Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x$-axis at which the net electric field due to these two point charges is zero is

The pressure versus temperature graph of an ideal gas is as shown in the figure. The density of the gas at point $A$ is ${\rho _0}$. The density at point $B$ will be

Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{40}{3 \pi} \times 10^6 \ N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $\left(g = 10 \ m s^{-2}\right)$

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be

Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The masses of gas in $A$ and $B$ are $m_A$ and $m_B$,respectively. The gases are allowed to expand isothermally to the same final volume $2V$. The changes in pressures of the gas in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$,respectively. Then:

At $27^{\circ} C$,a closed vessel contains a mixture of equal weights of helium (mol. wt. = $4$),methane (mol. wt. = $16$) and sulphur dioxide (mol. wt. = $64$). The pressure exerted by the mixture is $210 \ mm$. If the partial pressures of helium,methane and sulphur dioxide are $p_1, p_2$ and $p_3$ respectively,which one of the following is correct?