Examples

Q.

A small ball is projected horizontally between two large blocks. The ball is given a velocity $V$ m/s and each of the large blocks move uniformly with a velocity of $2V$ m/s. The ball collides elastically with the blocks. If the velocity of the blocks do not change due to the collision, then find out the velocity of the ball after the $2^{nd}$ collision.

1. 5V

2. 7V

3. 9V

4. None of these

Q.

The charge flown through a circuit in the time interval between t and t+dt is given by $dq=e^{-t/\tau }dt$, where $\tau$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $\tau$

1. 

2. 

3. 

4. None of these

Q.

From a stationary tank of mass 125000 pound a small shell of mass 25 pound is fired with a muzzle velocity of 1000 ft/sec. The tank recoils with a velocity of

1. 0.1 ft/sec

2. 0.2 ft/sec

3. 0.4 ft/sec

4. 0.8 ft/sec

Q. A rocket which is ejecting gas with a speed of $100\text{m/s}$ and the rate of ejection of the gas from the rocket is $800\text{kg/s}$. If the mass of the rocket is $4000\text{kg}$, find out the initial acceleration of the rocket. Take $(g=10{\text{m/s}}^2)$

1. $8{\text{m/s}}^2$
2. $6{\text{m/s}}^2$
3. $12{\text{m/s}}^2$
4. $10{\text{m/s}}^2$

Q. Find the integration of $\int \frac{e^{{\sin }^{-1}x}}{\sqrt{1-x^2}}.dx$

1. $e^{{\sin }^{-1}x}+C$
2. $e^{-{\sin }^{-1}x}+C$
3. $\frac{e^{{\sin }^{-1}x}}{2}+C$
4. $e^{\sin x}+C$

Q.

The charge flown through a circuit in the time interval between t and t+dt is given by $dq=e^{-t/\tau }dt$, where $\tau$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $\tau$

1. $\tau (\frac{1}{e}-1)$

2. $\tau (1-\frac{1}{e})$

3. $\tau (1+\frac{1}{e})$

4. None of these

Q. Find the integral of $\int \frac{dx}{(x+1)(x+2)}$

1. $\log \frac{x+2}{x+1}+C$
2. $\log (x+1)+\log (x+2)+C$
3. $\log \frac{x+1}{x+2}+C$
4. $\log \frac{x}{x+2}+C$

Q.

Figure shows the curve $y=x^2$.Find the area of the shaded part between $x=0$ and $x=6$

1. $216uni{t}^2$

2. $72uni{t}^2$

3. $12uni{t}^2$

4. None of these

Q. Find the integral of $\int \frac{1}{(x+2)(x+3)}dx$

1. ${\log }_e\frac{(x+2)}{(x+3)}+C$
2. ${\log }_e(x+2)+{\log }_e(x+3)+C$
3. ${\log }_e\frac{(x+3)}{(x+2)}+C$
4. None of these

Q. The work done by a force on a body, over a closed loop, is not always zero.

1. False
2. True