The resistance $R = \frac{V}{I}$ where $V = (100 \pm 5) \text{ V}$ and $I = (10 \pm 0.2) \text{ A}$. The percentage error in $R$ is: (in $\%$)

In an experiment,the following observations were recorded: $L = 2.820 \, m, M = 3.00 \, kg, l = 0.087 \, cm$,Diameter $D = 0.041 \, cm$. Taking $g = 9.81 \, m/s^2$ and using the formula $Y = \frac{4MgL}{\pi D^2 l}$,the maximum permissible error in $Y$ is ......... $\%$.

If the random error in the arithmetic mean of $50$ observations is $\alpha$,then the random error in the arithmetic mean of $150$ observations would be

The period of oscillation of a simple pendulum is $T = 2\pi \sqrt{\frac{l}{g}}$. The measured value of $l$ is $20.0 \text{ cm}$ known to $1 \text{ mm}$ accuracy,and the time for $100$ oscillations of the pendulum is found to be $90 \text{ s}$ using a wristwatch of $1 \text{ s}$ resolution. The accuracy in the determination of $g$ is ........ $\%$

$A$ physical quantity $X$ is related to four measurable quantities $a$,$b$,$c$,and $d$ as $X = a^2 b^3 c^{5/2} d^{-2}$. The percentage errors in the measurement of $a$,$b$,$c$,and $d$ are $1\%$,$2\%$,$3\%$,and $4\%$ respectively. The percentage error in the measurement of quantity $X$ is: (in $\%$)

The period of an oscillating simple pendulum is $T = 2 \pi \sqrt{\frac{\ell}{g}}$,where the length $\ell = 100 \text{ cm}$ with an error of $1 \text{ mm}$. The period $T = 2 \text{ s}$. The time for $100$ oscillations is measured by a stopwatch with a least count of $0.1 \text{ s}$. The percentage error in the gravitational acceleration $g$ is: (in $\%$)