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FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
FIITJEE PET – XVI (REG_1ST YEAR) MAINS_SET–A
DATE: 09.12.2017 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.:
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
PET-XVI (1ST
YEAR)-2019-MPC-2
31. Two equal and unlike parallel forces each of magnitude 5 N act on a wheel of diameter 20 cm, as shown in the figure. Find the couple acting on the wheel.
(A) 10 Nm (B) 1.0 Nm (C) 0.5 Nm (D) 2 Nm
5F N
5F N 32. A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of 53° with it.
The other end rests on a rough horizontal floor. The normal force that floor exerts on the ladder is (A) 55 (B) 65 N (C) 98 N (D) none of these 33. A flywheel gains a speed of 540 rpm in 6 sec. Its angular acceleration will be
(A) 3 rad/sec2 (B) 18 rad/sec
2 (C) 54 rad/sec
2 (D) 9 rad/sec
2
34. A point mass is whirled in a circular path with a constant angular velocity and its angular momentum
is L. If the string is now halved keeping the angular velocity same, the angular momentum is: (A) L/4 (B) L (C) 2L (D) L/2 35. A uniform solid cylinder of mass M and radius R rolls down without slipping an inclined plane of height
h. The angular velocity of the cylinder when it reaches the bottom of the plane will be
(A)2
ghR
(B)2 gh
R 2 (C)
2 gh
R 3 (D)
1gh
2R
36. Suppose a body of mass M and radius R is allowed to roll on an inclined plane without slipping from its topmost point A. The velocity acquired by the body, as it reaches the bottom of the inclined plane, is given by:
(A) 2gh (B) 2gh (C)2gh
(D)
2gh
where β= 1 + 2
I
MR (I is the moment of inertia of the body about its axis of rotation).
37. A solid sphere and a solid cylinder of same mass are rolled down on two Inclined planes of heights h1
and h2 respectively. If at the bottom of the plane the two objects have same linear velocities, then the ratio of h1 : h2 is:
(A) 2 : 3 (B) 7 : 5 (C) 14 : 15 (D) 15 : 14 38. A solid cylinder of mass m = 4 kg and radius R = 10cm has two
ropes wrapped around it, one near each end. The cylinder is held horizontally by fixing the two free ends of the cords to the hooks on the ceiling such that both the cords are exactly vertical. The cylinder is released to fall under gravity. Find the linear acceleration of the cylinder.
(A) g
3 (B)
2g
3 (C)
4g
3 (D) none of these
39. Particle of mass m is projected with a velocity v0 making an angle of 45
0 with horizontal. The
magnitude of angular momentum of the projectile about the point of projection at its maximum height is
(A) Zero (B) g2mv3 (C) g24mv20
(D) 32ghm
40. A string is wrapped several times round a solid cylinder and then the end of the string is held
stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be
(A) 3
mgand
3
2g (B)
2
mgandg (C)
23
mgand
g (D)
32
mgand
g
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
PET-XVI (1ST
YEAR)-2019-MPC-3
41. A circular ring of mass M and radius R is rotating about its axis with constant angular velocity . Two objects each of mass m get attached to the rotating ring. The ring now rotates with an angular velocity
(A) mM
M
2
(B)
2mM
m
(C)
2mM
2m)M
(D)
m
2mM
42 A rod of mass m and length fits into a hollow tube of same
length and mass. The tube is rotated with an initial angular
velocity 0 and the rod slips through the rough hollow surface. The angular velocity of the rod as it slips out of the tube is
A
B
0
(A) 2
0 (B)
4
0 (C)
16
0 (D)
7
0
43 A uniform rod of length and mass M is suspended on two
vertical inextensible strings as shown in the figure. Calculate tension T in left string at the instant, when right string snaps.
(A) mg
2 (B) mg (C)
mg
4 (D)
mg
8
44 A uniform circular disc of radius r is placed on a rough horizontal surface
and given a linear velocity v0 and angular velocity 0 as shown. The disc comes to rest after moving some distance to the right. It follows that
v0
0
P
(A) 3 v0 = 20 r (B) 2 v0 = 0 r (C) v0 = 0 r (D) 2 v0 = 3 0 r
45. A disc is freely rotating with an angular speed on a smooth horizontal plane. It is hooked at a rigid peg P & rotates about P without bouncing. Its angular speed after the impact will be equal to.
P
(A) (B)3
(C)
2
(D) none of these
46. The moment of inertia of a uniform cylinder of length and radius R about its perpendicular bisector
is I. What is the ratio /R such that the moment of inertia is minimum ?
(A) 3
2 (B)
3
2 (C)
3
2 (D) 1
47. A slender uniform rod of mass M and length is pivoted at one
end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle with the vertical is .
(A) 2g
cos3
(B) 3g
sin2
(C) 2g
sin3
(D) 3g
cos2
Z
X
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
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PET-XVI (1ST
YEAR)-2019-MPC-4
48. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CE which are placed asymmetrically (see fig), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see fig). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to
(A) turn right (B) go straight (C) turn left and right alternately (D) turn left
O
B
A C
D
49. A particle of mass m is moving along the side of a square of
side ‘a’ with a uniform speed v in the x–y plane as shown in the figure:
Which of the following statements is false for the angular
momentum L about the origin ?
(A) R ˆL mv a k2
when the particle is moving
from C to D
(B) R ˆL mv a k2
when the particle is moving
from B to C
(C) 3mv ˆL Rk
2 when the particle is moving from D to A
(D) mv ˆL Rk
2 when the particle is moving from A to B
y
O x
R
450
a C D
a a
a
A B
v v
v
v
50. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of
inertia of cube about an axis passing through its centre and perpendicular to one of its faces is
(A) 2MR
16 2 (B)
24MR
9 3 (C)
24MR
3 3 (D)
2MR
32 2
51. The following four gases are at the same temperature. In which gas do the molecules have the
maximum root mean square speed ? (A) Hydrogen (B) Oxygen (C) Nitrogen (D) Carbon dioxide 52. Which of the following is correct for the molecules of a gas in equilibrium temperature ? (A) All have the same speed (B) Molecules have different speed distribution of which average remain constant (C) They have a certain constant average speed (D) They do not collide with one another 53. P–T diagram is shown below then choose the corresponding V–T
diagram
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
PET-XVI (1ST
YEAR)-2019-MPC-5
(A) (B)
(C) (D)
54. 0E and hE respectively represent the average kinetic energy of a molecule of oxygen and hydrogen.
If the two gases are at the same temperature, which of the following statements is true
(A) 0 hE E (B)
0 hE E
(C) 0 hE E
(D) Nothing can be said about the magnitude of 0E and
hE as the information given is insufficient
55. When an ideal gas is compressed isothermally then its pressure increase because (A) It potential energy increases (B) Its kinetic energy increase and molecules move apart (C) Its number of collisions per unit area with walls of container increases (D) Molecular energy increases 56. If k is the Boltzmann constant, the average translational kinetic energy of a gas molecules at absolute
temperature T is (A) k T / 2 (B) 3 k T/4 (C) k T (D) 3 k T/2 57. The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room temperature
the rms speed of oxygen molecules is v. The rms speed of the hydrogen molecule at the same temperature will be
(A) v/16 (B) v/4 (C) 4v (D) 16 v 58. The average kinetic energy of hydrogen molecules at 300 K is E. At the same temperature, the
average kinetic energy of oxygen molecules will be (A) E/16 (B) E/4 (C) E (D) 4 E 59. Same volumes of hydrogen and oxygen at the same temperature and pressure are mixed together so
that the volume of the mixture is same as the initial volume of the either gas. if the initial pressure be p, then the pressure of the mixture will be
(A) 4 p (B) 2p (C) p/2 (D) p/4
60. 32m of hydrogen and 32m of oxygen are at the same temperature. If the pressure of hydrogen be p, then that of oxygen will be
(A) 2 p (B) 4p (C) 8 p (D) 1 p
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
PET-XVI (1ST
YEAR)-2019-MPC-6
FIITJEE PET – XVI (REG_1ST YEAR)
MAINS_SET–A_ANSWERS DATE: 09.12.2017
MATHEMATICS
1. C 2. B 3. D 4. A
5. D 6. B 7. D 8. B
9. B 10. C 11. A 12. B
13. C 14. A 15. BONUS 16. B
17. C 18. D 19. C 20. C
21. C 22. B 23. B 24. B
25. D 26. C 27. B 28. D
29. B 30. B
PHYSICS
31. B 32. C 33. A 34. A
35. C 36. C 37. C 38. B
39. D 40. A 41. A 42. B
43. C 44. B 45. B 46. B
47. B 48. D 49. A & C 50. B
51. A 52. B 53. D 54. B
55. C 56. D 57. C 58. C
59. B 60. D
CHEMISTRY
61. A 62. C 63. A 64. D
65. C 66. B 67. B 68. A
69. BONUS 70. D 71. D 72. C
73. B OR D 74. A 75. A 76. B
77. BONUS 78. A 79. B 80. C
81. A 82. B 83. C 84. D
85. B 86. A 87. A 88. D
89. B 90. D
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
PET-XVI (1ST
YEAR)-2019-MPC-7
FIITJEE PET – XVI (REG_1ST YEAR) MAINS_SET–B
DATE: 09.12.2017 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.:
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
PET-XVI (1ST
YEAR)-2019-MPC-8
1. If f(x) = x 1
x 1
, then f(ax) in term of f(x) is equal to
(A) f(x) a
1 af(x)
(B)
a 1 f(x) a 1
a 1 f(x) a 1
(C)
a 1 f(x) a 1
a 1 f(x) a 1
(D) none of these
2. Let f(x) = 1 + |x|, x < –1
[x], x –1, (where [.] denotes the greatest integer function) Then f(f(–2.3)) is equal to (A) 4 (B) 3 (C) –3 (D) none of these 3. If (where [.] denotes the greatest integer function) then the domain of the real valued function
2
1x
2
log x x 2
is
(A) 3
,2
(B)
3,2 2,
2
(C)
1,2 2,
2
(D) none of these
4. Let f(x) = 2xlog 25 and g(x) = logx5, then f(x) = g(x) holds for x belonging to
(A) R (B) (0, 1) (1, +) (C) (D) none of these 5. Which of the following is an even function? Here [.] denotes the greatest integer function and f is any function. (A) [x] – x (B) f(x) – f(–x) (C) e
3 – 2x . tan
2x (D) f(x) + f(–x)
6. Let f(x) be a function whose domain is [–5, 7]. Let g(x) = |2x + 5|. Then the domain of (fog)(x) is (A) [–5, 1] (B) [–4, 0] (C) [–6, 1] (D) none of these
7. If the function f: [1, +) [1, +) is defined by f(x) = 2x(x – 1)
, then f–1
(x) is
(A)
x x 11
2
(B) 2
11 1 4log x
2 (C) 2
11 1 4log x
2 (D) not defined
8. The function f: R R defined by f(x) = 6x + 6
|x| is
(A) one-one and onto (B) many-one and onto (C) one-one and into (D) many-one and into 9. The range of the function y = log3(5 + 4x – x
2) is
(A) (0, 2] (B) (–, 2] (C) (0, 9] (D) none of these
10. The range of the function f(x) = |x – 1| + |x – 2|, –1 x 3, is (A) [1, 3] (B) [1, 5] (C) [3, 5] (D) none of these
Space for rough work
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
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PET-XVI (1ST
YEAR)-2019-MPC-9
11. Let f(1) = 1 and f(n) = n 1
r 1
2 f(r)
. Then m
n 1
f(n)
is equal to
(A) 3m – 1 (B) 3
m (C) 3
m – 1 (D) none of these
12. The largest set of real values of x for which f(x) = 2
1x 2 5 x
x 4
is a real function is
(A) [1, 2) (2, 5] (B) (2, 5] (C) [3, 4] (D) none of these
13. The domain of the function f(x) = 2x 1 x is
(A) 1 1
1, ,12 2
(B) [–1, 1]
(C) 1 1
, ,2 2
(D) 1
,12
14. Let f: X Y, f(x) = sin x + cos x + 2 2 is invertible, then X Y is
(A) 5
, 2,3 24 4
(B)
3, 2,3 2
4 4
(C) 3 3
, 2,3 24 4
(D)
3, 2,3 2
4 4
15. The domain of the function f(x) =
1
sinx sin x , (where {.} denotes the fractional part) is
(A) [0, ] (B) 2n 1
2
(C) (0, ) (D) none of these
16. The range of the function f defined by f(x) = 1
sin x
(where [.] and {.}, respectively, denotes the
greatest integer and the fractional part functions) is (A) I, the set of integers (B) N, the set of natural numbers (C) W, the set of whole numbers (D) {2, 3, 4, ......}
17. The domain of the function f(x) = 2
1
4x x 10x 9 is
(A) 7 40,7 40 (B) 0,7 40 (C) 7 40, (D) none of these
Space for rough work
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
FIITJEE Limited. Plot No. 39A, (Opp. Sashi Hospital), Gaddiannaram, Dilsukhnagar, Hyderabad, 5000036. Ph: 040–64569509.
PET-XVI (1ST
YEAR)-2019-MPC-10
18. The function f(x) =
1sec x
x x
, where [x] denotes the greatest integer less than or equal to x, is defined
for all x
(A) R (B) R – {(–1, 1) {n | n Z}}
(C) R+ – (0, 1) (D) R
+ – {n | n N}
19. If satisfies the inequation x2 – x – 2 > 0 then a value of exists for
(A) sin–1 (B) sec
–1 (C) cos
–1 (D) none of these
20. Let f(x) = sec
–1x + tan
–1x. Then f(x) is real for
(A) x [–1, 1] (B) x R (C) x (–, –1] [1, +) (D) none of these
21. The principal value of 1 1 3sin cos sin
2
is
(A) 6
(B)
3
(C)
3
(D) none of these
22. The domain of the function f(x) = log10log10(1 + x
3) is
(A) (–1, +) (B) (0, +) (C) [0, +) (D) (–1, 0)
23. If cos–1 + cos
–1 + cos
–1 = 3, then + + is equal to
(A) –3 (B) 0 (C) 3 (D) –1
24. The domain of the function f(x) = 11 x
sec2
is
(A) (–, –3] [3, +) (B) [3, +) (C) (D) R
25. Let f(x) = 2 2x xsin cos
2 2 and g(x) = sec
2x – tan
2x. The two functions are equal over the set
(A) (B) R (C) R x | x 2n 1 ,n z2
(D) none of these
26. If 10
1
ii 1
cos x 0
, then 10
ii 1
x
is
(A) 0 (B) 10 (C) 5 (D) none of these
Space for rough work
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
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PET-XVI (1ST
YEAR)-2019-MPC-11
27. Let f: {x, y, z} {a, b, c} be a one-one function and only one of the conditions
(i) f(x) b, (ii) f(y) = b, (iii) f(z) a is true, then the function f is given by the set (A) {(x, a), (y, b), (z, c)} (B) {(x, a), (y, c), (z, b)} (C) {(x, b), (y, a), (z, c)} (D) {(x, c), (y, b), (z, a)} 28. The domain of the real-valued function f(x) = loge|logex| is
(A) (1, +) (B) (0, +) (C) (e, +) (D) none of these
29. Let f(x) = sin (tan–1
x). Then f 3
, (where [.] denotes the greatest integer function) is
(A) 3
2 (B) 0 (C) –1 (D) none of these
30. If f(x) = cos []x + cos [x], where [y] is the greatest integer function of y then f2
is equal to
(A) cos 3 (B) 0 (C) cos 4 (D) none of these 31. The following four gases are at the same temperature. In which gas do the molecules have the
maximum root mean square speed ? (A) Hydrogen (B) Oxygen (C) Nitrogen (D) Carbon dioxide 32. Which of the following is correct for the molecules of a gas in equilibrium temperature ? (A) All have the same speed (B) Molecules have different speed distribution of which average remain constant (C) They have a certain constant average speed (D) They do not collide with one another 33. P–T diagram is shown below then choose the corresponding V–T
diagram
(A) (B)
(C) (D)
Space for rough work
FIITJEE (Hyderabad Classes) Limited. 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad. 500 063. Ph: 040-66777000 – 03 Fax: 04066777004 FIITJEE Limited. 22–97, Plot No.1, (Opp. Patel Kunta) Huda Park, Vijaynagar Colony, Kukatpally, Hyderabad. 500 072. Ph : 040–64601123
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PET-XVI (1ST
YEAR)-2019-MPC-12
34. 0E and hE respectively represent the average kinetic energy of a molecule of oxygen and hydrogen.
If the two gases are at the same temperature, which of the following statements is true
(A) 0 hE E (B)
0 hE E
(C) 0 hE E
(D) Nothing can be said about the magnitude of 0E and
hE as the information given is insufficient
35. When an ideal gas is compressed isothermally then its pressure increase because (A) It potential energy increases (B) Its kinetic energy increase and molecules move apart (C) Its number of collisions per unit area with walls of container increases (D) Molecular energy increases 36. If k is the Boltzmann constant, the average translational kinetic energy of a gas molecules at absolute
temperature T is (A) k T / 2 (B) 3 k T/4 (C) k T (D) 3 k T/2 37. The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room temperature
the rms speed of oxygen molecules is v. The rms speed of the hydrogen molecule at the same temperature will be
(A) v/16 (B) v/4 (C) 4v (D) 16 v 38. The average kinetic energy of hydrogen molecules at 300 K is E. At the same temperature, the
average kinetic energy of oxygen molecules will be (A) E/16 (B) E/4 (C) E (D) 4 E 39. Same volumes of hydrogen and oxygen at the same temperature and pressure are mixed together so
that the volume of the mixture is same as the initial volume of the either gas. if the initial pressure be p, then the pressure of the mixture will be
(A) 4 p (B) 2p (C) p/2 (D) p/4
40. 32m of hydrogen and 32m of oxygen are at the same temperature. If the pressure of hydrogen be p, then that of oxygen will be
(A) 2 p (B) 4p (C) 8 p (D) 1 p
41. Two equal and unlike parallel forces each of magnitude 5 N act on a wheel of diameter 20 cm, as shown in the figure. Find the couple acting on the wheel.
(A) 10 Nm (B) 1.0 Nm (C) 0.5 Nm (D) 2 Nm
5F N
5F N Space for rough work
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42. A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of 53° with it.
The other end rests on a rough horizontal floor. The normal force that floor exerts on the ladder is (A) 55 (B) 65 N (C) 98 N (D) none of these 43. A flywheel gains a speed of 540 rpm in 6 sec. Its angular acceleration will be
(A) 3 rad/sec2 (B) 18 rad/sec
2 (C) 54 rad/sec
2 (D) 9 rad/sec
2
44. A point mass is whirled in a circular path with a constant angular velocity and its angular momentum
is L. If the string is now halved keeping the angular velocity same, the angular momentum is: (A) L/4 (B) L (C) 2L (D) L/2 45. A uniform solid cylinder of mass M and radius R rolls down without slipping an inclined plane of height
h. The angular velocity of the cylinder when it reaches the bottom of the plane will be
(A)2
ghR
(B)2 gh
R 2 (C)
2 gh
R 3 (D)
1gh
2R
46. Suppose a body of mass M and radius R is allowed to roll on an inclined plane without slipping from
its topmost point A. The velocity acquired by the body, as it reaches the bottom of the inclined plane, is given by:
(A) 2gh (B) 2gh (C)2gh
(D)
2gh
where β= 1 + 2
I
MR (I is the moment of inertia of the body about its axis of rotation).
47. A solid sphere and a solid cylinder of same mass are rolled down on two Inclined planes of heights h1
and h2 respectively. If at the bottom of the plane the two objects have same linear velocities, then the ratio of h1 : h2 is:
(A) 2 : 3 (B) 7 : 5 (C) 14 : 15 (D) 15 : 14 48. A solid cylinder of mass m = 4 kg and radius R = 10cm has two
ropes wrapped around it, one near each end. The cylinder is held horizontally by fixing the two free ends of the cords to the hooks on the ceiling such that both the cords are exactly vertical. The cylinder is released to fall under gravity. Find the linear acceleration of the cylinder.
(A) g
3 (B)
2g
3 (C)
4g
3 (D) none of these
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49. Particle of mass m is projected with a velocity v0 making an angle of 450 with horizontal. The
magnitude of angular momentum of the projectile about the point of projection at its maximum height is
(A) Zero (B) g2mv3 (C) g24mv20
(D) 32ghm
50. A string is wrapped several times round a solid cylinder and then the end of the string is held
stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be
(A) 3
mgand
3
2g (B)
2
mgandg (C)
23
mgand
g (D)
32
mgand
g
51. A circular ring of mass M and radius R is rotating about its axis with constant angular velocity . Two objects each of mass m get attached to the rotating ring. The ring now rotates with an angular velocity
(A) mM
M
2
(B)
m
M 2m (C)
M 2m)
M 2m (D)
m
2mM
52 A rod of mass m and length fits into a hollow tube of same
length and mass. The tube is rotated with an initial angular
velocity 0 and the rod slips through the rough hollow surface. The angular velocity of the rod as it slips out of the tube is
A
B
0
(A) 2
0 (B)
4
0 (C)
16
0 (D)
7
0
53 A uniform rod of length and mass M is suspended on two
vertical inextensible strings as shown in the figure. Calculate tension T in left string at the instant, when right string snaps.
(A) mg
2 (B) mg (C)
mg
4 (D)
mg
8
54 A uniform circular disc of radius r is placed on a rough horizontal surface
and given a linear velocity v0 and angular velocity 0 as shown. The disc comes to rest after moving some distance to the right. It follows that
v0
0
P
(A) 3 v0 = 20 r (B) 2 v0 = 0 r (C) v0 = 0 r (D) 2 v0 = 3 0 r
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55. A disc is freely rotating with an angular speed on a smooth horizontal plane. It is hooked at a rigid peg P & rotates about P without bouncing. Its angular speed after the impact will be equal to.
P
(A) (B)3
(C)
2
(D) none of these
56. The moment of inertia of a uniform cylinder of length and radius R about its perpendicular bisector
is I. What is the ratio /R such that the moment of inertia is minimum ?
(A) 3
2 (B)
3
2 (C)
3
2 (D) 1
57. A slender uniform rod of mass M and length is pivoted at one
end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle with the vertical is .
(A) 2g
cos3
(B) 3g
sin2
(C) 2g
sin3
(D) 3g
cos2
Z
X
58. A roller is made by joining together two cones at their
vertices O. It is kept on two rails AB and CE which are placed asymmetrically (see fig), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see fig). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to
(A) turn right (B) go straight (C) turn left and right alternately (D) turn left
O
B
A C
D
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59. A particle of mass m is moving along the side of a square of
side ‘a’ with a uniform speed v in the x–y plane as shown in the figure:
Which of the following statements is false for the angular
momentum L about the origin ?
(A) R ˆL mv a k2
when the particle is moving
from C to D
(B) R ˆL mv a k2
when the particle is moving
from B to C
(C) 3mv ˆL Rk
2 when the particle is moving from D to A
(D) mv ˆL Rk
2 when the particle is moving from A to B
y
O x
R
450
a C D
a a
a
A B
v v
v
v
60. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of
inertia of cube about an axis passing through its centre and perpendicular to one of its faces is
(A) 2MR
16 2 (B)
24MR
9 3 (C)
24MR
3 3 (D)
2MR
32 2
61. +R power of the given groups
(1) (2) - NH2 (3) - OH (4) - NHCOCH3 (A) 1 > 2 > 3 > 4 (B) 4 > 3 > 2 > 1 (C) 1 > 3 > 2 > 4 (D) 1 > 4 > 3 > 2 62. Consider the given compounds
1) CH CH NH23 2 2) CH CH CN NH23
3) CH CH Cl NH23 4) 2C H NH C H5 2 5
Arrange basicity of these compounds in decreasing order in gaseous phase: (A) 4 > 1 > 2 > 3 (B) 4 > 1 > 3 > 2 (C) 1 > 4 > 2 > 3 (D) 2 > 1 > 4 > 3
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63. Among the following which is most stabilized cation :
(A)
(B)
(C)
(D)
64. Which of the following acids has highest Ka value ?
(A)
(B)
(C)
(D)
65. Which is the order of decreasing acidic character of the following compounds?
3 2CH CH CH CH COOH
Cl Cl
(I)
Cl Cl
3 2CH CH CH CH COOH (II)
3 2 2CH C CH CH COOH
Cl
Cl
(III) Cl
Cl
3 2 2CH CH CH C COOH
(IV)
3 2 2CH CH C CH COOH
Cl
Cl
(V)
(A) IV V III I II (B) IV I V II III
(C) I II III V IV (D) III V IV II I 66. Maximum – I effect is exerted by the group
(A)
3N H
(B) 6 5C H (C) –NO2 (D) –OCH3
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67. The stability of following carbocations in the order
2 3 3 3 23 2
I IVIIIII
Ph CH , CH C , CH C H, CH C H
(A) I > II > III > IV (B) II > I > III > IV (C) III > II > I > IV (D) IV > I > II > III 68. The correct stability order for the following species is
O ,
(I)
,
(II)
O ,
(III)
,
(IV)
(A) II > IV > I > III (B) I > II > III > IV (C) II > I > IV > III (D) I > III > II > IV 69. Identify the correct order of stability
CH2
NO2
CH2
NO2
CH2
NO2
CH2
:
(P) (Q)(R) (S)
(A) Q > R > P > S (B) S > R > Q > P (C) S > R > P > Q (D) R > P > Q > S 70. Which one among the following is the least basic ?
(A) CH3NH2 (B) 3NH (C) CH3CH2NH2 (D) 3 2 2CH CH NO NH
71. –CN(I) –COOH (II) –F(III) Among these groups, which of the following orders is correct for the magnitude of their– I effect ? (A) I > II > III (B) III > I > II (C) II > I > III (D) III > II > I 72. –I(I), –OH(II), –Cl(III) Among these groups, which of the following orders is correct, for the magnitude of their –I effect ? (A) I > III > II (B) III > II > I (C) III > I > II (D) II > III > I 73. –OPh(I), –OCH3(II), –OH(III) Among these groups, which of the following orders is correct for their –I effect ? (A) I > II > III (B) II > III > I (C) II > I > III (D) III > I > II
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74. Which of the following groups has +M effect ?
(A) –OCO–CH3 (B) –NH2 (C)
3N H
(D) (a) and (b)
75.
OCH3
OCH3
NH CH3
IIIIII
Which of the following orders is correct for the magnitude of +M effect among these groups ? (A) I > II > III (B) I > III > II (C) III > I > II (D) II > I > III 76.
O
O
N
CH3
I II III Which of the following orders is correct for the magnitude of +M effect among these groups ? (A) I > III > II (B) III > I > II (C) II > I > III (D) II > III > I 77. –OH(I), –F(II), –Cl (III) Which of the following orders is correct for the magnitude of +M effect among these groups ? (A) I > III > II (B) I > II > III (C) III > II > I (D) II > III > I 78.
NO2
NO2
OCH3
IIIIII
Which of the following orders is correct about the magnitude of –M effect among these groups ? (A) I > II > III (B) II > I > III (C) II > I > III (D) III > II > I 79. (I) CH2–O–CH=O (II) CH3–O–C(NH2)=O (III) CH3–O–C(OEt)=O In which of these cases, +M effect of –OCH3 group is operating most effectively ? (A) I (B) II (C) III (D) None of these
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80. Which of the following statements about conformers is correct ? (A) Conformers exist in a state of dynamic equilibrium (B) At equilibrium, population of more stable conformers will be more than that of less stable
conformer (C) Conformers cannot be separated (D) all of these 81. Which of the following compounds will exhibit conformational isomerism ?
(A) 3 2 3CH CH CH (B) 3 2 2 3CH CH CH CH
(C) 3 3 3CH CH CH CH (D) all of these
82. Number of which of the following isomers is always infinite ? (A) Geometrical isomers (B) Optical isomers (C) Conformational isomers (D) Structural isomers 83.
H H
HHH
H
Translating this eclipsed Newman projection formula of ethane into sawhorse projection appears as
(A) H
HH
H
HH
(B) H
HH
H
H
H (C) Both a and b (D) None of these
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84.
CH3
Br
H
CH3
Br
H
Translating this staggered new man projection formula of 2, 3–dibromobutane into staggered
sawhorse projection appears as
(A) CH3
BrH
CH3
Br H
(B) CH3
HBr
CH3
Br H
(C)
CH3
BrH
CH3
H Br
(D) All of these
85.
CH3
H Br
Br H
CH3 Translating this Fischer projection formula into eclipsed sawhorse projection appears as
(A) CH3
BrH
H
Br
CH3
(B) CH3
BrH
Br
H
CH3 (C) Both (a) and (b) (D) None of these
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86. Which two fischer formulas represent a pair of enantiomers ?
HO
CH3
H
H Cl
C2H5
H
CH3
Cl
HO H
C2H5
Cl
C2H5
H
HO H
CH3
HO
CH3
H
Cl H
C2H5 (A) I & II (B) III & IV (C) I & IV (D) II & III 87. Indicate the correct relation ship In the following three pairs respectively
F
Br
H
H
CH3
H
and CH2Br
H
CH3
F(I)
Cl
H
CH3
C2H5
H
Cl
and H
Cl
H3C
H
Cl
C2H5
(II)
CH3
H Br
CH3 H
Br
and
CH3
Br Br
H CH3
Br
(III)
(A) Enantiomeric pair, Diastereomeric pair, Enantiomeric pair (B) Identical, Enantiomeric pair, enantiomeric pair (C) Enantiomeric pair, Diastereomers pair, Identical (D) Enantiomeric pair, Identical, Identical
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88. Which of the following pairs of structures does not represent resonating structures ?
(A) CH3–CO–CH3 and CH3–C(OH)=CH2 (B) O and O
(C) CH3 C
O H
CH3CH3 C
OH
CH3and
(D) 2CH C O and
2C H C O
89. Arrange the stability of the given carbocations in decreasing order
CH2
NHCOCH3
(I)
CH2
OH
(II)
CH2
NH2
(III)
CH2
Cl
(IV)
(A) III > II > IV > I (B) III > II > I > IV (C) IV > I > II > III (D) II > III > I > IV 90. Which of the following effects of –NO2 group operates on–NH2 group in this
molecule? (A) Only –I effect (B) Only –M effect (C) both–I and –M effect (D) Only +M effect
NH2
NO2
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FIITJEE PET – XVI (REG_1ST YEAR)
MAINS_SET–B_ANSWERS DATE: 09.12.2017
MATHEMATICS
1. C 2. B 3. Bonus 4. B
5. D 6. C 7. B 8. D
9. B 10. B 11. C 12. B
13. D 14. A 15. D 16. B
17. D 18. B 19. B 20. C
21. A 22. B 23. C 24. A
25. BONUS 26. B 27. C 28. D
29. B 30. C
PHYSICS
31. A 32. B 33. D 34. B
35. C 36. D 37. C 38. C
39. B 40. D 41. B 42. C
43. A 44. A 45. C 46. C
47. C 48. B 49. D 50. A
51. A 52. B 53. C 54. B
55. B 56. B 57. B 58. D
59. A OR C 60. B
CHEMISTRY
61. A 62. B 63. C 64. D
65. B 66. A 67. A 68. D
69. B 70. D 71. A 72. C
73. A 74. D 75. C 76. B
77. B 78. A 79. BONUS 80. D
81. D 82. C 83. B OR D 84. A
85. A 86. B 87. BONUS 88. A
89. B 90. C
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