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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

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

For the circuits A and B as shown in the figure, identify the correct option

A) Circuit A is for accurate measurement of high resistance and B is for low resistance

B) Circuit A is for accurate measurement of low resistance and B is for high resistance

C) Both circuits can accurately measured high resistance only

D) Both circuits can accurately measured low resistance only

The logic circuit below has the truth table same as that of

A) NOR gate

B) NAND gate

C) AND gate

D) OR gate

Consider a car initially at rest, starts to move along a straight road first with acceleration 5 m/s² , then with uniform velocity and finally, decelerating at 5 m/s², before coming to a stop. Total time taken from start to end is t=25 s. If the average velocity during that time is 72 km/hr, the car moved with uniform velocity for a time of

A) 15 s

B) 30s

C) 155 s

D) 2s

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

Find the potential difference between a and b as shown in the below circuit

A) 165 V

B) 198 V

C) 213 V

D) 224 V

A photodiode sensor is used to measure the output of a 300W lamp kept 10 m away. The sensor has an opening of 2 cm in diameter. How many photons enter the sensor if the wavelength of the light is 660 nm and the exposure time is 100 ms.(Assume that all the energy of the lamp is given off as light and h=$6.6 \times 10^{-34}$ Js)

A) $3.6 \times 10^{13}$

B) $2.8 \times 10^{13}$

C) $2.5 \times 10^{13}$

D) $1.8 \times 10^{13}$

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

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

A carnot engine with efficiency $\eta$ operates between two heat reservoirs with temperatures $T_{1}$ and $T_{2}$ , where $T_{1} >T_{2}$ . If only $T_{1}$ is changed by 0.4% , the change in efficiency is $\triangle\eta_{1}$ , whereas if only $T_{2}$ is changed by 0.2% , the efficiency is changed by $\triangle\eta_{2}$ . The ratio $\frac{\triangle\eta_{1}}{\triangle\eta_{2}}$ is approximately

A) -2

B) -4

C) +3

D) +4

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) $\frac{6}{5}R$

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

Two particles carrying equal charges move parallel to each other with the speed 150 km/s. If $F_{1}$ and $F_{2}$ are magnetic and electric forces between two charged particles then

$\frac{|F_{1}|}{|F_{2}|}$ is $\left( Let \mu_{0}\epsilon_{0}=\frac{1}{9 \times 10^{16}} s^{2}/m^{2}\right)$

A) $1.0 \times 10^{-6}$

B) $1.5 \times 10^{-7}$

C) $3.0 \times 10^{-6}$

D) $2.5 \times 10^{-7}$

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) $\frac{\mu_{0}n^{}h}{2 \pi}ln\left(\frac{a}{b}\right)$

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