To manufacture a solenoid of length ' $l$ ' and inductance ' $L$ ', the length of the thin wire required is (Diameter of the solenoid is very less than length, $\mu_0=$ permeability of free space)

An engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{5}$. When $T_2$ is lowered by 45 K , its efficiency becomes $\frac{1}{2}$. Temperatures $T_1$ and $T_2$ are respectively

In an n-p-n transistor amplifier, the collector current is 8 mA . If $80 \%$ of the electrons from the emitter reach the collector, then ( $\alpha$ and $\beta$ are current ratios)

An electric dipole having each charge of magnitude $2 \mu \mathrm{C}$ is placed in an electric field of intensity $8 \times 10^{+4} \mathrm{~N} / \mathrm{C}$. If the maximum torque acting on the dipole is $4 \times 10^{-3} \mathrm{~N}-\mathrm{m}$, the length of the dipole is