The plates of a parallel plate capacitor are charged up to $100\;V$. $A$ $2\;mm$ thick plate is inserted between the plates. Then,to maintain the same potential difference,the distance between the plates is increased by $1.6\;mm$. The dielectric constant of the plate is:

$A$ current $I$ flows in an infinitely long wire with a cross-section in the form of a semicircular ring of radius $R$. The magnitude of the magnetic induction along its axis is

Secondary sewage treatment is mainly a

$A$ bullet of mass $10 ~g$ is fired horizontally with a velocity $1000 ~ms^{-1}$ from a rifle situated at a height $50 ~m$ above the ground. If the bullet reaches the ground with a velocity $500 ~ms^{-1}$,the work done against air resistance in the trajectory of the bullet is : $(g=10 ~ms^{-2})$ (in $~J$)

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 ~Hz$ when like poles are tied together and it is $2 ~Hz$ when the unlike poles are tied together,then the ratio $M_1: M_2$ is

What are $X$ and $Y$ in the following reaction sequence?
$C_2H_5OH$ $\xrightarrow{Cl_2} \underline{X}$ $\xrightarrow{Cl_2} \underline{Y}$