$A$ weak acid $HX$ has the dissociation constant $1 \times 10^{-5} \ M$. It forms a salt $NaX$ on reaction with alkali. The percentage hydrolysis of $0.1 \ M$ solution of $NaX$ is ........ $\%$.

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\,s$. In another $10\,s$ it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

On the interval $[0, 1]$,the function $f(x) = x^{25}(1-x)^{75}$ takes its maximum value at the point

The mirror image of the point $(1, 2, 3)$ in a plane is $\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$. Which of the following points lies on this plane?

Express $9072$ as a product of primes.