In agarose gel electrophoresis,$DNA$ molecules are separated on the basis of their

Two finite sets have $m$ and $n$ elements respectively. If the number of subsets of the first set is $56$ more than the number of subsets of the second set,then the values of $m$ and $n$ are:

$A$ particle of mass $m$ and charge $q$ moves with a constant velocity $v$ along the positive $x$-direction. It enters a region containing a uniform magnetic field $B$ directed along the negative $z$-direction,extending from $x = a$ to $x = b$. The minimum value of $v$ required so that the particle can just enter the region $x > b$ is

The maximum value of $\sin (\cos (\tan x))$ is

$A$ thin rectangular magnet suspended freely has a period of oscillation equal to $T.$ Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $T',$ the ratio $T'/T$ is :-

$A$ screen is placed $50 \, cm$ from a single slit, which is illuminated with $6000 \, \mathring{A}$ light. If the distance between the first and third minima in the diffraction pattern is $3 \, mm$, the width of the slit is.....$mm$