 2
(3) - 1 - 2
(4) -1 -2 -2-1
H-29/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
75. In a ABC, if two sides b & c and an angle B aregiven.Statement-1: Let b = 5 cm, c = 3 cm andB = 60o. Total number of possible triangles are 2.Statement-2: If c sin B < b < c and B is an acuteangle, then there are two possible values of C.(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanationfor statement-2
(2) Statement-1 is true, statement-2 is false(3) Statement-1 is false, statement-2 is true(4) Both statements are true, and statement-1 is the
true explanation of statement-276. For a series S = 1 – 2 + 3 – 4 … n terms,
Statement-1: Sum of series always dependent onthe value of n, i.e. whether it is even or odd.
Statement-2: Sum of series is n
2 when value of
n is any even integer.(1) Statement-1 is true, statement-2 is true
but statement-1 is not the correct explanationfor statement-2
(2) Statement-1 is true, statement-2 is false(3) Statement-1 is false, statement-2 is true(4) Both statements are true, and statement-1 is the
true explanation of statement-2
77. 2 2 2 2 2 2n
n 1 n 2 n 3 1lim ........
nn 1 n 2 n 3
(1) ln 24
(2) ln 2
4
(3) 1
ln24 2
(4)
1ln2
4 2
78. The area bounded by the curve x1
y e2
is
(1) 2 1 ln2 (2) 1
1 ln 22
(3) 2 ln2 1 (4) 1
1 ln 22
75. ABC b & c B -1: b = 5 cm, c = 3 cm B = 60o. -2: csin B < b < c B C (1) -1 -2 ; -2
-1 (2) - 1 - 2 (3) - 1 - 2 (4) -1 -2 -2
-1 76. S = 1 – 2 + 3 – 4 … n ,
-1: n n,
-2: n n
2
(1) -1 -2 ; -2-1
(2) - 1 - 2 (3) - 1 - 2 (4) -1 -2 -2
-1
77. 2 2 2 2 2 2n
n 1 n 2 n 3 1lim ........
nn 1 n 2 n 3
(1) ln 24
(2) ln 2
4
(3) 1
ln24 2
(4)
1ln2
4 2
78. x1y e
2
(1) 2 1 ln2 (2) 1
1 ln 22
(3) 2 ln2 1 (4) 1
1 ln 22
1001CT102116065H-30/33
Target : JEE (Main + Advanced) 2017/23-03-2017
79. If 0
A1 1
and 1 0
B5 1
, then the value of
for which 2A B is
(1) 1 (2) –1
(3) 4 (4) No real values
80. If n 2 3 n0 1 2 3 n1 x c c x c x c x ....... c x ,
then the value of
n0 1 2 nc 3c 5c ........ 1 2n 1 c is :
(1) nn 1 .2 (2) 0
(3) n 11 2n .2 (4) n1 n .2
81. For what value of k to the following system ofequations possess a non-trivial solution ?
x ky 3z 0
3x ky 2z 0
2x 3y 4z 0
(1) 11
14(2)
33
2 (3)
33
20(4)
33
2
82. The mean and variance of a binomial variable X are2 and 1 respectively. Then, the probability that X takesvalues greater than 1 is
(1) 15
16(2)
11
16(3)
5
16(4)
1
16
83. The curve for which the intercept cut off by anytangent on y-axis is proportional to the square of theordinate of the point of tangency is
(1) 2
1
cc x 1
y (2)
12
cc y 1
x
(3) 1 2c c
1x y (4) 2 3
1 2c y c x y
(where c1 and c
2 are arbitrary constants)
79. 0
A1 1
1 0
B5 1
,
2A B (1) 1 (2) –1
(3) 4 (4)
80. n 2 3 n0 1 2 3 n1 x c c x c x c x ....... c x
n0 1 2 nc 3c 5c ..... 1 2n 1 c
(1) nn 1 .2 (2) 0
(3) n 11 2n .2 (4) n1 n .2
81. k x ky 3z 0
3x ky 2z 0
2x 3y 4z 0
(1) 11
14(2)
33
2 (3)
33
20(4)
33
2
82. X 2 1 X
(1) 15
16(2)
11
16(3)
5
16(4)
1
16
83. y-
(1) 21
cc x 1
y (2) 1
2
cc y 1
x
(3) 1 2c c
1x y (4)
2 31 2c y c x y
(c1 c
2 )
H-31/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017
84. Evaluate x
dxx
(1) 2
(2)
2
(3) 2
(4)
285. The angle between the lines joining the origin to the
points of intersection of the straight line y 3x 2
with the curve 2 2x 2xy 3y 4x 8y 11 0 is
(1) 1tan 2 (2) 1 2
tan3
(3) 1 4
tan3
(4)
1 2 2tan
3
86. The tangents to the parabola y2 = 4ax makes angle
1 and
2 with the positive x-axis. Then, the locus of
their point of intersection if cot 1 + cot
2 = c is
(1) y = ac (2) x = ac
(3) xy = ac2 (4) xy = a
c
87. If two points P and Q on the hyperbola2 2
2 2
x y1
a b , whose centre is C, are such that CP
is perpendicular to CQ, ( a b ), then value of
2 2
1 1
CP CQ
(1) 1
ab(2) 2 2
1 1
a b
(3) 2 2
1 1
a b (4) 2 2
1
a b
84.x
dxx
(1) 2
(2)
2
(3) 2
(4)
2
85. 2 2x 2xy 3y 4x 8y 11 0 y = 3x+2
(1) 1tan 2 (2) 1 2
tan3
(3) 1 4
tan3
(4)
1 2 2tan
3
86. y2 = 4ax x-1
2 cot
1 + cot
2 = c
(1) y = ac (2) x = ac
(3) xy = ac2 (4) xy = a
c
87. 2 2
2 2
x y1
a b P Q C,
CP, CQ ( a b ) ,
2 2
1 1
CP CQ
(1) 1
ab(2) 2 2
1 1
a b
(3) 2 2
1 1
a b (4) 2 2
1
a b
1001CT102116065H-32/33
Target : JEE (Main + Advanced) 2017/23-03-2017
88. Tangent is drawn to ellipse 2
2xy 1
27 at
3 3 cos , sin (where 0, 2
). Then, the
value of such that sum of intercepts on the axes
made by this tangent is minimum, is
(1) 3
(2)
6
(3) 8
(4)
4
89. Solution of the equation
x 3 4 x 1 x 8 6 x 1 1 is
(1) x 4, 9 (2) x 3, 8
(3) x 5, 10 (4) x 4, 7
90. Let 2A : 2cos sin 2 and
3B :
2 2
, then A B is
(1) 3
: , 2
(2) 7
: , 2 6
(3) : , 2 6
(4) 5 3
: , , 2 6 2
88. 2
2xy 1
27 3 3 cos , sin
( 0, 2
)
(1) 3
(2)
6
(3) 8
(4)
4
89. x 3 4 x 1 x 8 6 x 1 1
(1) x 4, 9 (2) x 3, 8
(3) x 5, 10 (4) x 4, 7
90. 2A : 2cos sin 2
3B :
2 2
, A B
(1) 3
: , 2
(2) 7
: , 2 6
(3) : , 2 6
(4) 5 3
: , , 2 6 2
H-33/331001CT102116065
Leader Course (Score-I) & Enthusiast Course (Score-II)/23-03-2017