1 The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then A) the resistance and the specific resistance, will both remain unchanged B) the resistance will be doubled and the specific resistance will be halved C) the resistance will be halved and the specific resistance will remain unchanged D) the resistance will be halved and the specific resistance will be doubled
2 If the kinetic energy of a free electron doubles, it's de-Broglie wavelength changes by the factor A) 2 B) $\frac{1}{2}$ C) $\sqrt{2}$ D) $\frac{1}{\sqrt{2}}$
3 The ratio of the energies of the hydrogen atom in its first to second excited states is A) $\frac{1}{4}$ B) $\frac{4}{9}$ C) $\frac{9}{4}$ D) 4
4 The equivalent capacitance of the combination of the capacitors is A) 3.20µF B) 7.80µF C) 3.90µF D) 2.16µF
5 The half-life period and the mean life period of a radioactive element are denoted respectively by Th and Tm. Then A) $T_{h} = T_{m}$ B) $T_{h}>T_{m}$ C) $T_{h}<T_{m}$ D) $T_{h}\geq T_{m}$
6 Consider a pair of insulating blocks with thermal resistances R1 and R2 as shown in the figure. The temperature θ at the boundary between the two blocks is A) $\frac{\theta_{1}\theta_{2}\sqrt{R_{1}R_{2}}}{(\theta_{1}+\theta_{2})(R_{1}+R_{2})}$ B) $\frac{\theta_{1}R_{1}+ \theta_{2}R_{2}}{(R_{1}+R_{2})}$ C) $\frac{\left[\left(\theta_{1}+ \theta_{2}\right) R_{1}R_{2}\right]}{\left(R_1^2+ R_2^2\right)}$ D) $\frac{\left(\theta_{1}R_{2}+ \theta_{2}R_{1}\right)}{R_{1}+ R_{2}}$
7 A mass of 0.5 kg moving with a speed of 1.5 m/ s on a horizontal smooth surface, collides with a nearly weightless spring of force constant k: 50N/m. The maximum compression of the spring would be A) 0.5m B) 0.15m C) 0.12m D) 1.5m
8 The Young's modulus of a perfectly rigid body is A) Unity B) Zero C) Infinity D) Some finite non zero constant
9 A particle covers half of the circle of radius r. Then the displacement and distance of the particle are respectively A) $2\pi r, 0$ B) $2r, \pi r$ C) $\frac{\pi r}{2}$, 2r D) $\pi r, r$
10 A metal ring is held horizontally and the bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet A) is equal to g B) is less than g C) is more than g D) depends on the diameter of ring and length of magnet
11 For a series RLC circuit R = XL = 2Xc. The impedance of the circuit and phase difference between V and I respectively will be A) $\frac{\sqrt{5}r}{2}$, $\tan^{-1}$(2) B) $\frac{\sqrt{5}r}{2}$, $\tan^{-1}$ $\frac{1}{2}$ C) $\sqrt{5X_{c}}$, $\tan^{-1}$(2) D) $\sqrt{5R}$, $\tan^{-1}$ $\frac{1}{2}$
12 A man holding a rifle (mass of person and rifle together is 100kg) stands on a smooth surface and fires 10 shots horizontally in 5 sec. Each bullet has a mass of 10 g with a muzzle velocity of 800 ms-1 . The velocity which the rifleman attains after firing 10 shots will be A) 8 m/s B) 0.8m/s C) 0.08 m/s D) -0.8m/s
13 Escape velocity when a body of mass m is thrown vertically from the surface of the earth is v, what will be the escape velocity of another body of mass 4 m is thrown vertically A) v B) 2v C) 4v D) None of these
14 A block of mass 5 kg resting on a horizontal surface is connected by a cord, passing over a light frictionless pulley to a hanging block of mass 5 kg. The coefficient of kinetic friction between the block and the surface is 0.5. Tension in the cord is : (g = 9.8 m/sec2) A) 49 N B) Zero C) 36.75 N D) 2.45 N