1 Ball-I is dropped from the top of a building from rest . At the same moment, ball -2 is thrown upward towards ball -1 with a speed 14 m/s from a point 21 m below the top of building . How far will the ball -1 have dropped when it passes ball-2, (Assume , acceleration due to gravity , g=10 $m/s^{2}$) A) $\frac{45}{4}$ m B) $\frac{52}{6}$ m C) $\frac{37}{2}$ m D) $\frac{25}{2}$ m
2 A vertical spring mass system has the same line period as simple pendulum undergoing small oscillations .Now , both of them are put in an elevator going downwards with an acceleration 5 m/s2 . The ratio of time period of the spring mass system to the time period of the pendulum is (Assume, acceleration due to gravity , g= 10 m/s2) A) $\sqrt{\frac{3}{2}}$ B) $\sqrt{\frac{2}{3}}$ C) $\frac{1}{\sqrt{2}}$ D) $\sqrt{2}$
3 Consider a spherical planet which is rotating about its axis such that the speed of a point on its equator is v and the effective acceleration due to gravity on the equator is $\frac{1}{3}$ of its value at the poles. What is the escape velocity for a particular at the pole of this planet A) 3 v B) 2 v C) $\sqrt{3}$ v D) $\sqrt{2}$ v
4 In Young's double slit experiment, mth order and n th order of bright fringes are formed at point P on a distant screen if monochromatic source of wavelength 400 nm and 600 nm are used respectively . The minimum vale of m and n are respectively , A) 4.6 B) 3.2 C) 2.3 D) 4.2
5 The space between the two large parallel plates is filled with a material of uniform charge density $\rho$ . Assume that one of the plate is kept at x=0 . The potential at any point x between these plates is given by (A and B are constants) A) $-\frac{\rho x^{3}}{2\epsilon_{0}}$ B) $-\left(\frac{\rho x^{2}}{2\epsilon_{0}}+Ax\right)$ C) $-\left(\frac{\rho x^{2}}{2\epsilon_{0}}+Ax+B\right)$ D) $-\left(\frac{\rho x^{3}}{4\epsilon_{0}}+Ax^{2}+Bx\right)$
6 The collision of an electron with kinetic energy 5.5 eV and a hydrogen atom in its ground state can be described as A) completely inelastic B) may be completely inelastic C) may be partially elastic D) elastic
7 The logic circuit below has the truth table same as that of A) NOR gate B) NAND gate C) AND gate D) OR gate
8 A ball is projected vertically up from ground. Boy A standing at the window of first floor of a nearby building observes that the time interval between the ball crossing him while going up and the ball crossing him while going down is 2s . Another boy B standing on the second floor notices that time interval between the ball passing him twice, during up motion and down motion is 1s . Calculate the difference between the vertical positions of boy B and boy A (Assume , acceleration due to gravity ,g=10 m/s2) A) 8.45 m B) 3.75 m C) 4.25 m D) 2.50 m
9 A solid spherical ball rolls on a horizontal surface at 10 m/s and continuous to roll up on an inclined surface as shown in the figure.If the mass of balls is 11 kg and frictional losses are negligible, the value of h where the ball stop and starts rolling down the inclination is (Assume , g =10 m/s2 ) A) 8 m B) 6 m C) 7 m D) 10 m
10 Albert Einstein was confirmed with the Nobel prize physics for his work on A) special theory of relativity B) Bose-Einstein statistics C) photoelectric effect D) general realtivity
11 A rocket motor consumes 100 kg of fuel per second exhausting it with a speed of 5 km/s. The speed of the rocket when its mass is reduced to $\frac{1}{20}^{th}$ of its initial mass, is [Assume initial speed to be zero and ignored gravitational and viscous forces] A) 20 km/s B) 40 in (2) km/s C) 5 in (20) km/s D) 10 in (10) km/s
12 Identify the correct option A) The rang of the gravitonal force is large but not infinite B) The range of electromagnetic force is large but lesser than the range of gravitational force C) The range of weak nuclear force is smaller than the range of strong nuclear force, gravitation force and electromagnetic force D) The range of the weak as well as strong nuclear force is of the the order of $10^{-10}$ m
13 A current carrying conductor obeys Ohm's law (V= RI). If the current passing through the conductor is $l=(5\pm0.2)$A and voltage developed is $V=(60\pm6)$ V , then find the percentage of error is resistance, R A) 18 B) 6 C) 14 D) 2
14 An iron rod of length 1.5 m lying on a horizontal table is pulled up from one end along a vertical line so as to move it with a constant velocity 3 m/s. while the other end of the rod slides along the floor. After how much time the speed of the end sliding on the floor equals to the speed of the end being pulled up A) $\frac{1}{2\sqrt{2}}s$ B) $\frac{1}{\sqrt{2}}s$ C) $3\sqrt{2}$s D) $\frac{1}{4}$
15 A person applies a sine wave and square wave to an AND gate as shown in the figure (i) and (ii) . Assuming that both the voltages are applied in phase , the person observers the output at E and F on (i) and (ii) , respectively. [Assume minimum voltage of 5V is equivalent to logic (i)] A) Sqaure wave at 50 Hz and square wave at 100 Hz B) Sine wave at 50 Hz and square wave at 100 Hz C) No output and sine wave at 100 Hz D) No output and pulsed wave at 100 Hz
