$A$ student measures time for $20$ oscillations of a simple pendulum as $30 \ s, 32 \ s, 35 \ s$ and $35 \ s$. If the minimum division in the measuring clock is $1 \ s$,then the correct mean time (in seconds) is:

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \text{ g}$, $8.35 \pm 0.05 \text{ mm}$ and $20.20 \pm 0.02 \text{ mm}$, respectively. The calculated percentage fractional error in $\rho$ is . . . . . . . (in $\%$)

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

$A$ student performs an experiment for the determination of $g = \frac{4 \pi^{2} \ell}{T^{2}}$. Given $\ell = 1 \, m$,the student commits an error of $\Delta \ell$. For $T$,the student measures the time of $n$ oscillations using a stopwatch with a least count of $\Delta T$ and commits a human error of $0.1 \, s$. For which of the following data will the measurement of $g$ be the most accurate?

If the maximum percentage error in the measurement of distance $(h)$ and time $(t)$ are '$e_1$' and '$e_2$' respectively,the percentage error in the measurement of acceleration of gravity $(g)$ is [use $h=\frac{1}{2} gt^2$].

What is the estimation of error? Write the methods for estimation.