Part – III : Physics
SECTION – I (Single Correct Choice Type)
This Section contains 6 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.
1. A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is
(A) 0.02 mm
(B) 0.05 mm
(C) 0.1 mm
(D) 0.2 mm
2. A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms−1, the mass of the string is
(A) 5 grams
(B) 10 grams
(C) 20 grams
(D) 40 grams
3. A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is
(A) virtual and at a distance of 16 cm from the mirror
(B) real and at a distance of 16 cm from the mirror
(C) virtual and at a distance of 20 cm from the mirror
(D) real and at a distance of 20 cm from the mirror
4. A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is
(A) 4.50 J
(B) 7.50 J
(C) 5.06 J
(D) 14.06 J
5. A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 
When the field is switched off, the drop is observed to fall with terminal velocity 2 × 10−3 ms−1. Given g = 9.8 ms−2, viscosity of the air = 1.8 × 10−5 Ns m−2 and the density of oil = 900 kg m−3, the magnitude of q is
(A) 1.6 × 10−19 C
(B) 3.2 × 10−19 C
(C) 4.8 × 10−19 C
(D) 8.0 × 10−19 C
6. A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to
(A) 
(B) 
(C) 
(D) 
SECTION –II (Integer Type)
This Section contains 5 questions. The answer to each question is a single-digit integer, ranging from 0 to 9.
7. A diatomic ideal gas is compressed adiabatically to 1/32 of its initial volume. If the initial temperature of the gas is Ti (in Kelvin) and the final temperature is aTi, the value of a is
8. At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them becomes 4 volt?
[take ℓn 5 = 1.6, ℓn 3 = 1.1]
9. Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 
in 30 seconds. What is the speed of the object in km per hour?
10. A large glass slab (μ = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?
11. To determine the half life of a radioactive element, a student plots a graph of 
versus t. Here 
is the rate of radioactive decay at time t. If the number of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is
SECTION –III (Paragraph Type)
This Section contains 2 paragraphs. Based upon each of the paragraphs 3 multiple choice questions have to be answered. Each of these questions has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Paragraphs for Question 12 To 14
When liquid medicine of density ρ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When the force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
12. If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r << R) is
(A) 2πrT
(B) 2πRT
(C) 
(D) 
13. If r = 5 × 10−4 m, ρ = 103 kg m−3, g = 10 m/s2, T = 0.11 Nm−1, the radius of the drop when it detaches from the dropper is approximately
(A) 1.4 × 10−3 m
(B) 3.3 × 10−3 m
(C) 2.0 × 10−3 m
(D) 4.1 × 10−3 m
14. After the drop detaches, its surface energy is
(A) 1.4 × 10−6 J
(B) 2.7 × 10−6 J
(C) 5.4 × 10−6 J
(D) 8.1 × 10−6 J
Paragraph for questions 15 to 17
The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantization condition.
15. A diatomic molecule has moment of inertia I. By Bohr’s quantization condition its rotational energy in the nth level (n = 0 is not allowed) is
(A) 
(B) 
(C) 
(D) 
16. It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to 
Then the moment of inertia of CO molecule about its centre of mass is close to (Take h = 2π × 10−34 Js)
(A) 2.76 × 10−46 kg m2
(B) 1.87 × 10−46 kg m2
(C) 4. 67 × 10−47 kg m2
(D) 1.17 × 10−47 kg m2
17. In a CO molecule, the distance between C (mass = 12 a.m.u) and O (mass = 16 a.m.u.), where 1 a.m.u. 
is close to
(A) 2.4 × 10−10 m
(B) 1.9 × 10−10 m
(C) 1.3 × 10−10 m
(D) 4.4 × 10−11 m
SECTION – IV (Matrix Type)
This Section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, against statement B.
18. Two transparent media of refractive indices μ1 and μ3 have a solid lens shaped transparent material of refractive index μ2 between them as shown in figures in Column II. A ray traversing these media is also shown in the figures. In Column I different relationships between μ1, μ2 and μ3 are given. Match them to the ray diagram shown in Column II.
(A) (A) → (p, r), (B) → (q, s, t), (C) → (p, r, t), (D) → (q, s)
(B) (A) → (q, s), (B) → (r, p, q), (C) → (s, t, p), (D) → (r, t)
(C) (A) → (s, t), (B) → (p, r, s), (C) → (p, t, q), (D) → (r, s)
(D) (A) → (q, t), (B) → (t, p, s), (C) → (q, s, r), (D) → (p, t)
19. You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current I (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V1 and V2. (indicated in circuits) are related as shown in Column I. Match the two
(A) (A) → (p, r, q), (B) → (s, p, t, r), (C) → (r, s), (D) → (p, q, r, s)
(B) (A) → (r, s, t), (B) → (q, r, s, t), (C) → (p, q), (D) → (q, r, s, t)
(C) (A) → (p, q, s), (B) → (t, q, r, s), (C) → (t, s), (D) → (p, q, t, r)
(D) (A) → (t, r, s), (B) → (p, q, r, s), (C) → (r, t), (D) → (s, p, r, q)
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