PART I – PHYSICS
Section-1
•This section contains FIVE questions
• Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.
1. A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular prism of refractive index n = √ Light undergoes total internal reflection in the prism at the face PR when α has a minimum value of 45°. The angle θ of the prism is
(A) 15°
(B) 22.5°
(C) 30°
(D) 45°
2. In a historical experiment to determine Planck’s constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (λ) of incident light and the corresponding stopping potential (V0) are given below:
Given that c = 3 × 108 m s−1 and e = 1.6 × 10−19 C, Planck’s constant (in units of J s) found from such an experiment is
(A) 6.0 × 10−34
(B) 6.4 × 10−34
(C) 6.6 × 10−34
(D) 6.8 × 10−34
3. A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30℃and the entire stored 120 litres of water is initially cooled to 10℃. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is
(Specific heat of water is 4.2 kJ kg−1 K−1 and the density of water is 1000 kg m−3)
(A) 1600
(B) 2067
(C) 2533
(D) 3933
4. An infinite line charge of uniform electric charge density λ lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity ε and electrical conductivity σ. The electrical conduction in the material follows Ohm’s law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?
(A) 
(B) 
(C) 
(D) 
5. A uniform wooden stick of mass 1.6 kg and length ℓ rests in an inclined manner on a smooth, vertical wall of height h(< ℓ) such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of 30° with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the tick is equal in magnitude to the reaction of the floor on the stick. The ratio
(g = 10 ms−2)
(A) 
(B) 
(C) 
(D) 
SECTION 2
• 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.
6. The position vector 
of a particle of mass m is given by the following equation
Where α = 10/3 ms−3, β = 5 ms−2 and m = 0.1 kg. At t = 1 s, which of the following statement (s) is (are) true about the particle?
(A) The velocity 
(B) The angular momentum 
with respect to the origin is given by 
(C) The force 
(D) The torque 
with respect to the origin is given by 
7. A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2(> n1), as shown in the figure. A ray of light is incident with angle θi from medium 1 and emerges in medium 2 with refraction and θf with a lateral displacement ℓ.
Which of the following statement (s) is (are) true ?
(A) ℓ is independent of n2
(B) n1 sin θi = n2 sin θf
(C) ℓ is dependent on n(z)
(D) n1 sin θi = (n2 – n1) sin θf
8. A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is(are) true?
(A) The refractive index of the lens is 2.5
(B) The radius of curvature of the convex surface is 45 cm
(C) The faint image is erect and real
(D) The focal length of the lens is 20 cm
9. Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n >>1. Which of the following statement(s) is(are) true?
(A) Relative change in the radii of two consecutive orbitals does not depend on Z
(B) Relative change in the radii of two consecutive orbitals varies as 1/n
(C) Relative change in the energy of two consecutive orbitals varies as 1/n3
(D) Relative change in the angular momenta of two consecutive orbitals varies as 1/n
10. A length-side (ℓ) depends on the permittivity (ε) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for ℓ is(are) dimensionally correct?
(A) 
(B) 
(C) 
(D) 
11. Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vP, vQ and vR be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 m/s. Which of the following statement(s) is(are) true regarding the sound heard by the person?
(A) The plot below represents schematically the variation of beat frequency with time 
(B) vP + vR = 2vQ
(C) The plot below represents schematically the variation of beat frequency with time 
(D) The rate of change in beat frequency is maximum when the car passes through Q.
12. A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90° vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 A s−1. Which of the following statement(s) is(are) true?
(A) The induced current in the wire is in opposite direction to the current along the hypotenuse
(B) The magnitude of induced emf in the wire is (μ0/π) volt
(C) There is a repulsive force between the wire and the loop
(D) If the loop is rotated at a constant angular speed about the wire, an additional emf of (μ0/π) volt is induced in the wire
Answer: (B, C)
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13. An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?
(A) The temperature distribution over the filament is uniform
(B) The resistance over small sections of the filament decreases with time
(C) The filament emits more light at higher band of frequencies before it breaks up
(D) The filament consumes less electrical power towards the end of the life of the bulb
SECTION 3
•This section contains FIVE questions.
• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.
14. The inductor L1 (inductance 1 mH, internal resistance 3 Ω) and L2 (inductance 2 mH, internal resistance 4 Ω), and a resistor R (resistance 12 Ω) are all connected in parallel across a 5 V battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (Imax/Imin) drawn from the battery is
15. A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has scale that displays log2(P/P0), where P0 is a constant. When the metal surface is at a temperature of 487℃, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767℃?
16. A hydrogen atom in its ground state is irradiated by light of wavelength 970A. Taking hc/e = 1.237 × 10−6 eVm and the ground state energy of hydrogen atom as −13.6 eV, the number of lines present in the emission spectrum is
17. Consider two solid spheres P and Q each of density 8 gm cm−3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 08. gm cm−3 and viscosity η = 3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm−3 and viscosity η = 2 poiseulles. The ratio of the terminal velocities of P and Q is
18. The isotope 
having a mass 12.014 u undergoes β-decay to 
has an excited state of nucleus 
at 4.041 MeV above its ground state. If 
decays to 
, the (1 u = 931.5 MeV/c2), where c is the speed of light in vacuum)
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