Physics
SECTION – 1 : (Maximum Marks : 32)
• This section contains EIGHT questions
• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive
1. The densities of two solid spheres A and B of the same radii R vary with radial distance r as 
respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are IA and IB, respectively. If 
the value of n is :
2. Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 
When they are superposed, the intensity of the resulting wave is nI0. The value of n is :
3. For a radioactive material, its activity A and rate of change of its activity R are defined as 
where N(t) is the number of nuclei at time t. Two radioactive sources P(mean life τ) and Q (mean life 2τ) have the same activity at t = 0. Their rates of change of activities at t = 2 τ are RP and RQ, respectively. If 
then the value of n is :
4. A monochromatic beam of light is incident at 60º on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle θ(n) with the normal (see the figure). For n = √3alue of θ is 60° and 
The value of m is :
5. In the following circuit, the current through the resistor R (= 2Ω) is I Amperes. The value of I is :
6. An electron in an excited state of Li2+ ions has angular momentum 3h/2π. The de-Broglie wavelength of the electron in this state is pπa0 (where a0 is the Bohr radius). The value of p is
7. A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length ℓ and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3ℓ from M, the tension in the rod is zero for 
The value of k is
8. The energy of a system as a function of time t is given as E(t) = A2 exp(–at), where a = 0.2s–1. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t = 5 s is
SECTION – 2 : (Maximum Marks : 32)
• This section contains EIGHT questions
• Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct
9. A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivity’s (ε1 = 2 and ε2 = 4) are introduced between the two plates as shown in the figure, the capacitance becomes C2. The ratio 
is
(A) 6/5
(B) 5/3
(C) 7/5
(D) 7/3
10. An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. the gas is then heated very slowly to temperature T2, pressure P2 and volume V2. During this process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement(s) is(are)
(A) If 
then the energy stored in the spring is 
(B) If 
then the change in internal energy is
(C) If 
then the work done by the gas is
(D) If 
then the heat supplied to the gas is 
11. A fission reaction is given by 
where x and y are two particles. Considering 
to be at rest, the kinetic energies of the products are denoted by Kxe, KSr, Kx (2MeV) and Ky(2MeV), respectively. Let the binding energies per nucleon of 
be 7.5 MmeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct option (s) is (are)
(A) 
(B) 
(C) 
(D) 
12. Two spheres P and Q of equal radii have densities ρ1 and ρ2, respectively. The spheres are connected by a massless string and placed in liquids L1 and L2 of densities σ1 and σ2 and viscosities η1 and η2, respectively. The float in equilibrium with the sphere P in L1 and sphere Q in L2 and the string being taut(see figure). If sphere P alone in L2 has terminal velocity 
and Q alone in L1 has terminal velocity 
, then
(A) 
(B) 
(C) 
(D) 
13. In terms of potential difference V, electric current I, permittivity ε0, permeability μ0 and speed of light c, the dimensionally correct equation(s) is (are)
(A) 
(B) 
(C) 
(D) 
14. Consider a uniform spherical charge distribution of radius R1 centred at the origin O. In this distribution, a spherical cavity of radius R2, centred at P with distance OP = a = R1 – R2 (see figure) is made. If the electric field inside the cavity at position 
is 
(A) 
is uniform, its magnitude is independent of 
but its direction depends on 
(B) 
uniform, its magnitude independs of 
and its direction depends on 
(C) is uniform, its magnitude is independent of a but its direction depends on
15. In plotting stress versus strain curves for the materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)
(A) P has more tensile strength than Q
(B) P is more ductile than Q
(C) P is more brittle than Q
(D) The Young’s modulus of P is more than that of Q.
16. A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r(r < R), then the correct option(s) is (are)
(A) 
(B) 
(C) 
(D) 
SECTION – 3 : (Maximum Marks : 16)
• This section contains TWO paragraphs
• Based on each paragraph, there will be TWO questions.
• Each equation has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct
PARAGRAPH – I
(17 to 18)
In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively.
A uniform magnetic field 
is applied on the strip along the positive y-direction. Due to this, the charge carriers experience a net deflection along the z-direction. This results in accumulation of charge carriers on the surface PQRS and is appearance of equal and opposite charges on the face opposite to PQRS. A potential difference along the z-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.
17. Consider two different metallic strips (1 and 2) fo the same material. Their lengths are the same, width are w1 and w2 and thicknesses are d1 and d2, respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V1 and V2 are the potential differences between K and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is (are)
(A) 
(B) 
(C) 
(D) 
18. Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n1 and n2, respectively. Strip 1 is placed in magnetic field B1 and strip 2 is placed in magnetic field B2, both along positive y-directions. Then V1 and V2 are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is (are)
(A) 
(B) 
(C) 
(D) 
PARAGRAPH – 2
(19 to 20)
Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n1 surrounded by a medium of lower refractive index n2. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n1 and n2 as shown in the figure. All rays with the angle of incidence i less than a particular value im are confined in the medium of refractive index n1. The numerical aperture (NA) of the structure is defined as sin im.
19. For two structures namely S1 with 
and n2 = 3/2, and S2 with n1 = 8/5 and n2 = 7/5 and taking the refractive index of water to be 4/3 and that of air to be 1, the correct option(s) is (are)
(A) NA of 
immersed in water is the same as that of 
immersed in a liquid of refractive index 
(B) NA of 
immersed in liquid of refractive index 
is that as that of 
(C) NA of 
placed in air is the same as that of 
immersed in liquid of refractive index 
(D) NA of 
placed in air is the same as that of 
20. If two structures of same cross-sectional area, but different numerical apertures NA1 and NA2 (NA2 < NA1) are joined longitudinally, the numerical aperture of the combined structure is
(A) 
(B) 
(C) 
(D) 
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