$100 \ mL$ of $0.6 \ M$ acetic acid is shaken with $2 \ g$ of activated charcoal. After adsorption,the final concentration of the solution becomes $0.5 \ M$. The amount of acetic acid adsorbed per gram of carbon is .......... $g$.

The set of all solutions of the inequation $x^2 - 2x + 5 \leq 0$ in $R$ is

The angle between the lines whose direction cosines are $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{\sqrt{3}}{2}\right)$ and $\left(\frac{\sqrt{3}}{4}, \frac{1}{4}, \frac{-\sqrt{3}}{2}\right)$ is:

When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \, cm$ or $100 \, cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $ \, Hz$)

$A$ stone thrown upwards has its equation of motion $s = 490t - 4.9t^2$. Then the maximum height reached by it is

The compound insoluble in acetic acid is