An $e.m.f.$ of $15 \ V$ is applied in a circuit containing $5 \ H$ inductance and $10 \ \Omega$ resistance. The ratio of the currents at time $t \to \infty$ and at $t = 1 \ s$ is:

$A$ bullet of mass $0.02 \ kg$ travelling horizontally with velocity $250 \ ms^{-1}$ strikes a block of wood of mass $0.23 \ kg$ which rests on a rough horizontal surface. After the impact,the block and bullet move together and come to rest after travelling a distance of $40 \ m$. Find the coefficient of sliding friction of the rough surface. (Take $g = 9.8 \ ms^{-2}$)

If $m$ and $\sigma^2$ are the mean and variance of the random variable $X$,whose distribution is given by:

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

Then:

What does the cell wall of algae consist of?

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then

In the Young's double slit experiment,the intensities at two points $P_1$ and $P_2$ on the screen are respectively $I_1$ and $I_2$. If $P_1$ is located at the centre of a bright fringe and $P_2$ is located at a distance equal to a quarter of fringe width from $P_1$,then $I_1/I_2$ is: