It is estimated that per minute each $cm^2$ of the Earth receives about $2 \ cal$ $(1 \ cal = 4.18 \ J)$ of heat energy from the Sun. This is called the Solar constant. In $SI$ units,the value is:

Two moles of ideal helium gas are in a rubber balloon at $30^\circ C$. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $35^\circ C$. The amount of heat required in raising the temperature is nearly...... $J$ (take $R = 8.31$ $J/mol \cdot K$)

Heating $(NH_4)_2Cr_2O_7$ liberates a gas. The same gas is obtained by:

If the vector $a = 2\hat{i} + 3\hat{j} + 6\hat{k}$ and $b$ are collinear and $|b| = 21$,then $b$ is equal to:

If $\frac{x^3}{(2 x-1)(x+2)(x-3)} = A+\frac{B}{2 x-1}+\frac{C}{x+2}+\frac{D}{x-3}$,then $A$ is equal to

If $y=\frac{\log _e x}{x}$ and $z=\log _e x$,then $\frac{d^2 y}{d z^2}+\frac{d y}{d z}$ is equal to