The resistance across $M$ and $N$ in the given figure is

In an $ac$ circuit,the instantaneous values of e.m.f. and current are $e = 200 \sin(314t) \text{ V}$ and $i = \sin(314t + \frac{\pi}{3}) \text{ A}$. The average power consumed in watt is

The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index $n$) is

Identify the plant shown in the given figure.

$A$ ray of light is incident along a line which meets another line,$7x - y + 1 = 0$,at the point $(0, 1)$. The ray is then reflected from this point along the line $y + 2x = 1$. Find the equation of the line of incidence of the ray of light.

If $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 2 \\ 0 & 0 & 4 \end{bmatrix}$,then show that $|3A| = 27|A|$.