1 Two thin lenses are in contact and the focal length of the combination is 80 cm. If the focal length of one lens is 20 cm, then the power of the other lens will be A) 1.66D B) 4.00D C) -100D D) -3.75D
2 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
3 The velocity-time graph of a body moving in a straight line is shown in fig. Find the displacement and distance travelled by the body in 10 seconds A) 50 m, 90m B) 5m , 9m C) 9m , 5m D) 90m , 50m
4 A person swims in a river aiming to reach exactly on the opposite point on the bank of a river His speed of swimming is 0.5 m/s at an angle of 120° with the direction of flow of water. The speed of water is A) 1.0m/s B) 0.5m/s C) 0.25m/s D) 0.43m/s
5 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) $\frac{\left(\theta_{1}R_{2}+ \theta_{2}R_{1}\right)}{R_{1}+ R_{2}}$
6 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
7 The Young's modulus of a perfectly rigid body is A) Unity B) Zero C) Infinity D) Some finite non zero constant
8 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) $\pi r, r$
9 A solid cylinder of mass m and radius R rolls down the inclined plane without slipping. The speed of its C.M. when it reaches the bottom is A) $\sqrt{2gh}$ B) $\sqrt{\frac{4gh}{3}}$ C) $\sqrt{\frac{3}{4gh}}$ D) $\sqrt{4gh}$
10 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
11 A and B are two wires. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is A) equal to that on A B) four times that on A C) two times that on A D) half that on A
12 A liquid is allowed to flow into a tube of truncated cone shape. Identify the correct statement from the following. A) The speed is high at the wider end and low at the narrow end B) The speed is low at the wider end and high at the narrow end. C) The speed is same at both ends in a stream line flow. D) The liquid flows with uniform velocity in the tube
13 A planet revolves in an elliptical orbit around the sun. The semi-major and semi-minor axes are a and b. Then the square of time period T is directly proportional to A) $a^{3}$ B) $b^{3}$ C) $\left(\frac{a + b}{2}\right)^3$ D) $\left(\frac{a - b}{2}\right)^3$
14 Tube A has both ends open while tube B has one end closed, otherwise, they are identical. The ratio of the fundamental frequency of tube 'A and B' is A) 1 : 2 B) 1 : 4 C) 2 : 1 D) 4 : 1
15 In Young's double-slit experimental setup if the wavelength alone is doubled, the bandwidth β becomes A) $\frac{\beta}{2}$ B) $2\beta$ C) $3\beta$ D) $\beta$