1 A ball of mass 2kg is thrown from a tall building with velocity, v=$ (20 m/s)\hat{i}+(24 m/s)\hat{j}$ at time t=0 s. Change in the potential energy of the ball after, t=8 s is ( The ball is assumed to be in air during its motion between 0s and 8 s , $\hat{i}$ is along the horizontal and $\hat{j}$ is along the vertical direction. (Take $g=10 m/s^{2}$) A) -2.56 kJ B) 0.52 kJ C) 1.76 kJ D) -2.44 kJ
2 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
3 The magnitude of the force vector acting on a unit length of a thin wire carrying a current I= 8A at a point O, if the wire is bent as shown in the figure with a radius , $R=10 \pi$ cm is A) 64 $\mu N/m $ B) 32 $\mu N/m $ C) 20 $\mu N/m $ D) 100 $\mu N/m $
4 An inductor coil is connected to a capacitor and an AC source of rms voltage 8V in series . The rms current in the circuit is 16 A and is in phase with emf . If this inductor coil is connected to 6 V DC battery, the magnitude of steady current is A) 8 A B) 10 A C) 12 A D) 16 A
5 An electromagnetic wave of frequency 3.0 MHz passes from vacuum into a non-magnetic medium with permittivity, $\epsilon=16 \epsilon_{0}$ . where $ \epsilon_{0}$ is the free space permittivity. The change in wavelength is A) -75 m B) +75 m C) -50 m D) +50 m
6 The logic circuit below has the truth table same as that of A) NOR gate B) NAND gate C) AND gate D) OR gate
7 Which of the following represents fundamental force of nature ? A) Gravitational force, Coulomb's force : strong surface tension force; weak van der Waal's force B) Gravitational force; electromagnetic force; strong viscous force; weak nuclear force C) Gravitational force; magnetostatic force; strong nuclear force; weak frictional force D) Gravitational force; electromagnetic force; strong nuclear force; Weak nuclear force
8 A copper wire of cross-sectional area 0.01 cm2 is under a tension of 22 N. Find the percentage change in the cross-sectional area, (Young's modulus of copper =$1.1 \times 10^{11} N/m^{2}$ and Poisson's ratio =0.32) A) $12.6 \times 10^{-3}$ B) $8.6 \times 10^{-3}$ C) $6.4 \times 10^{-3}$ D) $2.8 \times 10^{-3}$
9 Statement A Convection involves the flow of matter within a fluid due to unequal temperature of its parts Statement B A hot bar placed under a running tap water loses heat due to the effect of convection with in water Statement C Heat transfer always involves temperature different between two systems. Identify the correct option A) A, B, C are true B) Only A and C are true C) Only A and B are true D) Only B and C are true
10 A body of mass 0.3 kg hangs by a spring with a force constant of 50N/m . The amplitude of oscillations is damped and reaches $\frac{1}{e}$ of its original value in about 100 oscillations. If $\omega$ and $\omega'$ are the angular frequencies of undamped and damped oscillations respectively , then percentage of $\left(\frac{\omega-\omega'}{\omega}\right)$ is A) $\left(\frac{1}{800 \pi}\right)$ B) $\left(\frac{\pi^{2}}{600 }\right)$ C) $\left(\frac{1}{800\pi^{2} }\right)$ D) $\left(\frac{\pi}{400 }\right)$
11 A water tank kept on the ground has an orifice of 2 mm diameter on the vertical side. What is the minimum height of the water above the orifice for which the output flow of water is found to be turbulent? [ Assume g=10 m/s2, $\rho_{water}$= 103 kg/m3, viscosity =1 centi-poise] A) 3 cm B) 4 cm C) 6 cm D) 2 cm
12 A drone fitted with siren in flying directly away from the drone operator and towards a distant building at a speed of 15 m/s . The siren produces the sound of frequency 780Hz. What is the frequency that the operator hears in the echo refected from the building,[ speed of sound is 340 m/s] A) 766 Hz B) 800 Hz C) 816Hz D) 840Hz
13 Assertion (A) Si and GaAs are the preferred materials for solar cells Reason (R) Both these materials have energy band gaps much below the energy level corresponding to the maximum solar irradiance in the solar spectrum The correct answer is A) (A) is correct but (R) is incorrect B) Both (A) and (R) are correct and (R0 is the correct explanation of (A) C) Both (A) and (R) are correct. but (R0 is not the correct explanation of (A) D) Both (A) and (R) are incorrect
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 boy standing on a moving truck throws a projectile such that he is able to catch it back after the truck has moved 100 m. if the truck is moving horizontally along a straight line with a constant speed 30 m/s, at what speed (relative to the truck) must the projectile is thrown.(Assume, g=10 m/s2) A) $\frac{55}{3} m/s$ B) $\frac{43}{2} m/s$ C) $\frac{50}{3} m/s$ D) $\frac{23}{3} m/s$
