$A$ $x : 1$ molar mixture of $He$ and $CH_4$ is contained in a vessel at $20 \ bar$ pressure. Due to a hole in the vessel,the gas mixture leaks out. If the composition of the mixture effusing out initially is $8 : 1$,then the value of $x$ will be

An inductance of $1 \ H$ is connected in series with an $AC$ source of $220 \ V$ and $50 \ Hz$. The inductive reactance (in ohm) is (in $\pi$)

In Gattermann reaction,a diazonium group is replaced by $\underline{X}$ using $\underline{Y}$. $\underline{X}$ and $\underline{Y}$ are:
$\underline{X} \quad \underline{Y}$

$\int_0^3 \frac{3x+1}{x^2+9} dx$ is equal to :

The potential energy between two atoms in a molecule is given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are positive constants and $x$ is the distance between the atoms. The atoms are in stable equilibrium when:

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \ mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $\alpha = 10 \times 10^{-6} \ K^{-1}$)