$ \cos^4 \frac{\pi}{8} + \cos^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \cos^4 \frac{7\pi}{8} = $

An inductor coil stores $U$ energy when $i$ current is passed through it and dissipates energy at the rate of $P$. The time constant of the circuit,when this coil is connected across a battery of zero internal resistance is

$A$ ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and each one is equal to $3/4$th the angle of the prism. The angle of deviation is (in $^{\circ}$)

The reaction $2A_{(g)} + B_{(g)} \rightleftharpoons 3C_{(g)} + D_{(g)}$ is begun with the concentrations of $A$ and $B$ both at an initial value of $1.00 \ M$. When equilibrium is reached,the concentration of $D$ is measured and found to be $0.25 \ M$. The value for the equilibrium constant for this reaction is given by the expression

If the equation $2x^2 + kxy - 6y^2 + 3x + y + 1 = 0$,$(k > 0)$ represents a pair of straight lines,then their point of intersection is

In organic reactions,sodium in liquid ammonia is used as