The random error in the arithmetic mean of $100$ observations is $x$; then the random error in the arithmetic mean of $400$ observations would be

Two capacitors with capacitance values $C_1 = 2000 \pm 10 \text{ pF}$ and $C_2 = 3000 \pm 15 \text{ pF}$ are connected in series. The voltage applied across this combination is $V = 5.00 \pm 0.02 \text{ V}$. The percentage error in the calculation of the energy stored in this combination of capacitors is . . . . . .

Two students $P$ and $Q$ perform an experiment to verify Ohm's law for a conductor with resistance $R$. They use a current source and a voltmeter with least counts of $0.1 \, mA$ and $0.1 \, mV$,respectively. The plots of the variation of voltage drop $V$ across $R$ with current $I$ for both are shown below. Which statement is most likely to be correct?

The initial and final temperatures of water in a container are observed to be $16 \pm 0.6 \ ^\circ C$ and $56 \pm 0.3 \ ^\circ C$. What will be the rise in temperature of the water?

$A$ student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90\;s$,$91\;s$,$95\;s$,and $92\;s$. If the minimum division in the measuring clock is $1\;s$,then the reported mean time should be

If the maximum and minimum temperatures at a place on a day are measured as $44^{\circ} C \pm 0.5^{\circ} C$ and $22^{\circ} C \pm 0.5^{\circ} C$ respectively,then the temperature difference is