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. \( 2{gH}={n}^2{u}^2\)

Two stones are thrown up simultaneously from the edge of a cliff \(240~\text{m}\) high with an initial speed of \(10~\text{m/s}\) and \(40~\text{m/s}\) respectively. Which of the following graph best represents the time variation of the relative position of the second stone with respect to the first?
(Assume stones do not rebound after hitting the ground and neglect air resistance, take
\(g= 10~\text{m/s}^2\)${\mathrm{}}^{}$)
(The figures are schematic and not drawn to scale)

1.		2.
3.		4.

A body is thrown vertically upwards. Which one of the following graphs correctly represents the velocity vs time?

1.		2.
3.		4.

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)

A ball is thrown vertically up (taken as \(+z\)-axis) from the ground. The correct momentum\(\text-\)height (\(p\text{-}h\)) diagram is:

1.		2.
3.		4.

The position of a particle as a function of time \(t\), is given by;
\(x(t)=a t+b t^2-c t^3\)
where \(a\), \(b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be:
1. \( a+\frac{b^2}{4 c} \)
2. \( a+\frac{b^2}{c} \)
3. \( a+\frac{b^2}{3 c} \)
4. \( a+\frac{b^2}{2 c}\)