The intensity of radiation emitted by the Sun has its maximum value at a wavelength of $510 \ nm$ and that emitted by the North Star has the maximum value at $350 \ nm$. If these stars behave like black bodies,then the ratio of the surface temperature of the Sun and the North Star is

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P, Q,$ and $R$ having emf's $E, E,$ and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively,then the ratio $\frac{T_2}{T_1}$ is:

The compound $CH_3-C(CH_3)=CH-CH_3$ on reaction with $NaIO_4$ in the presence of $KMnO_4$ gives :-

Which of the following liquid mixtures shows a positive deviation from Raoult's law?

What is obtained by the electrolysis of carnallite?