The amplitude and the time period in a $S.H.M.$ are $0.5 \, cm$ and $0.4 \, s$ respectively. If the initial phase is $\pi / 2 \, rad$,then the equation of $S.H.M.$ will be

$A$ ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If $\mu$ is the refractive index of the material of the prism,the maximum value of the base angle for which light is totally reflected from the hypotenuse is

$\int \left( \frac{2 - \sin 2x}{1 - \cos 2x} \right) e^x \, dx$ is equal to

Two charges $2 C$ and $6 C$ are separated by a finite distance. If a charge of $-4 C$ is added to each of them,the initial force of $12 \times 10^3 ~N$ will change to

Ferrous ion changes to $X$ ion upon reacting with acidified hydrogen peroxide. The number of $d$-electrons present in $X$ and its magnetic moment (in $BM$) are,respectively:

Four charges are placed at the circumference of the dial of a clock as shown in the figure. If the clock has only an hour hand,then the resultant force on a positive charge $q_0$ placed at the center points in the direction which shows the time as: (in $:30$)