PART I : PHYSICS
Section 1 : (one or more options correct Type)
This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
1. The figure below shows the variation of specific heat capacity (C) of solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is(are) correct to a reasonable approximation.
(A) the rate at which heat is absorbed in the range 0 − 100 K varies linearly with temperature T.
(B) heat absorbed in increasing the temperature from 0 − 100 K is less than the heat required for increasing the temperature from 400 − 500 K.
(C) there is no change in the rate of heat absorption in the range 400 − 500 K.
(D) the rate of heat absorption increases in the range 200 − 300 K.
2. The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a0, where a0 is the Bohr radius. Its orbital angular momentum is 
It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)
(A) 
(B) 
(C) 
(D) 
3. Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding angles θ in the range 0 to 90º. The wavelength λ is exactly known and the error in θ is constant for all values of θ. As θ increases from 0º.
(A) the absolute error in d remains constant.
(B) the absolute error in d increases.
(C) the fractional error in d remains constant.
(D) the fractional error in d decreases.
4. Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +ρ and −ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,
(A) the electrostatic field is zero.
(B) the electrostatic potential is constant.
(C) the electrostatic field is constant in magnitude.
(D) the electrostatic field has same direction.
5. A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are)
(A) In the region 0 < r < R, the magnetic field is non-zero.
(B) In the region R < r < 2R, the magnetic field is along the common axis.
(C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis.
(D) In the region r > 2R, the magnetic field is non-zero.
6. Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is V. The correct statements(s) is (are)
(A) If the wind blows from the observer to the source, f2 > f1.
(B) If the wind blows from the source to the observer, f2 > f1.
(C) If the wind blows from observer to the source, f2 < f1.
(D) If the wind blows from the source to the observer, f2 < f1.
7. Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)
(A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 
(B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 
(C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 
(D) The energy of the mass m remains constant.
8. A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collision,
(A) the speed of the particle when it returns to its equilibrium position is u0.
(B) the time at which the particle passes through the equilibrium position for the first time is 
(C) the time at which the maximum compression of the spring occurs is 
(D) the time at which the particle passes through the equilibrium position for the second time is 
SECTION 2 : (Paragraph Type)
This section contains 4 paragraphs each describing theory, experiment, data etc. Eight questions relate to four paragraphs with two questions on each paragraph. Each question of a paragraph has only one correct answer among the four choices (A), (B), (C) and (D).
Paragraph for Questions 9 and 10
A small block of mass 1 kg is released from rest at the top of a rough track. The track is a circular arc of radius 40 m. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure below, is 150 J. (Take the acceleration due to gravity, g = 10 ms−2).
9. The speed of the block when it reaches the point Q is
(A) 5 ms−1
(B) 10 ms−1
(C) 10√3 ms−1
(D) 20 ms−1
10. The magnitude of the normal reaction that acts on the block at the point Q is
(A) 7.5 N
(B) 8.6 N
(C) 11.5 N
(D) 22.5 N
Paragraph for Questions 11 and 12
A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with a power factor unity. All the currents and voltages mentioned are rms values.
11. If the direct transmission method with a cable of resistance 0.4Ω km−1 is used, the power dissipation (in%) during transmission is
(A) 20
(B) 30
(C) 40
(D) 50
12. In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1:10. If the power to the consumers has to be supplied at 200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is
(A) 200 : 1
(B) 150 : 1
(C) 100 : 1
(D) 50 : 1
Paragraph for Questions 13 and 14
A point charge Q is moving in a circular orbit of radius R in the x-y plane with an angular velocity ω. This can be considered as equivalent to a loop carrying a steady current 
A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from 0 to B in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant γ.
13. The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is
(A) BR/4
(B) BR/2
(C) BR
(D) 2BR
14. The change in the magnAnswer:etic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is
(A) 
(B) 
(C) 
(D) 
Paragraph for Questions 15 and 16
The mass of a nucleus is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m1 and m2 only if (m1 + m2) < M. Also two light nuclei of masses m3 and m4 can undergo complete fusion and form a heavy nucleus of mass M′ only if (m3 + m4) > M′. The masses of some neutral atoms are given in the table below :
15. The correct statement is
(A) The nucleus 
can emit an alpha particle.
(B) The nucleus 
can emit a proton.
(C) Deuteron and alpha particle can undergo complete fusion.
(D) The nuclei 
can undergo complete fusion.
16. The kinetic energy (in keV) of the alpha particle, when the nucleus 
at rest undergoes alpha decay, is
(A) 5319
(B) 5422
(C) 5707
(D) 5818
SECTION 3 : (Matching List Type)
This section contains 4 multiple choice questions. Each question has matching lists. The codes for the lists have choices (A), (B), (C) and (D) out of which ONLY ONE is correct
17. One mole of a monatomic ideal gas is taken along two cyclic processes E → F → G → E and E → F → H → E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.
Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given
(A) P – 4 ; Q – 3 ; R – 2 ; S – 1
(B) P – 4 ; Q – 3 ; R – 1 ; S – 2
(C) P – 3 ; Q – 1 ; R – 2 ; S – 4
(D) P – 1 ; Q – 3 ; R – 2 ; S – 4
18. Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists:
(A) P – 4 ; Q – 3 ; R – 2 ; S – 1
(B) P – 4 ; Q – 3 ; R – 1 ; S – 2
(C) P – 3 ; Q – 1 ; R – 2 ; S – 4
(D) P – 1 ; Q – 3 ; R – 2 ; S – 4
19. A right angled prism of refractive index μ1 is placed in a rectangular block of refractive index μ2, which is surrounded by a medium of refractive index μ3, as shown in the figure. A ray of light ‘e’ enters the rectangular block at normal incidence. Depending upon the relationships between μ1, μ2 and μ3, it takes one of the four possible paths ‘ef’, ‘eg’, ‘eh’ or ‘ei’.
Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:
(A) P – 2 ; Q – 3 ; R – 1 ; S – 4
(B) P – 1 ; Q – 2 ; R – 4 ; S – 3
(C) P – 4 ; Q – 1 ; R – 2 ; S – 3
(D) P – 2 ; Q – 3 ; R – 4 ; S – 1
20. Match List I with List II and select the correct answer using the codes given below the lists:
List I List II
P. Boltzmann constant 1. [ML2T−1]
Q. Coefficient of viscosity 2. [ML−1T−1]
R Planck constant 3. [MLT−3T−1]
S. Thermal conductivity 4. [ML2T−2K−1]
(A) P – 3 ; Q – 1 ; R – 2 ; S – 4
(B) P – 3 ; Q – 2 ; R – 1 ; S – 4
(C) P – 4 ; Q – 2 ; R – 1 ; S – 3
(D) P – 4 ; Q – 1 ; R – 2 ; S – 3
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