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 m

2.  250 m

3.  125 m

4.  450 m

A point moves in a straight line under the retardation a${\mathrm{v}}^2$. If the initial velocity is u, the distance covered in 't' seconds is-

1.  $\mathrm{aut}$

2.  $\frac{1}{\mathrm{a}}\ln \left(\mathrm{aut}\right)$

3.  $\frac{1}{\mathrm{a}}\ln \left(1+\mathrm{aut}\right)$

4.  $\mathrm{a} \ln \left(\mathrm{aut}\right)$