$A$ gas is filled in a cylinder. Its temperature is increased by $20\%$ on the Kelvin scale and its volume is reduced by $10\%$. How much percentage of the gas will leak out at constant pressure?

The solution of $\frac{dy}{dx} = (\frac{x}{y})^{-1/3}$ is

If the rate of disappearance of $N_2O_5$ in the following reaction is $1.2 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$,the rate of production of $NO_2$ in $mol \ L^{-1} \ s^{-1}$ is:
$2 \ N_2O_{5(g)} \longrightarrow 4 \ NO_{2(g)} + O_{2(g)}$

If the direction cosines of two lines satisfy the equations $l+m+n=0$ and $2lm+2ln-mn=0$, then the acute angle between those two lines is

The probability of choosing randomly a number $c$ from the set $\{1, 2, 3, \ldots, 9\}$ such that the quadratic equation $x^2 + 4x + c = 0$ has real roots is

Evaluate the sum: $\sum\limits_{k = 1}^n {\frac{1}{{{{\log }_{{2^k}}}(a)}}}$