Section A |

**1. The mass density of a spherical galaxy varies as k/r over a large distanceʻr’ from its center. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as:**

(1)

(2) T² ∝ R

(3) T ∝ R

(4) T² ∝ R³

**2. An amplitude modulated wave is represented by expression Vm = 5 (1 +0.6 cos 6280 t) sin (211 x 10⁴t) volts. The minimum and maximum amplitudes of the amplitude modulated wave are, respectively :**

(1) 5 V, 8 V

(2) 5/2 V,8 V

(3) 3 V,5 V

(4) 3/2 V,5 V

**3. A spherical mirror is obtained as shown in the figure from a hollow glass sphere. if an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale).**

(1) Inverted, real and magnified

(2) Erect, virtual and unmagnified

(3) Inverted, real and unmagnified

(4) Erect, virtual and magnified

**4. A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is a rad s-¹. The difference in the height, h (incm) of liquid at the centre of vessel and at the side will be :**

**5. If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be:**

(1) FA²v^{–}³

(2) FA²v^{–}¹

(3) FA²v^{–}²

(4) FA^{–}¹v⁰

**6. A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = Cx² and rotating with angular speed ω (see figure). The value of is (neglect friction)**

**7. Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required ?**

(1) T: Large retentivity, large coercivity

(2) P: Large retentivity, large coercivity

(3) T: Large retentivity, small coercivity

(4) T: Small retentivity, large coercivity

**8. Interference fringes are observed on a screen
by illuminating two thin slits 1 mm apart with a light source (λ = 632.8 nm). The distance between the screen and the slits is 100 cm. If a bright fringe is observed on a screen at distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close to :**

(1) 2.87nm

(2) 2 nm

(3) 1.27 μm

(4) 2.05 μm

**9. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :**

(1) 15

(2) 13

(3) 20

(4) 11

**10. A plane electromagnetic wave, ha frequency of 2.0 x 10¹⁰ Hz and its enero density is 1.02 X 10 ^{–}⁸ J/m³ in vacuum. TÁ amplitude of the magnetic field of the wave is close to and speed of light = 3 x 108 m s^{–}¹):**

(1) 160 nT

(2) 180 nT

(3) 190 nT

(4) 150 nT

**11. Consider four conducting materials copper. tungsten, mercury and aluminium with resistivity ρ _{C}, ρ_{T}, ρ_{M} and pa respectively. Then :**

(1) ρ_{C} > ρ_{A} > ρ_{T}

(2) ρ_{A} > ρ_{T} > ρ_{C}

(3) ρ_{A} > ρ_{M} > ρ_{C}

(4) ρ_{M} > ρ_{A} > ρ_{C}

**12. A beam of protons with speed 4 x 10⁵ ms ^{–}¹ enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to : (Mass of the proton = 1.67 x 10^{–}²⁷ kg, charge of the proton = 1.69 x 10¹⁹C)**

(1) 12 cm

(2) 2 cm

(3) 4 cm

(4) 5 cm

**13. Two identical strings X and Z made of same material have tension T _{x} and T_{z} in them If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio T_{x}/T_{z} is :**

(1) 1.25

(2) 0.44

(3) 1.5

(4) 2.25

**14. A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:
**

**15. In a reactor, 2 kg of ₉₂U²³⁵ fuel is fully used up in 30 days. The energy released per fission is 200 MeV given that the Avogadro number, N = 6.023 x 10²⁶ per kilo mole and 1 eV = 1.6 x 10 ^{–}¹⁹) J. The power output of the reactor is close to :**

(1) 54 MW

(2) 60 MW

(3) 125 MW

(4) 35 MW

**16. A charged particle (mass m and charge q) moves along X axis with velocity V₀. When it passes through the origin it enters a region having uniform electric field which extends upto x = d. Equation of path of electron in the region x > d is :
**

**17. Train A and train B are running on parallel tracks in opposite directions with speeds 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/hour. Speed (in ms ^{–}¹) of this person as observed from train B will be close to :
(take the distance between the tracks as negligible)**

(1) 30.5 m s^{–}¹

(2) 29.5 m s^{–}¹

(3) 31.5 m s^{–}¹

(4) 28.5 m s^{–}¹

**18. Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass m’ and has another weight of mass 2m hung at a distance of 75 cm from A. The tension in the string at Ais :**

(1) 0.75 mg

(2) 1 mg

(3) 0.5 mg

(4) 2 mg

**19. The least count of the main scale of a vernier callipers is 1 mm . Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7 _{th} division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4_{th} VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)**

(1) 2.99 cm

(2) 3.07 cm

(3) 3.21 cm

(4) 3.2 cm

**20. A particle of mass m with an initial velocity ui collides perfectly elastically with a mass 3m at rest. It moves with a velocity uj after collision, then, v is given by :**

Section B |

**21. A small block starts slipping down from a point B on an inclined plane AB, which is making an angle A with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction u. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by μ = k tan θ. The value of k is ……..**

**22. An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to1/10 ^{th} of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ……….**

**23. When radiation of wavelength λ is used to illuminate a metallic surface, the stopping potential is V. When the same surface is
V
illuminated with radiation of wavelength 3λ, the stopping potential is V/4. If the threshold wavelength for the metallic surface is nλ then value of n will be :**

**24. A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 x 10 ^{–}⁵ T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced
(in μV) in the coil will be close to the integer…..**

**25. A 5μF capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 μF capacitor. If the energy change during the charge redistribution is X/100 J then value of X to the nearest integer is :**