The least count of a stopwatch is $\frac{1}{5} \, s$. The time of $20$ oscillations of a pendulum is measured to be $25 \, s$. The maximum percentage error in the measurement of time will be ..... $\%$

$50 \ mL$ of $H_2O$ is added to $50 \ mL$ of $1 \times 10^{-3} \ M$ barium hydroxide solution. What is the $pH$ of the resulting solution?

$A$ gas is compressed at a constant pressure of $50 \ N/m^2$ from a volume of $10 \ m^3$ to a volume of $4 \ m^3$. Energy of $100 \ J$ is then added to the gas by heating. Its internal energy is:

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials with refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses,then the focal length of the combination is

Consider two reactions:
$I.$ $Zn +$ conc. $HNO_3$ (hot) $\rightarrow Zn(NO_3)_2 + X + H_2O$
$II.$ $Zn +$ dil. $HNO_3$ (cold) $\rightarrow Zn(NO_3)_2 + Y + H_2O$
Compounds $X$ and $Y$ are respectively:

The work function of nickel is $5 \text{ eV}$. When light of wavelength $2000 \text{ \AA}$ falls on it, it emits photoelectrons. The potential difference necessary to stop the fastest electrons emitted is (given $h = 6.67 \times 10^{-34} \text{ J-s}$): (in $\text{ V}$)