The random error in the arithmetic mean of $100$ observations is $x$. What is the random error in the arithmetic mean of $400$ observations?

Write the rule for the error produced in the result due to the addition and subtraction of physical quantities.

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 . . . . . .

While measuring the acceleration due to gravity by a simple pendulum,a student makes a positive error of $1\%$ in the length of the pendulum and a negative error of $3\%$ in the value of time period. His percentage error in the measurement of $g$ by the relation $g = 4{\pi ^2}(l/T^2)$ will be ........ $\%$

$A$ student uses a simple pendulum of exactly $1 \ m$ length to determine $g$,the acceleration due to gravity. He uses a stopwatch with a least count of $1 \ s$ for this and records $40 \ s$ for $20$ oscillations. For this observation,which of the following statement$(s)$ is (are) true?
$(A)$ Error $\Delta T$ in measuring $T$,the time period,is $0.05 \ s$
$(B)$ Error $\Delta T$ in measuring $T$,the time period,is $1 \ s$
$(C)$ Percentage error in the determination of $g$ is $5 \%$
$(D)$ Percentage error in the determination of $g$ is $2.5 \%$

Two resistors of resistances $R_1 = (100 \pm 3) \,\Omega$ and $R_2 = (200 \pm 4) \,\Omega$ are connected in series. The maximum absolute error and percentage error in the equivalent resistance of the series combination are: