The principal value of ${\sin ^{ - 1}}\left( { - \frac{1}{2}} \right)$ is

Three waves of equal frequency having amplitudes $10\, \mu m, 4\, \mu m$ and $7\, \mu m$ arrive at a given point with successive phase difference of $\pi/2$. The amplitude of the resulting wave in $\mu m$ is given by

The electric field associated with an $e.m.$ wave in vacuum is given by $\vec E = \hat i\,40\,\cos \left( {kz - 6 \times {{10}^8}\,t} \right)$,where $E$,$z$,and $t$ are in $V/m$,$m$,and $s$ respectively. The value of the wave vector $k$ is ....... $m^{-1}$.

$A$ point is moving on $y=4-2x^2$. The $x$-coordinate of the point is decreasing at the rate of $5 \text{ units/s}$. Then,the rate at which the $y$-coordinate of the point is changing when the point is at $(1,2)$ is

$A$ $100\%$ efficient transformer has $100$ turns in the primary and $25$ turns in its secondary coil. If the current in the secondary coil is $4\, A$,then the current in the primary coil is.....$A$.

The freezing point of a $1.00 \, m$ aqueous solution of $HF$ is $-1.91^o C$. The freezing point depression constant of water $K_f$ is $1.86 \, K \, kg \, mol^{-1}$. The percentage of dissociation of $HF$ at this concentration is ......... $\%$