Evaluate the sum: $\sum\limits_{k = 1}^n {\frac{1}{{{{\log }_{{2^k}}}(a)}}}$

If $200 \text{ MeV}$ of energy is released in the fission of one nucleus of ${ }_{92}^{235} \text{U}$,then the number of nuclei that must undergo fission to release an energy of $1000 \text{ J}$ is

$A$ capacitor is charged by using a battery,which is then disconnected. $A$ dielectric slab is then inserted between the plates. What is the result?

$A$ train whistling at a constant frequency is moving towards a station at a constant speed $V_s$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve.

The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, is . . . . . . . . . . .
($g =$ gravitational acceleration)