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. \(\frac{3}{5}\)
2. \(\frac{2}{5}\)
3. \(\frac{1}{5}\)
4. \(\frac{4}{5}\)

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