An inductor and a resistor are connected in series to an $AC$ source of $10 \ V$. If the potential difference across the inductor is $6 \ V$,then the potential difference across the resistor is: (in $V$)

If the distance between the plane $Ax - 2y + z = d$ and the plane containing the lines $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$ and $\frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5}$ is $\sqrt{6}$,then $|d|$ is

The magnetic susceptibility of the material of a rod is $499$. Permeability of vacuum is $4 \pi \times 10^{-7} \ H/m$. Absolute permeability of the material of the rod in $H/m$ is:

Which one of the following is not a biopolymer?

If $a>0$,then $\int_{-\pi}^\pi \frac{\sin ^2 x}{1+a^x} d x$ is equal to

$A$ thin metallic spherical shell contains a charge $Q$ on it. $A$ point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in the figure. All the three charges are positive. The force on the charge at the centre is: