If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$,then the ratio of the radiant energy received on earth to what it was previously will be

$8 \ mol$ of $AB_{3(g)}$ are introduced into a $1.0 \ dm^3$ vessel. If it dissociates as $2AB_{3(g)} \rightleftharpoons A_{2(g)} + 3B_{2(g)}$. At equilibrium,$2 \ mol$ of $A_2$ are found to be present. The equilibrium constant of this reaction is

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 north star is

The $pK_a$ values of four carboxylic acids are given below. Identify the weakest carboxylic acid.

When a wire of length $10 \ m$ is subjected to a force of $100 \ N$ along its length,the lateral strain produced is $0.01 \times 10^{-3} \ m$. The Poisson's ratio was found to be $0.4$. If the area of cross-section of the wire is $0.025 \ m^2$,its Young's modulus is

The value of $\frac{\cot 54^\circ}{\tan 36^\circ} + \frac{\tan 20^\circ}{\cot 70^\circ}$ is