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FIITJEE PET – X (REG_2ND YEAR) MAINS

DATE: 19.08.2017 Time: 3 hours Maximum Marks: 360 INSTRUCTIONS:

Instructions to the Candidates 1. This Test Booklet consists of 90 questions.

Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.

2. For each correct answer 4 Marks will awarded and for each wrong answer 1 Mark will be deducted.

3. Attempt all questions.

4. In case you have not darkened any bubble you will be awarded 0 mark for that question.

5. Use of calculator/logarithmic table is not permitted. Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:



PET-X (2ND YEAR)-SET-A-2018-MPC-2

1. / 2

0

x dx

sinx cos x

=

(A) log 2 12 2

(B) log 2 1

2 2

(C) log 2 1

2

(D) none of these

2.

2

2x 1 sinx

1 cos x

dx is

(A) 2

4

(B) 2 (C) zero (D)

2

3. 0

x tanxdx

sec x tanx

(A) 2

2

(B)

2

2

(C)

2

2

(D)

2

2

4. The value of 1

20

8log 1 xdx

1 x

is

(A) log22

(B) log 2 (C) log 2 (D) log2

8

5. 1 1

20

x sin xdx

1 x

(A) 0 (B) 1 (C) 1

2 (D) 2

6. / 2

0

log sinx dx

(A) log 2 (B) – log 2 (C) log22

(D) log2

2

Space for rough work




7. 1 1

0

sin xdx

x

=

(A) log 2 (B) – log 2 (C) log22

(D) log2

2

8. If I = 1

1

0

1 xcos 2cot

1 x

dx, then

(A) I > 1

2 (B) I =

1

2 (C) I <

1

2 (D) I =

1

2

9. If f(x) = x

x

e

1 e, I1 =

f (a)

f ( a)

xg x 1 x

dx and I2 = f (a)

f ( a)

g x 1 x

dx, then the value of 2

1

I

I is

(A) 2 (B) 1 (C) –1 (D) –3

10. 1

27 x

1

x cosx e

dx =

(A) 1

2ee

(B) 1

ee

(C) 1

ee

(D) 1

e

11. 2

0

xcos dx

2

(A) 1

(B)

2

(C)

3

(D)

4

12. / 4

0

1 sin2xdx

1 sin2x

(A) 1

log22

(B) 1

log22

(C) log 2 (D) –log 2





13. /3

0

tanx 1 dx

(A) 1

log24 2

(B)

6

(C)

3

(D)

1log2

6 2

14. / 2

10

0

cos x dx

(A) 63

510

(B)

63

512

(C)

36

512

(D)

63

500

15. / 2

8 2

0

sin xcos x dx

(A) 512

(B)

3

512

(C)

5

512

(D)

7

512

16. / 2

0

1dx

4 5cosx

(A) 1

log25

(B) 1

log22

(C) 1

log33

(D) 1

log23

17. / 2

2 20

1dx

4cos x 9sin x

(A) 12

(B)

10

(C)

5

(D)

2

18. The value of the integral, 6

3

xdx

9 x x is

(A) 2 (B) 1 (C) 1

2 (D)

3

2





19. 2

20

2x 2dx

2x x

(A) 0 (B) 2 (C) 3 (D) 4

20. / 2

3 2

3 / 2

x cos x 3 dx

=

(A) 2

(B) 1

4

(C) 4

32

(D)

2

32 2

21. If [x] denotes the greatest integer function, then the value of 4 5 1

0 5 1

x dx x dx

is

(A) 9 (B) 8 (C) 7 (D) 6

22. The value of 4

2x 1

0

3 dx is

(A) 6 4

13log3 log3

(B)

66

log3 (C)

6 513

log3 log3

(D) none of these

23. The integral 1/ 2

1/ 2

1 xx log dx

1 x

(A) 1

2 (B) 0 (C) 1 (D)

12log

2

24. / 6

4 2

0

cos 3 sin 6 d

(A) 5

192 (B)

5

256

(C)

5

192

(D)

96





25. The value of the integral I = 2

3 21

x 2

x x 1

dx is

(A) 0 (B) 2

3 (C)

4

3 (D) none of these

26. 3

2

xdx

5 x x

(A) 1

2 (B)

3

2 (C)

5

2 (D) 0

27. 2cos2x sin3x dx

(A) – (B) 0 (C) (D) 2

28. / 2

/ 2

2 sinlog d

2 sin

(A) 0 (B) 1 (C) 2 (D) –1

29. If [x] stands for the greatest integer function, then 28

2 22

x dx

x 20x 100 x

=

(A) 0 (B) 10 (C) 3 (D) 12

30.

2

1

e

e

logxdx

x

(A) 3

2 (B)

5

2 (C) 3 (D) 5





31. A uniform magnetic field B and a uniform electric field E act in a common region. An electron is

entering this region of space. The correct arrangement for its to escape undeviated is

(A) (B)

(C) (D)

32. A proton accelerated by a potential difference 500 kV moves

through a transverse magnetic field of 0.51 T as shown in fig. The angle through which the proton deviates from the initial direction of its motion is

(A) 015 (B) 030 (C) 045 (D) 060

33. An electron moving with a speed u along the positive x–axis

at y=0 enters a region of uniform magnetic field 0ˆB B k

which exists to the right of y –axis. The electron exits from the region after some time with the speed v at co–ordinate y, then

(A) v u,y 0 (B) v u,y 0

(C) v u,y 0 (D) v u,y 0





34. A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively . When a current I passes through the coil, the magnetic field at the centre is

(A) 0NI

b

(B) 02 NI

a

(C)

0NI b

In2 b a a

(D)

0IN bIn

2 b a a

35. A non – planar loop of conducting wire carrying a current I

is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic filed due to this loop at the point P (a,0,a) points in the direction

(A) 1 ˆ ˆj k2

(B) 1 ˆ ˆ ˆj k i3

(C) 1 ˆ ˆ î j k3

(D) 1 ˆ î k2

36. A long straight wire along the z–axis carries a current I in the negative z direction. The magnetic

vector field B

at a point having coordinates (x,y) in the z=0 plane is

(A)

0

2 2

ˆ Î yi xj

2 x y

(B)

0

2 2

ˆ Î xi yj

2 x y

(C)

0

2 2

ˆ Î xj yi

2 x y

(D)

0

2 2

ˆ Î xi yj

2 x y

37. A particle of charge +q and mass m moving under the

influence of a uniform electric field Êi and a uniform

magnetic field ˆBk follows trajectory from P to Q as shown in

figure. The velocities at P and Q are ˆv i and ˆ2vj

respectively. Which of the following statements (s) is / are correct

(A) 23 mv

E4 qa

(B) Rate of work done by electric field at P is 33 mv

4 a

(C) Rate of work done by both the fields at Q is zero (D) All





38. A thin circular wire carrying a current I has a magnetic moment M. the shape of wire is changed to a

square and it carries the same current. It will have a magnetic moment

(A) M (B) 2

4M

(C)

4M

(D) M

4

39. A particle of charge q and mass m moves in a circular orbit of radius r with angular speed . The

ratio of the magnitude of its magnetic moment to that of its angular momentum depends on (A) and q (B) q and m (C) q and m (D) and m

40. Figure shows a square loop ABCD with edge length a. The

resistance of the wire ABC is r and that of ADC is 2r. The value of magnetic field at the centre of the loop assuming uniform wire is

(A) 02 i

3 a

(B) 02 i

3 a

(C) 02 i

a

(D) 02 i

a

41. A long wire AB is placed on a table. Another wire PQ of

mass 1.0 g and length 50 cm is set to slide on two rails PS and QR. A current of 50 A is passed through the wires. At what distance above AB, will the wire PQ be in equilibrium

(A) 25 mm (B) 50 mm (C) 75 mm (D) 100 mm

S R

p Q

B A 50A

42. In the given figure net magnetic field at O will be

(A) 202 i4

3 a

(B) 20i 4

3 a

(C) 202

2 i4

3 a

(D) 202 i

43 a

43. In the following figure a wire bent in the form of a regular

polygon of n sides is inscribed in a circle of radius a. net magnetic field at centre will be

(A) 0i tan2 a n

(B) 0nitan

2 a n

(C) 0

2 nitan

a n

(D) 0

nitan

2a n





44. A proton and an particle enter a uniform magnetic field moving with the same speed. If the proton

takes 25s to make 5 revolutions, then the periodic time for the particle would be

(A) 50 s (B) 25 s (C) 10 s (D) 5 s

45. An electron is launched with velocity v

in a uniform magnetic field B

. The angle between v

and B

lies between 0 and / 2 . Its velocity vector v

returns to its initial value in a time interval of

(A) 2 m

eB

(B) 2 2 m

eB

(C) m

eB

(D) depends upon angle between v

and B

46. A rectangular coil of wire of 100 turns and 10 15 cm2 size carrying a current of 2 Amp is in magnetic field of induction 2 103 wb/m2. If the normal drawn to the plane of the coil makes an angle 300 with the field, then the torque on the coil is

(A) 53 10 N m (B) 33 10 N m (C) 53 3 10 N m (D) 33 3 10 N m

47. In a moving coil galvanometer, a coil of area 2.2 104 m2 having 100 turns is suspended freely in a

magnetic field of 0.5 TA deflection of 70 is produced when current of 1mA flows through the coil. The couple per unit twist is

(A) 9 108 N-m/rad (B) 9 105 N-m/rad (C) 9 103 N-m/rad (D) 9 106 N-m/rad

48. A soft iron cylinder is arranged at the center of the gap between the magnetic poles to make the magnetic field

(A) perfectly radial and strong (B) radial but weak (C) non-radial and strong (D) non-radial and weak 49. The restoring couple for the coil of galvanometer [suspension coil type] is provided by (A) the magnetic field (B) material of the coil (C) twist produced in the suspension (D) current in the coil





50. A current carrying square loop (made of uniform wire) is placed near an

infinitely long current carrying wire as shown in figure. The torque acting on the loop is

(A) 0 1 2i i a

2 2

(B) 0 1 2i i a

2

(C) 0 1 2i i aln(2)

2

(D) zero

i1 i2

a a

a

51. Current density in a conductor of radius R is J. The magnetic field at a distance ( )r R< from the axis

of the wire is

(A) zero (B) 02m JR

(C) 02Jrm

(D) 0 Jrm

52. A long straight wire of radius R carries current i . The magnetic field inside the wire at distance r from

its centre is expressed as;

(A) 02

.i

rR

(B) 02

2.

ir

R

(C) 02

.2

ir

R

(D) 02

.2

ir

R

53. A current I flows along an infinitely long straight thin walled tube. The magnetic induction at a point inside the tube at a distance r from its wall is

(A) infinite (B) zero (C) 0 2I

4 r

(D) 2I

r

54. A long solenoid has 800 turns per unit length. A current of 1.6A flows through it. The magnetic

induction at the end of the solenoid on its axis is

(A) 416 10 T-´ (B) 48 10 T-´ (C) 432 10 T-´ (D) 44 10 T-´ 55. Three infinitely long wires are placed equally apart on the circumference of a circle of radius a,

perpendicular to its plane. Two of the wires carry current I each, in the same direction, while the third carries current 2I along the direction opposite to the other two. The magnitude of the magnitude of

the magnetic induction B

at a distance r from the centre of the circle, for r a , is

(A) 0 (B) 02 I

r

(C) 02 I

r

(D) 0

2

2 Ia

r





56. The magnetic field at the mid-point along the length of a solenoid is 0B . If the solenoid is stretched to

double its length and current through the coil is also doubled. Then the new magnetic field at the new mid point is close to

(A) 0B (B) 0

2

B (C) 02B (D) 04B

57. Ratio of magnetic field induction at the centre of a current carrying coil of radius ‘r’ and at a distance ‘3r’ on its axis is

(A) 10 (B) 2 10 (C) 10 10 (D) 20 10 58. A coil with n turns can create a field of B at it’s centre. The coil is rewound into 2n turns and same

current is made to pass. Find the field at its centre now (A) B (B) 2B (C) 3B (D) 4B 59. A wire is bent into a circular loop of radius R and carries a current I. The magnetic field at the centre

of the loop is B. The same wire is now bent into a double loop. If both loops carry the same current I in the same direction, the magnetic field at the centre of the double loop will be

(A) zero (B) 2 B (C) 4 B (D) 8 B

60. Current of 10 ampere and 2 ampere are passed through two parallel wires A and B respectively in opposite directions. If the wire A is infinitely long and the length of the wire B is 2 m, the force on the conductor B which is situated at 10 cm distances from A will be

(A) 8 10-5 N (B) 4 10-5 N (C) 8 10-7 N (D) 4 10-7 N 61. Regarding aniline, the incorrect statement among the following is (A) in the formation of anilinium salts, aniline acts as Lewis base (B) 93 grams of aniline can react with a maximum of three moles of methyl iodide (C) aniline is more basic than ammonia (D) impure aniline is purified by steam distillation 62. By passing the mixture of the vapours of alcohol and excess of ammon Ia over heated alumina at

350°C, the main product obtained is: (A) primary amine (B) secondary amine (C) tertiary amine (D) a mixture of pri., sec. and tert. amines 63. The best method for the preparation of primary amines is

(A) R–X 3NH R–NH2 (B) R–X 3

4

(i)NaN

(ii)LiAlH R–NH2

(C) R–OH 3

2 3

NH

Al O /R–NH2 (D) R–X 2NaNH R–NH2





64. The total number of organic products formed at the end of the reaction sequence is / are

C6H5-CO-CH3 2NH OH 2 5P O 2H O / OH

(A) 1 (B) 2 (C) 3 (D) 4 65.

NK

CO

CO

t BuCl A 2H O /H

B. The final product is

(A) 1, 3-butadiene (B) t-Bu-NH2 (C) isobutene (D) isobutanol 66. O

(CH)2CN

2H ,Pd

A. A is

(A)

(CH2)3 NH2

(B)

NH

(C)

O

(CH2)3 NH2 (D)

(CH2)2 CN

67. H5C2

CH3

H

NH2

O

(+) 2-methyl butanamide

Br2/KOH

Identify the correct statement regarding product. (A) It is optically active with opposite configuration (B) It is optically active with same configuration (C) A racemic mixture is formed (D) It does not show optical isomerism 68. Which one of the following amines will not liberate nitrogen on reaction with nitrous acid? (A) 3 2CH NH (B) 3 2 2CH CH NH (C) 3 22

CH CNH (D) 3 3CH N

69. The more active reagent for the acetylation of aniline is (A) ethyl ethanoate (B) ethanoyl ethanoate (C) ethanal (D) ethanoyl chloride 70. Which reagent is used to distinguish between 2 5 2

C H NH and 2 5 3C H N?

(A) NaOH (B) Dil.HCl (C) 6 5 2C H SO Cl (D) 4KMnO





71.

NH

O

O

I) KOH

II)

III)

Br

hydrolysis

?

(A) NH2 (B) NH2

(C) NH (D) Any of the above

72. The basic character of methylamines in vapour phase is : (A) 3 > 2 > 1 > NH3 (B) 2 > 3 > 1 > NH3 (C) 1 > 2 > 3 > NH3 (D) none of these 73. Which of the following is not formed in the reaction?

CH3NH2

NaNO2 / HCl?

(A)

CH3

OH

(B)

OH

CH3

(C)

CH3

(D) CH3

OH

CH3

74. Which of the following compounds exists as a nonresolvable racemic mixture ?

(A) NH2 (B) NH (C)

NH2 (D) NH

75. Consider the following sequence of reactions.

2H ,NiAgCN2 5C H Br A B

The final product (B) is (A) CH3CH2CH2NH2 (B) CH3CH2NHCH3 (C) (CH3CH2)2NH (D) CH3CH2NH2 76. A compound (X) having the molecular formula C3H9N reacts with benzenesulphonyl chloride to form a

solid that is insoluble in alkalis. The compound (X) is (A) CH3CH2CH2NH2 (B) (CH3)2CHNH2 (C) CH3CH2NHCH3 (D) (CH3)3N





77. An organic compound (A) on reduction gives a compound (B) which on reaction with CHCl3 and KOH forms (C). The compound (C) on catalytic reduction gives N–methylaniline. The compound (A) is

(A) nitrobenzene (B) benzonitrile (C) benzamide (D) aniline 78. Identify ‘Z’ in the sequence :

2 2NaNO HCl H / H OCuCN6 5 2 273 K Boil

C H NH X Y Z

(A) C6H5CN (B) C6H5CONH2 (C) C6H5COOH (D) C6H5CH2NH2 79. The following sequence of reactions on A gives

CH2CONH2

COOCH3

1. Br2/NaOH

2. Heat

(A) O

O

O

(B) NH

O

O

(C) NH

O

(D)

O

O 80. The end product of the reaction sequence

43

2

i LiAlHCHCl ,KOH6 5 2 ii H O

C H NH A B is

(A) C6H5NHCH3 (B) C6H5CH2NH2 (C) C6H5NHCHO (D) C6H5NC 81. Me

N+

BuEt

Me

n

HO

The alkene formed as a major product in the above elimination reaction is

(A) Me

(B) CH2 = CH2 (C)

Me

(D)

Me





82. Identify Z in the sequence

CH3COONH4 2 5 2P O H O / HX Y Z

(A) CH3CH2CONH2 (B) CH3CN (C) CH3COOH (D) (CH3CO)2O 83. Given the following sequence of reaction,

2Br /NaOHNaCN OH3 2 Partial

hydrolysis

CH CH I A B C

The major product C is (A) CH3CH2NH2 (B) CH3CH2CONHBr (C) CH3CH2COONH4 (D) CH3CH2CONBr2 84. A compound with molecular mass 180 is acylated with CH3COCl to get a compound with molecular

mass 390. The number of amino groups present per molecule of the former compound is : (A) 5 (B) 4 (C) 6 (D) 2 85. The major product of the following reaction is

C

NH

C

O

O

CH2ClBr(ii)

(i) KOH

(A)

C

N

C

O

O

CH2 Br (B)

C

N

C

O

O

CH2Cl

(C)

C

N

C

O

O CH2 Br

(D)

C

N

O

O CH2Cl





86.

In the reaction CCH3

NH2

O

Cl

O

( 1) NaOH/Br2

( 2)

T

the structure of the product T is

(A)

CCH3

O

O

C

O

(B) NH

C

O

CH3

(C) NH

C

O

CH3

(D)

CCH3

NH

O

C

O

87. CH3 – NH2 + CHCl3 Alc.KOH KCl + H2O + N containing compound. Find N containing compound.

(A) CH3 – CN (B) CH3 – N C (C) CH3 – N C

(D) CH3 - NHCl





88.

N

H

CH3I (excess)

Ag2O/Products.

One of the product is (A) 1, 3 diene (B) 1, 4 diene (C) Alkyne (D) 1, 2 diene

89. NBS CN LAH

2 3H C CH CH A B C

. ‘C’ is

(A) H2C=CH–CH2–CH2–NH2 (B) H2C=CH–CH2–NH2 (C) H3C–CH2–CH2–CH2–NH2 (D) H3c–CH2–CH2–NH2 90. The product which is not formed in the reaction below.

NH2

NaNO2

dil. HCl, is

0°C

(A) OH

(B) CH3

OH

(C)

OH

(D)

CH3

OH





FIITJEE PET – X (REG_2ND YEAR) MAINS_SET–A_ANSWERS

DATE: 19.08.2017

MATHEMATICS

1. B 2. B 3. B 4. C

5. B 6. C 7. D 8. B

9. A 10. C 11. D 12. A

13. B 14. B 15. D 16. D

17. A 18. D 19. A 20. A

21. A 22. D 23. A 24. C

25. A 26. A 27. D 28. A

29. C 30. B

PHYSICS

31. C 32. B 33. D 34. C

35. D 36. A 37. D 38. D

39. C 40. B 41. A 42. B

43. B 44. C 45. A 46. B

47. B 48. A 49. C 50. D

51. C 52. C 53. B 54. B

55. A 56. A 57. A 58. D

59. C 60. A

CHEMISTRY

61. C 62. A 63. B 64. D

65. BONUS 66. BONUS 67. B 68. D

69. D 70. C 71. A 72. A

73. A 74. D 75. B 76. C

77. A 78. C 79. C 80. A

81. B 82. C 83. A 84. A

85. A 86. C 87. B 88. A

89. A 90. D




FIITJEE PET – X (REG_2ND YEAR)

MAINS_SET–B_ANSWERS DATE: 19.08.2017

MATHEMATICS

1. D 2. A 3. D 4. A

5. A 6. A 7. D 8. A

9. C 10. A 11. A 12. D

13. A 14. C 15. B 16. B

17. B 18. B 19. C 20. B

21. C 22. D 23. B 24. A

25. C 26. D 27. A 28. B

29. B 30. D

PHYSICS

31. B 32. B 33. A 34. C

35. D 36. C 37. C 38. B

39. B 40. A 41. A 42. A

43. D 44. C 45. A 46. C

47. B 48. D 49. C 50. D

51. A 52. D 53. D 54. C

55. B 56. A 57. B 58. B

59. C 60. A

CHEMISTRY

61. C 62. A 63. C 64. C

65. A 66. B 67. C 68. A

69. A 70. A 71. C 72. B

73. A 74. A 75. D 76. C

77. A 78. B 79. D 80. BONUS

81. BONUS 82. B 83. D 84. D

85. C 86. A 87. A 88. A

89. D 90. B

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