The oxidation potential of a hydrogen electrode at $pH = 10$ and $P_{H_2} = 1 \ atm$ will be ............ $V$.

$A$ ball at rest is dropped from a height of $12 ~m$. It loses $25 \%$ of its kinetic energy on striking the ground and bounces back to a height '$h$'. Then the value of '$h$' is: (in $~m$)

Currents flowing in each of the following circuits $A$ and $B$ respectively are:

Electrons with de-Broglie wavelength $\lambda$ fall on the target of an $X$-ray tube. The cut-off wavelength of the emitted $X$-ray is:

$A$ tuning fork vibrating with a sonometer having $20 \, cm$ wire produces $5$ beats per sec. The beat frequency does not change if the length of the wire is changed to $21 \, cm$. The frequency of the tuning fork must be ..... $Hz$.

The probabilities of $A$ and $B$ dying in a year are $p$ and $q$ respectively. What is the probability that only one of them will be alive at the end of the year?