From a tower of height \(H\), a particle is thrown vertically upwards with a speed \(u\). The time taken by the particle, to hit the ground, is \(n\) times that taken by it to reach the highest point of its path. The relation between \(H,u\) and \(n\) is:
1. \( g H=(n-2)^2 u^2 \)
2. \( 2{gH}={nu}^2({n}-2) \)
3. \( g H=(n-2) u^2 \)
4. \( 2{gH}={n}^2{u}^2\)

The four graphs below are intended to represent the same motion. However, one of them is incorrect. Identify the graph that does not accurately depict the motion.

1.		2.
3.		4.

A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(x\text-\)axis. Identify all figures that correctly represent the motion qualitatively.
(\(a=\) acceleration, \(v=\) velocity, \(x=\) displacement, \(t=\) time)

(A)		(B)
(C)		(D)

An engine of a train moving with uniform acceleration passes the signal post with velocity \(u\) and the last compartment passes the same post with velocity \(v\). The velocity with which the middle point of the train passes the signal post is:
1. \(\sqrt{\dfrac{v^2+u^2}{2}}\)
2. \(\dfrac{v-u}{2}\)
3. \(\dfrac{v+u}{2}\)
4. \(\sqrt{\dfrac{v^2-u^2}{2}}\)

A stone is dropped from the top of a building. When it crosses a point \(5\) m below the top, another stone starts to fall from a point \(25\) m below the top. Both stones reach the bottom of the building simultaneously. The height of the building is:
1. \(35~\text{m}\)
2. \(45~\text{m}\)
3. \(50~\text{m}\)
4. \(25~\text{m}\)