The frequency for which a $5\,\mu F$ capacitor has a reactance of $\frac{1}{1000}\,\Omega$ is given by

$A$ diode detector is used to detect an amplitude-modulated wave of $60\%$ modulation by using a capacitor of capacity $250 \text{ pF}$ in parallel with a load resistance of $100 \text{ k}\Omega$. Find the maximum modulation frequency which could be detected by it.

An oscillator is nothing but an amplifier with

The line $x=\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x$,$y=\cos x$ and the $x$-axis $(0 \leq x \leq \frac{\pi}{2})$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2$ equals (in $: 1$)

$A$ beam of monochromatic light is incident at $i = 50^{\circ}$ on one face of an equilateral prism. If the angle of emergence is $e = 40^{\circ}$,then the angle of minimum deviation is:

If $\alpha + \beta = \frac{\pi}{2}$ and $\beta + \gamma = \alpha$,then $\tan \alpha$ equals