PART-I Physics
SECTION – I
Straight Objective Type
This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
1. In the experiment to determine the speed of sound using a resonance column,
(A) prongs of the tuning fork are kept in a vertical plane
(B) prongs of the tuning fork are kept in a horizontal plane
(C) in one of the two resonances observed, the length of the resonating air column is close to the wavelength of sound in air
(D) in one of the two resonances observed, the length of the resonating air column is close to half of the wavelength of sound in air
2. A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ±0.05 mm at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of ±0.01 mm. Take g = 9.8 m/s2 (exact). The Young’s modulus obtained from the reading is
(A) (2 .0 ± 0.3) × 1011 N/m2
(B) (2 .0 ± 0.2) × 1011 N/m2
(C) (2 .0 ± 0.1) × 1011 N/m2
(D) (2 .0 ± 0.05) × 1011 N/m2
3. A particle moves in the X-Y plane under the influence of a force such that its linear momentum is 
where A and k are constants. The angle between the force and the momentum is
(A) 0°
(B) 30°
(C) 45°
(D) 90°
4. A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 
with respect to the initial position. The object is
(A) ring
(B) solid sphere
(C) hollow sphere
(D) disc
5. Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is ρ, the surface tension of water is T and the atmospheric pressure is P0. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude
(A) |2P0Rh + πR2ρgh − 2RT|
(B) |2P0Rh + Rρgh2 – 2RT|
(C) |P0πR2 + R ρgh2 – 2RT|
(D) |P0πR2 + R ρgh2 + 2RT|
6. A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is
(A) zero everywhere
(B) non-zero and uniform
(C) non-uniform
(D) zero only at its center
7. Positive and negative point charges of equal magnitude are kept at 
The work done by the electric field when another positive point charge is moved from (−a, 0, 0) to (0, a, 0) is
(A) positive
(B) negative
(C) zero
(D) depends on the path connecting the initial and final positions
8. A magnetic field 
exists in the region a < x < 2a and 
, in the region 2a < x < 3a, where B0 is a positive constant. A positive point charge moving with a velocity 
where v0 is s positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like,
(A) 
(B) 
(C) 
(D) 
9. Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is
(A) 
(B) 
(C) 
(D) 
SECTION – II
Assertion – Reason Type
This section contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
10. STATEMENT-1
If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.
because
STATEMENT-2
The linear momentum of an isolated system remains constant.
(A) Statement -1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
(B) Statement -1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
(C) Statement -1 is True, Statement-2 is False.
(D) Statement -1 is False, Statement-2 is True.
11. STATEMENT-1
A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.
because
STATEMENT-2
For every action there is an equal and opposite reaction.
(A) Statement -1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
(B) Statement -1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
(C) Statement -1 is True, Statement-2 is False.
(D) Statement -1 is False, Statement-2 is True.
12. STATEMENT-1
A vertical iron rod has a coil of wire wound over it at the bottom end.
An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.
Because
STATEMENT-2
In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.
(A) Statement -1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
(B) Statement -1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
(C) Statement -1 is True, Statement-2 is False.
(D) Statement -1 is False, Statement-2 is True.
13. STATEMENT-1
The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.
(A) Statement -1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.
(B) Statement -1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1.
(C) Statement -1 is True, Statement-2 is False.
(D) Statement -1 is False, Statement-2 is True.
SECTION – III
Linked Comprehension Type
This section contains 2 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph for Question Nos. 14 to 16
Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A blows a long whistle.
Assume that the sound of the whistle is composed of components varying in
frequency from f1 = 800 Hz to f2 = 1120 Hz, as shown in the figure. The spread in the frequency (highest frequency − lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s.
14. The speed of sound of the whistle is
(A) 340 m/s for passengers in A and 310 m/s for passengers in B
(B) 360 m/s for passengers in A and 310 m/s for passengers in B
(C) 310 m/s for passengers in A and 360 m/s for passengers in B
(D) 340 m/s for passengers in both the trains
15. The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by
(A) 
(B) 
(C) 
(D) 
16. The spread of frequency as observed by the passengers in train B is
(A) 310 Hz
(B) 330 Hz
(C) 350 Hz
(D) 290 Hz
Paragraph for Question Nos. 17 to 19
The figure shows a surface XY separating two transparent media, medium – 1 and medium -2. The lines ab and cd represent wavefronts of a light wave travelling in medium-1 and incident on XY. The lines ef and gh represent wavefronts of the light wave in medium-2 after refraction.
17. Light travels as a
(A) parallel beam in each medium
(B) convergent beam in each medium
(C) divergent beam in each medium
(D) divergent beam in one medium and convergent beam in the other medium.
18. The phases of the light wave at c, d, e and f are ϕc, ϕd, ϕe and ϕf It is given that ϕc ≠ ϕf
(A) ϕc cannot be equal to ϕd
(B) ϕd can be equal to ϕe
(C) (ϕd – ϕf) is equal to (ϕc – ϕe)
(D) (ϕd – ϕc) is not equal to (ϕf – ϕe)
19. Speed of the light is
(A) the same in medium-1 and medium-2
(B) larger in medium-1 than in medium-2
(C) larger in medium-2 than in medium-1
(D) different at b and d
SECTION – IV
Matrix-Match Type
This section contains 3 questions. Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column I have to be matched with statements (p, q, r, s) in column II.
20. Column I describe some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situation in Column I with the characteristics in Column II.
(A) A− (p), B − (q) & (r), C − (p), D − (r) & (q)
(B) A− (s), B − (p) & (q), C − (r), D − (s) & (p)
(C) A− (r), B − (s) & (q), C − (s), D − (p) & (s)
(D) A− (q), B − (p) & (s), C − (q), D − (s) & (p)
21. Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II
(A) A− (q) & (r), B − (p), C − (q) & (r), D − (q)
(B) A− (p), B − (p) & (s), C − (q), D − (s) & (p)
(C) A− (r), B − (s) & (q), C − (s), D − (p) & (s)
(D) A− (s), B − (p) & (s), C − (q), D − (s) & (p)
22. Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II
(A) A− (s), B − (q), C − (p), D − (r)
(B) A− (p), B − (p) & (s), C − (q), D − (s) & (p)
(C) A− (r), B − (s) & (q), C − (s), D − (p) & (s)
(D) A− (s), B − (p) & (s), C − (q), D − (s) & (p)
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