If $x$ $=$ $3$ $-4t^2$ $+$ $t^3$, then work done in the first 4s will be:
(Mass of the particle is 3 gram)
1.  384 mJ
2.  168 mJ
3.  192 mJ
4.  None of the above

Two identical balls A and B are moving with velocity $+0.5$ $m{s}^{-1}$ and $-0.3$ $m{s}^{-1}$ respectively. If they collide head on elastically, then their velocities after collision will be:

1. $-0.3$ $m{s}^{-1}$ $and$ $0.5$ $m{s}^{-1}$

2. $+0.5$ $m{s}^{-1}$ $and$ $+$ $0.3$ $m{s}^{-1}$

3. $-0.4$ $m{s}^{-1}$ $and$ $0.3$ $m{s}^{-1}$

4. $-0.3$ $m{s}^{-1}$ $and$ $-0.4$ $m{s}^{-1}$

A ball is dropped from a height of $5~\text {m}.$ If it rebounds up to a height of $1.8~\text {m},$ then the ratio of velocities of the ball after and before the rebound will be:
1. $\dfrac{3}{5}$

2. $\dfrac{2}{5}$

3. $\dfrac{1}{5}$

4. $\dfrac{4}{5}$

The kinetic energy of a person is just half of the kinetic energy of a boy whose mass is just half of that person. If the person increases his speed by $1~\text{m/s},$ then his ​​​​​​​kinetic energy equals to that of the boy, then the initial speed of the person was:
1. $\left( \sqrt{2}+1 \right)~\text{m/s}$
2. $\left( 2+\sqrt{2} \right)~\text{m/s}$
3. $2\left( 2+\sqrt{2} \right)~\text{m/s}$
4. none of the above

A particle projected with velocity 'u' makes an angle θ with respect to horizontal. Now it breaks in two identical parts at highest point of trajectory. If one part retraces its path, then velocity of the other part is:
1. 3u cos θ
2. 2u cos θ
3. u cos θ
4. u

If two springs, A and B $(K_A$ $=$ $2$ $K_B),$ are stretched by the same suspended weights, then the ratio of work done in stretching is equal to:
1.  1 : 2
2.  2 : 1
3.  1 : 1
4.  1 : 4

When a spring is subjected to 4 N force, its length is a metre and if 5 N is applied, its length is b metre. If 9 N is applied, its length will be:

1.  4b – 3a

2.  5b – a

3.  5b – 4a

4.  5b – 2a

The bob of a simple pendulum having length $l,$ is displaced from the mean position to an angular position $\theta$ with respect to vertical. If it is released, then the velocity of the bob at the lowest position will be:

1. $\sqrt{2 g l \left(\right. 1 - \cos \theta \left.\right)}$
2. $\sqrt{2 g l \left(\right. 1 + \cos\theta)}$
3. $\sqrt{2 g l\cos\theta}$
4. $\sqrt{2 g l}$

If $\vec{F} = (60\hat{i} + 15\hat{j}-3\hat{k})$ N and $\vec{v} = (2\hat{i} - 4\hat{j}+5\hat{k})$ m/s, then instantaneous power is:
1. $195$ watt
2. $45$ watt
3. $75$ watt
4. $100$ watt

A child is sitting on a swing. Its minimum and maximum heights from the ground are $0.75$ m and $2$ m, respectively. Its maximum speed will be: (take $g=10$ m/s²)
1. $10$ m/s
2. $5$ m/s
3. $8$ m/s
4. $15$ m/s