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FIITJEE

ALL INDIA TEST SERIES

FULL TEST – IV

JEE (Advanced)-2019

PAPER – 2

Time Allotted: 3 Hours Maximum Marks: 231 General Instructions: The test consists of total 69 questions.

Each subject (PCM) has 23 questions.

This question paper contains Three Parts.

Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.

Each Part is further divided into Three Sections: Section-A, Section-C & Section-D.

Section-A (01 – 03, 24 – 26, 47 – 49) contains 9 multiple choice questions which have only one correct answer. Each question carries +3 marks for correct answer and –1 mark for wrong answer.

Section-A (04 – 08, 27 – 31, 50 – 54) contains 15 multiple choice questions which have one or more than one correct answer. Each question carries +4 marks for correct answer and –2 mark for wrong answer. Partial Marks +1 for each correct option provided no incorrect options is selected. Section-A (09 – 10, 32 – 33, 55 – 56) contains 3 paragraphs. Based upon paragraph, 2 multiple choice questions have to be answered. Each question has only one correct answer and carries +3 marks for correct answer. There is no negative marking.

Section-C (11 – 20, 34 – 43, 57 – 66) contains 30 Numerical based questions with answer as numerical value from 0 to 9 and each question carries +3 marks for correct answer. There is no negative marking.

Section-D (21 – 23, 44 – 46, 67 – 69) contains 9 Numerical answer type questions with answer XXXXX.XX and each question carries +4 marks for correct answer and –1 mark for wrong answer.

AITS-FT-IV (Paper-2)-PCM-JEE(Advanced)/19


2

Physics PART – I

SECTION – A (Single Correct Choice Type)

This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. In the diagram shown, the charge +Q is fixed. Another

charge + 2q, is projected from a distance R from the fixed charge. The minimum separation between the two charges

when the velocity becomes 13

times of the projected

velocity, is (Assume gravity to be absent)

(A) 3 R2

(B) 3 R

(C) 1R2

(D) 4 R

R +Q M, +2q

30o

V

2. A conducting sphere of radius R and charge Q is placed near a

uniformly charged non-conducting infinitely large thin plate having surface charge density . Then find the potential at point A (on the surface of sphere) due to charge on sphere

oo

1here K ,4 3

(A) 0

QK RR 4

(B)

0

QKR 2

(C) QKR

(D) None of these

+ + + + + +

+Q A

O 4R

0

3. Two heavy right circular rollers of radii R and r respectively rest on a

rough horizontal plane as shown in figure. The larger roller has a string wound around it to which a horizontal force P can be applied as shown. Assuming that the coefficient of friction has the same value for all surfaces of contact and the smaller cylinder should neither roll nor slide. The minimum coefficient of friction so that the larger roller can be pulled over the smaller one is

(A) rR

(B) 2r

R

(C) r3R

(D) rR

P

Space for Rough work



3

(One or More than one correct type)

This section contains 5 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct. 4. Two point coherent sources separated by d = 2D emits light of

wavelength D in phase. A circular wire of radius R R D has its centre at point O.

(A) Points A, B C and D are points of maxima (B) Total number of maxima on screen is eight (C) Total number of minima on screen is eight (D) None of the above

B

A

D

C S1 S2 O

d 2 D

5. As shown in the figure a liquid of density is standing in a sealed container to a height h. The

container contains compressed air at a gauge pressure of P. The horizontal outlet pipe has a cross-sectional area is A/2 at E. Find the correct options.

P

h

A B C D E

(A) The velocity of liquid at C will be

1/2(P gh)

4

(B) The velocity of liquid at C will be

1/22(P gh)

(C) The discharge rate is given by

1/2A (P gh)2

(D) The discharge rate is given by

1/2A (P gh)2




4

6. A light cylindrical tube ‘T’ of length and radius 'r ' containing air is inverted in water (density d). One end of the tube is open and the other is closed. A block ‘B’ of density 2d is kept on the tube as shown in the figure. The tube stays in equilibrium in the position shown. (Assume the atmospheric pressure is to be 0P .). Pick up the correct statement(s).

air

B h

l l / 3

T r

(A) the volume of block B is 2r l

3

(B) the volume of block B is 22 r l

3

(C) the pressure of air trapped in the tube is 0lP dg h3

(D) the pressure of air trapped in the tube is 02lP dg h3

7. A rod of copper, uniform along its length land of a rectangular cross section of sides of length a

and width b(<a) has one end maintained at o100 C and the other end at o0 C . The rod is insulated so that no heat is lost from the sides. Let 1Q be the amount of heat per second that is transmitted along its length, aQ the heat/s transmitted parallel to a and bQ the heat/s transmitted parallel to b across any section after the steady state conditions are reached. Then,

(A) 1 a bQ constant, Q Q 0 (B) 1 a bQ 0, Q Q 0 (C) 1 a bQ 0, Q Q 0 (D) 1Q constant




5

8. The y-x curve at an instant for a wave travelling along x axis on a string is shown. Slope at the point A on the curve, as shown, is o53 . Which of the following is/are correct?

(A) Transverse velocity of the particle at point A is positive if the wave is travelling along positive x axis.

(B) Transverse velocity of the particle at point A is positive if the wave is travelling along negative x axis of the particle at point A.

(C) Magnitude of transverse velocity of the particle at point A is greater than wave speed.

(D) Magnitude of transverse velocity of the particle at point A is lesser than wave speed.

y

x

o53 A

Paragraph type (One Option Correct)

This section contains 1 paragraph each describing theory, experiment, data etc. Two questions relate to the paragraph. Each question of a paragraph has Only One correct answer among the four choices (A), (B), (C) and (D).

Paragraph for Questions 9 & 10

An accelerator produces a narrow beam of protons, each having an initial speed of vo. The beam is directed towards an initially uncharged distant metal sphere of radius R and centered at point O, The initial path of the beam is parallel to the axis of the sphere at a distance of (R/2) from the axis, as indicated in the diagram.

Acce

lera

tion

O R

R/2

Axis of sphere

Proton beam

The protons in the beam that collide with the sphere will cause it to become charged. The subsequent potential field at the accelerator due to the sphere can be neglected. The angular momentum of a particle is defined in a similar way to the moment of a force. It is defined as the moment of its linear momentum; linear momentum replacing the force. We may assume the conserved, Assume the mass of the proton as mp and the charged on it as e. Given that the potential of the sphere increases with time and eventually reaches a constant value.

9. The total energy (E) of a proton in the beam travelling with speed v at a distance of r r R from

point O. Assuming that the sphere has acquired an electrostatic charge Q is

(A) 0

eQ4 r

(B) 0

eQless than 4 r

(C) 0

eQgreater than 4 r

(D) zero




6

10. After a long time, when the potential of the sphere reaches a constant value, the trajectory of proton is correctly sketched as (A) 1

(B) 2 (C) 3 (D) 4

R O

R/2 1 2

3 4

SECTION – C (Single digit integer type)

This section contains 10 questions. The answer to each question is a Single Digit Integer ranging from 0 to 9, both inclusive. 11. Binding energy per nucleon of a fixed nucleus XA is 6 MeV. It absorbs a neutron moving with KE=

2 MeV, and converts into Y, emitting a photon of energy 1 MeV. If the Binding Energy per

nucleon of Y (in MeV) is found to be xA 1

.A 1

Find the value of x.

12. In the given circuit, all the capacitors are initially uncharged. After closing the switch S1 for a long

time suddenly S2 is also closed and kept closed for a long time. Find the total heat produced after closing S2 (in joules).

C E

C

C

C

E

E

E S2

S1




7

13. Figure shows a ball of mass m connected with two ideal springs of force constant k, kept in equilibrium on a smooth incline, suddenly right spring is cut. What is magnitude of instantaneous acceleration (in m/s2) of ball?

45o

x

y

45o

45o

14. A thin glass plate of area A and mass m is

hinged along one of its sides. The speed with which the air should be blown parallel to its upper surface to hold the plate horizontal is

mg18pA

. Find the value of . The density of

air is p.

Glass plate

Air

15. A soap film is made by dropping a circular frame of radius b in

soap solution. A bubble is formed by blowing air with speed v in the form of a cylinder. Air stops after striking surface of soap bubble. Density of air is . The radius of the bubble is R > b. The radius R of the bubble when the soap bubble separates from the

ring is 2

Tv

. Find the value of (where surface tension of liquid

is T).

b R

v

16. In the figure shown AB, BC and PQ are thin, smooth, rigid wires.

AB and AC are joined at A and fixed in vertical plane. oBAC 2 9 and line AD is angle bisector of angle BAC. A

liquid of surface tension T 0.205 N / m forms a thin film in the triangle formed by intersection of the vires AB, AC and PQ. In the figure shown the uniform wire PQ of mass 1 gm is horizontal and in equilibrium under the action of surface tension and gravitational force. Find the time period of SHM of PQ in vertical plane for small

displacement from its mean position, in the form sX and fill value

of X.

P Q

C B

D

A




8

17. Three identical ideal springs, each of force constant k are

joined to three identical balls (each of mass m) as shown in the figure. O is centroid of the triangle. Initially, each of the springs is in its natural length. Now all the three balls are simultaneously given small displacements of equal magnitude along the directions shown in the figure. The

oscillation frequency of balls is 1 k2 2m

. Find the value of .

m

k k

m m

k

O

18. An ant with mass m is standing peacefully on top of a horizontal, stretched rope. The rope has

mass per unit length and is under tension F. Without warning, a student starts a sinusoidal transverse wave of wavelength propagating along the rope. What minimum wave amplitude (in mm) will make the ant feel weightless momentarily? Assume that m is very small and that the presence of the ant has no effect on the propagation of the wave. (Given:

1 20.5m, 0.1kgm , F 3.125N, g ) . 19. In a car race sound signals emitted by the two cars are detected by the detector on the straight

track at the end point of the race. Frequency observed are 330 Hz and 360 Hz and the original frequency is 300 Hz of both cars. Race ends with the separation of 100 m between the cars. Assume both cars move with constant velocity and velocity of sound is 330 m/s. Find the time (in sec) taken by winning car.

20. Two identical wires are stretched by the same tension of 100 N and each emits a note of

frequency 200 Hz. The tension in one wire is increased by 1 N. Calculate the number of beats heard per second when the wires are plucked.




9

SECTION – D (Numerical Answer Type)

This section contains 3 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded‐off to the second decimal place; e.g. xxxxx.xx). 21. A glass beaker of mass 400 g floats in water with the open end just touching the surface of water

and half of the beaker filled with water. The inner volume of the beakers is 500 cm3. What is the density (in g cm-3) of the material of beaker?

22. The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given

by y = 2 cm sin 1 10.6 cm x cos 500 s t The length of the string is:

23. An open organ pipe containing air resonates in fundamental mode due to a tuning fork. The

measured values of length in cml of the pipe and radius r (in cm) of the pipe are 94 0.1 r = 5 0.05. l The velocity of the sound in air is accurately known. The maximum

percentage error in the measurement of the frequency of that tuning fork by this experiment, will be




10

Chemistry PART – II


This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

24.Ph

Br

Ai) HCHO

ii) H+

Mg

etherB; Prodcut B is

(A) C

CH2

Ph

OH(B)Ph C C CH2 CH2 CH2OH

(C) (D)Ph C C CH

OH

CH3 Ph CH2C C CH2 CH2 OH

25. In a unit cell of AB if all the atoms along one of the tetrad axis of symmetry and one of the diad

axis of symmetry are removed, then the resultant formulae of the unit cell will be (Atoms ‘A’ occupy all T.V. and atoms ‘B’ form fcc) (A) A5B6 (B) A5B11 (C) A2B3 (D) No change in formula.

26. Consider the following reactions (I) 2 2 3Na S O dil HCl (II) 2 2 3 2 2Na S O Cl H O (III) 2 2SO H S (IV) 2 2 2H S H O The reactions which give yellow turbidity are

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




11


This section contains 5 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct. 27. For aq. solution of potash alum, which is/true are

(A) One gm eq of potash alum will give 1 gm eq of K+ (B) One gm eq of potash alum will give 1 gm eq of Al3+

(C) One gm eq of potash alum will give 2 gm eq of 24SO

(D) 18

mole of potash alum will give 1 gm eq of 24SO

28. If a coordination complex M(CO)6 is colored due to d – d transition & its CFSE corresponds to

that wavelength which an electron emits on de – excitation from 4th orbit to 3rd orbit in 2Li ion. Find the value of CFSE for the given complex. 7 1 34take R 10 m Ch 6.62 10

(A) 199.53 10 J (B) 181.36 10 J (C) 201.97 10 J (D) 172.59 10 J

29. Which of the following Newmann projection is correct for 2 – methyl butane?

(A)

(C)

(B)

(D)

H

HCH3

H H

H

CHMe2H

H

MeH

H

EtMe

HH

H

Et

MeH

H

H

H

CH3




12

30. Which of the following is correct order as per the mention property?

(A)

(B)

(C)

(D)

COOH

Cl

COOH

F

COOH

I

COOH

NO2

OH

NO2

NH2

OMe

COOH

NO2

OH

NO2

NH2

COOH

NO2

OH

NO2

NH2

OMe

> >

> > >

> > >

> > >

NH2

OMe

OH

COOH

(acidic strength)

(acidic strength)

(acidic strength)

(basic strength)




13

31. If at 25oC an aq solution of 0.4 M Na2SO4 and water are separated by SPM as mentioned below

SPM

2H O 2 4

aqNa SO

If a pressure of 2 atm is applied on solution, find what will happen.

(A) Reverse osmosis takes place (B) Osmosis takes place (C) Na2SO4 will move from solution to solvent side (D) Nothing will happen




2alkali Metal

2

2

M N A

A H O B C

C CaOCl D E F

o1100 C2

burn2

2 lower mol.wt as compare to C

D CaC C HH O One compound gas is proudced

C+H O I J

32. Which is true for ‘J’?

(A) H is metal oxide (B) H gives Nesseler’s test (C) Salt of H with strong base undergoes anionic hydrolysis to give alkaline solution (D) H can be obtained by treating D with H2O




14

33. Which of the following statements is correct? (A) M is Na Metal (B) C can be obtained by strong heating of 4 2 72

NH Cr O (C) The gas produced by combustion of H is also produced by heating compound ‘I’ (D) Gas D can not be obtained by heating NH4NO3

SECTION – C

(Single digit integer type)

This section contains 10 questions. The answer to each question is a Single Digit Integer ranging from 0 to 9, both inclusive. 34. Compound (A) gives positive Lucas test in 5 min. when 6.0 gm of (A) is reacted with Na metal,

1120 mL of 2H is evolved at STP. Assuming A to contain one oxygen per molecule, the number of carbon atom per molecule in (A) will be_____.

35. How many of following will give same 1 2& products ( )SN SN excluding stereo isomers ?

Cl

Cl

ClPh CH

CH3

CH

Cl

CH3

36. Calculate the pH at which an acid indicator with 51 10ka changes color when indicator

concentration is 31 10 M . 37. 100 mL of hydrocarbon is mixed with excess of oxygen and exploded. Our cooling the mixture

was reported to have contraction of 250 mL the remaining gas when passed through a solution of eq. KOH, The mixture shows a further contraction of 300 mL. Find the number of carbon atoms per molecule of hydrocarbon.

38. The critical temperature and pressure CO2 gas are 304.2 k and 72.9 atm respectively. If the

radius of CO2 molecules is 1.62 × 10–xcm. Assuming it to behave as Vander Waal’s gas find x. 39. 30 mL of a solution containing 9.15 gm/lt of an oxalate KxHy(C2O4)z.nH2O are required for titrating

27 mL of 0.12 N NaOH and 36 ml of 0.12 M KMnO4 separately x + y + z is______.




15

40. A 2.18 gm sample contain a mixture of XO and X2O3. If reacts with 0.015 moles of K2Cr2O7 to oxidize the sample completely to form 4XO and 3Cr . If 0.0187 moles of 4XO is formed; the atomic mass of x was found to by approx. 2a 10 . Calculate a.

41. If Ma3b3 has x pairs of enantiomers, M(AA)3 has y pairs of enantiomers & 2 2 2Ma b c has z pairs of enantiomers Find the value of x + y + z. (a,b & c are monodentate & AA is symmetrical bidentate ligand) 42. In how many of the following reactions black ppt is produced?

(i) 2 2Ag O H S (v)

4 2aq

CuSO H S

(ii) 2Ag H S (vi)

4 2aq

CdSO H S

(iii) 22

aqHg H S (vii)

3AgNO dil. HCl

(iv) 2 2

aqPbCl H S (viii) 3

4 4Fe NH Cl NH OH

43. Which of the following species can be oxidized by O3? 2 2 4 2 2 4HF,HCl,PbS,As in water ,I ,K MnO ,Hg,SO ,KI,K SO




16


This section contains 3 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded‐off to the second decimal place; e.g. xxxxx.xx). 44. If a sample of 2 – bromopentane shows specific rotation of + 30o & specific rotation of optically

pure 2 – bromobentane in the 40o, find % of (d) 2 – bromopentane in the given sample. 45. If Cu atoms form fcc (ABC ABC…………..) and nearest distance between two ‘A’ layer is 8 6 nm

then find the radius of atoms (in nm) that exactly fits into the octahedral void (do not round off) 46. How many of the following reactions will release a gas as any product (at 25oC)?

(i) 4NH OH (vi) electric spark

3 2PH NO (ii)

2Al NaOH H O (vii) 3 2NH CaOCl

(iii) 3Al OH NaOH (viii)

2 2SOCl H O (iv) Ba cold water (ix)

2 3SnCl HCl O (v) 4 2 72

NH Cr O




17

Mathematics PART – III


This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

47. 1 n n 1Let a 1; and a n a 1 for n = 2, 3,.......... define n1 2 n

1 1 1P 1 1 ........... 1a a a

nnThen lim P is

(A) 1 + e (B) e (C) 1 (D)

48. If the roots of the equation 4 3 2x ax bx cx d 0 are in geometric progression, then (A) 2b ac (B) 2a b (C) 2 2 2a b c (D) 2 2c a d

49. 11/x

1/ x1

3f ' x then f ' x dx1 3

and

1

1

xf " x dx

(A) 1, 1/ 2 (B) 1/ 2, 0

(C) 1, 12

(D) 1/ 2, 1


This section contains 5 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are) correct. 50. If a tangent on ellipse at A (1, 1) intersect its directrix at B (7, –6) and S be the focus of ellipse

and C , is the centre of SAB , then (A) 1 (B) 7 (C) 2SC 20.5 (D) 2SC 21.25




18

51. If curve A z :| z 3 | | z 3 | 8 & B z :| z 3 | K , K R touches the curve ‘A’

internally, and given another curve C z : | z 3 | | z 3 | 4 , then; (A) A & C intersect orthogonally & k = 1 (B) K = 1 (C) K = 3/2 (D) B touches also C internally

52. If 3 2 33 0f x x f x x , then f x

dxx is equal to

(A) f x c (B) f x c

(C) 2 f x c (D) 'xf x c

53. If 0

2A

and 2det 2 2 144A A , then possible correct statement is (for real part)

(A) tr 6A (B) det 9A

(C) det 4A (D) tr 1A 54. If ˆ ˆ ˆu x xi sinx j 1 sin x k

, ˆ ˆ ˆv x i cosx j k

and ˆ ˆw x sinx j k

, all are linearly

dependent vectors for x , then 2

can be equal to

(A) 101 (B) 1001 (C) 2012 (D) 2011




19




If f(x) & g (x) are two real valued functions such that

2

2

8 for x 1 33f ' xf(sinx) f(cos x) 2x and F x = & g(x) F(x)2 4

0 for x 1.

55. The range of f x is

(A) 3, 2

(B) 3 , 2

(C) 3 , 2 2

(D) none of these

56. The only one solution of sin2 4xf x

for

32 2

x is . Then

(A) 1 (B) 1 (C) 1 (D) 1

SECTION – C

(Single digit integer type)

This section contains 10 questions. The answer to each question is a Single Digit Integer ranging from 0 to 9, both inclusive. 57. If 2 2x y 16 is director circle of locus of centre of a moving ellipse touches both the axes in first

quadrant, then if major axis and minor axis are not fixed, then maximum value of product of semi-major and semi-minor axis is




20

58. If i 1

xf xi 1 x 1 ix 1

, then 1f 2017 f

2017

is equal to

59. If 1 2 1 2 1 2cos 2 x sin 2 x tan x3

have no solution if x or x for , then

21 min ..........max

60. If

2 33 2

1 2

3 53 and ln 1 ln 2

xx xI dx J dxx x

, then I Je equals ………..

61. Position vector of a point A is ˆˆ ˆai bj ck and 2 2 2 4a b c ; and position vector of

another point B is ˆˆ ˆpi qj rk and 2 2 2 9p q r . Given 1 12cos5

AOB , where O is

origin. If AQ is perpendicular to angle bisector of AOB i.e. line OQD where D lies on AB, then value of 25 QD = ?

62. If 2

4 2

3 1

x f xx x

, where f x is a constant function in 0 2x , then minimum value of

22

4 20

3 1x dx

x x

is ………

63. If AB BA I such that

2 2ijA a

, 2 2ijB b

, ii iia b , 12 12a b , 21 21a b and ija

are co prime natural numbers, then 21 12a a ……….




21

64. If f ' x 0 x R where f : R R and 11 1f x f

x f x

and

1 1f 0f x

then

1sin f 2

is equal to

65. If rS is sum of infinite G.P. 3r , where first term is

21 !

rr

and common ratio

11r

, then

2011

2

3

20111 4 22009 !

r

rr

r r S

is equal to …………

66. If 2

3x 0

atan x bsin x cx x 3lim2x

then, a b c is equal to ________ . (where [.] denotes

greatest integer part)


This section contains 3 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded‐off to the second decimal place; e.g. xxxxx.xx).

67. The length of focal chord AB of ellipse 2 2x y 1

4 3 is: 8 3 3Given A ,

5 5

68. How many matrices X with entries {0, 1, 2} are there for which sum of diagonal entries of TX.X is

7? 69. If 2 2

3x 4 2x 1log 4x x 1 log 6x 11x 4 then x is ________.


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