1 Match the following fundamental forces of nature with their relative strength . A) A:II,B:IV,C:I,D:III B) A:III ,B:II,C:IV, D:I C) A:II,B:III,C:IV,D:I D) A:IV,B:II,C:I,D:II
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 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
5 A mass of 2kg initially at a height of 1.2 m above an uncompressed spring with spring constant $2 \times 10^{4} $ N/m, is released from rest to fall on the spring. Taking the acceleration due to gravity as 10 m/s2 and neglecting the air resistance, the compression of the spring in mm is A) 20 B) 40 C) 50 D) 60
6 An ideal gas is placed in a tank at $27^{0} C$. The pressure is initially 600 kPa. One-fourth of the gas is then released from the tank and thermal equilibrium is established. What will be the pressure if the temperature is $327^{0}$ C? A) 900 kPa B) 1000 kPa C) 1050 kPa D) 1250 kPa
7 In Young's double-slit experiment , a thin sheet of refractive index 1.6 is used to cover one slit while a thin the sheet of refractive index 1.3 is used to cover the second slit. The thickness of both the sheets are same and the wavelength of light used in 600nm. If the central point on the screen is now occupied by what had been the 10th bright fringe (m=10) , then the thickness of covering sheets is A) 50$\mu$ m B) 8$\mu$ m C) 20$\mu$ m D) 40$\mu$ m
8 A particle A moves along the line, y=30m with a constant velocity, v parallel to the x-axis. At the momemt particle A passes the y-axis, particle B starts from the origin witrh zero initial speed and a constant acceleration .$a=0.40 m/sec^{2}$ . The angle between a and y-axis is $60^{0}$. If the particles A and B collide after sometimes , then the value of |v| will be A) 2 m/s B) 3 m/s C) 4 m/s D) 5 m/s
9 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
10 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
11 For the circuit shown in the figure, calculate the resistance between points A and B A) 0.5 R B) R C) 15 R D) $\frac{6}{5}R$
12 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) $\frac{1}{4}$
13 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) $\frac{23}{3} m/s$
14 Consider a toroid with rectangular cross-section, of inner radius a, outer radius b and height h, carrying n number of turns. Then the self-inductance of the toroidal coil when current I passing through the toroid is A) $\frac{\mu_{0}n^{2}h}{2 \pi}ln\left(\frac{b}{a}\right)$ B) $\frac{\mu_{0}n^{}h}{2 \pi}ln\left(\frac{b}{a}\right)$ C) $\frac{\mu_{0}n^{2}h}{2 \pi}ln\left(\frac{a}{b}\right)$ D) $\frac{\mu_{0}n^{}h}{2 \pi}ln\left(\frac{a}{b}\right)$
15 A message signal is used to modulate a carrier signal of frequency 5 MHz and peak voltage of 40 V . In the process, two side-bands are produced separated by 40 kHz. If the modulation index is 0.75, then the peak voltage and frequency of the messages signal, respectively are A) 60 V, 10 kHz B) 60 V, 20 kHz C) 30 V, 10 kHz D) 30V, 20 kHz
