PART - I : PHYSICS

SECTION-1

This section contains 20 Multiple Choice Questions. Each question has 4 choices (A),
(B), (C) and (D), out of which ONLY ONE CHOICE is correct.

1. If the wavelength of  -line of Lyman series in hydrogen atom is  , find the wavelength of
ß -line of Paschen series.

32  5 6 36  53 33  52 32  53
(a)  (b)  (c)  (d) 
23 22 26 26

2. If temperature of a liquid is increased, choose the correct option regarding change in its surface
tension and viscosity.
(a) Surface tension decreases while viscosity increases
(b) Surface tension increases while viscosity decreases
(c) Both increases
(d) Both decreases
3. A proton of mass m and charge q enters a region of uniform magnetic field of a magnitude B
with a velocity v directed perpendicular to the magnetic field. It moves in a circular path and
leaves the magnetic field after completing a quarter of a circle. The time spent by the proton
inside the magnetic field is proportional to:
(a) v −1/ 2 (b) v1/ 2 (c) v 0 (d) v
4. Abhishek and Deepak have two samples of magnetic materials X and Y. Experimentally they
determine the following properties of the samples.
Retentivity Coercivity
X 1.5 T 20 Am-1
Y 1.0 T 100 Am-1
Considering this, choose best choice
(a) X and Y both for electromagnets
(b) X for electromagnetic and Y for permanent magnets
(c) X and Y both for permanent magnets
(d) X for permanent magnets and Y for electromagnets

5. Three thin rods of mass m and length a each are joined to form a triangle ABC in vertical
plane. The triangle is pivoted at the vertex A such that it can rotate in the vertical plane. It is
 released from rest when the side AB is horizontal as shown. As the triangle rotates, the
maximum velocity of the vertex B, vMAX , is given by:

4 ga 2 ga ga
(a) v 2 MAX = (b) v 2 MAX = 3 ga (c) v 2 MAX = (d) v 2 MAX =
3 3 3
6. To a ground observer the block C is moving with v0 and the block A with v1 . B is moving
with v2 relative to C as shown in the figure. Identify the correct statement.

(a) v1 − v2 = v0 (b) v1 = v2 (c) v1 + v0 = v2 (d) None of these

7. A particle free to move along x - axis is acted upon by a force F = −ax + bx 2 where a and b
are positive constants. For x  0 , the correct variation of potential energy function U(x) is
best represented by (take U(0) = 0).

(a) (b) (c) (d)

8. In system of particles, internal forces can change:

(a) The linear momentum but not the kinetic energy
(b) The kinetic energy but not the linear momentum
(c) Linear momentum as well as kinetic energy
(d) Neither the linear momentum nor the kinetic energy
9. From a point on smooth floor of a room, a ball is shot to hit a wall. The ball then returns back
to the point of projection. If the time taken by the ball in returning is twice the time taken in
reaching the wall, find the coefficient of restitution.
1 1 1
(a) e = (b) e = (c) e = (d) e = 0.2
2 3 4
10. A ball is projected horizontal with a velocity of 5ms−1 from the top of a building 20m.
Displacement of ball when it hits the ground is : (g = 10m/s2)

(a) 10 m (b) 20 m (c) 10 3m (d) 10 5m

11. A planet is revolving around the sun in an elliptical orbit. The mass of planet is m, angular
momentum of planet about sun is 𝐿, and length of semi major axis is a and eccentricity are 𝑒. Time
period of revolution of planet is given by

2𝜋𝑚𝑎 2 √1+𝑒 2 𝜋𝑚𝑎 2 √1−𝑒 2

(a) 𝑇 = 𝐿
(b) 𝑇 = 𝐿

2𝜋𝑚𝑎 2 √1−𝑒 2 𝜋𝑚𝑎 2 √1−𝑒 2

(c) 𝑇 = 𝐿
(d) 𝑇 = 3𝐿

12. An ideal gas undergoes a thermodynamic process in which internal energy (𝑈) of the
gas depends on pressure (𝑃) of the gas as = 𝑎𝑃 , where a is a positive constant. Assuming gas
4

to be monoatomic, the molar heat capacity of the gas for given process will be

3𝑅 2𝑅
(a) 4
(b) 3
9𝑅 4𝑅
(c) (d)
4 9

13. A vertical cylindrical vessel contains a half litre of water having column height of 60 𝑐𝑚. If
the density and bulk modulus of water are 103 𝑘𝑔 𝑚–3 and 2 × 109 𝑁 𝑚–2 respectively, then the
elastic deformation potential energy (approximately) of water, is

(a) 1.8 𝜇𝐽 (b) 1.5 𝜇𝐽

(c) 2.1 𝜇𝐽 (d) 2.4 𝜇𝐽

14. For an SHM oscillator, the amplitude is 5 cm and its time period is 4 seconds. The minimum
time taken by the particle to pass between points which are at distances 4 cm and 3 cm from the
centre of oscillation on the same side of it will be

(a) 0.13 𝑠𝑒𝑐𝑜𝑛𝑑 (b) 0.18 𝑠𝑒𝑐𝑜𝑛𝑑

(c) 0.26 𝑠𝑒𝑐𝑜𝑛𝑑 (d) 0.35 𝑠𝑒𝑐𝑜𝑛𝑑
15. A simple 𝐿𝑅 circuit is connected to a battery at 𝑡 = 0. The time instant at which rate of energy
storage in inductor is half of power delivered by battery

2𝐿 𝐿 3
(a) 𝐼𝑛 2 (b) 𝐼𝑛 ( )
𝑅 𝑅 2
𝐿 𝐿
(c) 𝐼𝑛 2 (d) 𝐼𝑛 3
𝑅 𝑅

16. A uniform rod, of mass 𝑚, length 𝑙 and 𝑟 radius of cross section, is rotated about an axis
passing through one of its ends and perpendicular to its length with constant angular velocity
𝜔 in horizontal plane. If 𝑌 is the Young’s modulus of the material of rod, the increase in its
length due to rotation of rod is

𝑚𝜔2 𝐿2 𝑚𝜔2 𝐿2
(a) 𝜋𝑟 2 𝑌
(b) 2𝜋𝑟 2 𝑌
𝑚𝜔2 𝐿2 2𝑚𝜔2 𝐿2
(c) 3𝜋𝑟 2 𝑌
(d) 𝜋𝑟 2 𝑌

17. A free particle having one electronic charge with initial kinetic energy 9 𝑒𝑉 and de Broglie
wavelength 1 𝑚𝑚 enters a region of 𝑉0 potential difference such that new de Broglie
wavelength is now 1.5 𝑚𝑚. Then 𝑒𝑉0 is

(a) 5 𝑒𝑉 (b) 6 𝑒𝑉
(c) 13.5 𝑒𝑉 (d) 15 𝑒𝑉
18. A radioactive 𝛽 −emission. A detector records 𝑛 𝛽 −particles in 2𝑠 and by next 2𝑠
(accumulatively) it records 1.1 𝑛 𝛽 −particle. Number of 𝛽 −particles recorded by detector
after a long time, is

11𝑛 12𝑛
(a) (b)
10 10
10𝑛
(c) 2𝑛 (d)
9

19. Consider the given arrangement. The two slits 𝑆1 and 𝑆2 are illuminated by monochromatic
𝜆𝐷
light of wavelength 𝜆. Slits 𝑆3 and 𝑆4 are at separation 𝑑1 = 3𝑑 , then ratio of maximum and

minimum intensity on the screen will be

 (a) 9 : 1 (b) 8 : 1
(c) 4 : 1 (d) 2 : 1
20. A sine wave is travelling in a medium. The minimum distance between the two particles,
always having same speed, is

𝜆 𝜆
(a) 4 (b) 3
𝜆
(c) 2 (d) 𝜆

SECTION – II

Numerical Value Type Questions: This section contains 10 questions. The answer to each
questions 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. 06.25, 07.00,
-00.33, -00.30, 30.27, -27.30) using the mouse and the on-screen virtual numeric keypad in
the place designated to enter the answer. You have to attempt any five.

1. 0.056 kg of Nitrogen is enclose in a vessel at a temperature of 127°C. The amount of heat

required to double the speed of its molecules is ___________ k cal.
2. Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in
contact with each other. The space between the lenses is filled with a liquid of refractive
index 1.25. The focal length of the combination is ________ cm.
3. A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV
is added to the base-emitter voltage, the base current changes by 10µA and the collector
current changes by 1.5 mA. The load resistance is 5 k. The voltage gain of the transistor
will be ________.
4. As shown in the figure an inductor of inductance 200 mH is connected to an AC source of
emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the
a
peak value of current is A. The value of a is __________.

5. Sodium light of wavelength 650nm and 655 nm is used to study diffraction at a single slit of
aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation
between the positions of the first maximum of diffraction pattern obtained in the two cases is
_________× 10−5 m.
6. A sample contains 10-2kg each of two substances A and B with half lives 4s and 8s
respectively. The ration of their atomic weights is 1 : 2. The ratio of the amounts of A and
x
B after16s is . The value of x is ______.
100
7. A ray of light is incident at an angle of incidence 60 on the glass slab of refractive index
3. After refraction, the light ray emerges out from other parallel faces and lateral shift
between incident ray and emergent ray is 4 3 cm. The thickness of the glass slab is
_______cm.
8. A circular coil of 1000 turns each with area 1m2 is rotated about its vertical diameter at the
rate of one revolution per second in a uniform horizontal magnetic field of 0.07 T. The
maximum voltage generation will be ________V.
Q
9. A monoatomic gas performs a work of where Q is the heat supplied to it. The molar heat
4
capacity of the gas will be ________ R during this transformation. Where R is the gas
constant.
10. In an experiment to verigy Newton’s law of cooling, a graph is plotted between, the
temperature difference ( T ) of the water and surrounding and time as shown in figure. The
initial temperature of water is taken as 80C. The value of t2 as mentioned in the graph will
be _______.