A ball is thrown upward with a certain speed. It passes through the same point at \(3\) second and \(7\) second from the start. The maximum height achieved by the ball is:

1.  \(500\text{ m}\)

2.  \(250\text{ m}\)

3.  \(125\text{ m}\)

4.  \(450\text{ m}\)

A body is thrown vertically up to reach its maximum height in \(t\) seconds. The total time from the time of projection to reach a point at half of its maximum height while returning (in seconds) is:

1. \(\sqrt2\ t\)

2. \(\left(1+\dfrac{1}{\sqrt2}\right)t\)

3. \(\dfrac{3t}{2}\)

4. \(\dfrac{t}{\sqrt2}\)

A stone falls freely from rest from a height \(h\) and it travels a distance \(\dfrac{9h}{25}\) in the last second. The value of \(h\) is: (Take \(g=10\ \text{m/s}^2\))

1. \(145\ \text{m}\)

2. \(100\ \text{m}\)

3. \(125\ \text{m}\)

4. \(200 \ \text{m}\)

A bullet loses \(\dfrac{1}{20}\) of its velocity passing through a plank. The least number of planks required to stop the bullet is: (All planks offers same retardation)
1. \(10\)
2. \(11\)
3. \(12\)
4. \(23\)

A point moves with uniform acceleration, and \(v_1,\ v_2\) and \(v_3\) denote the average velocities in the three successive intervals of time \(t_1,\ t_2\) and \(t_3\). Which of the following relations is correct?

1. \((v_1 - v_2):(v_2 - v_3) = (t_1 - t_2):(t_2 + t_3)\)
2. \((v_1 - v_2):(v_2 - v_3) = (t_1 + t_2):(t_2 + t_3)\)
3. \((v_1 - v_2):(v_2 - v_3) = (t_1 - t_2):(t_2 - t_3)\)
4. \((v_1 - v_2):(v_2 - v_3) = (t_1 + t_2):(t_2 - t_3)\)