$A$ scientist performs an experiment in order to measure a certain physical quantity and takes $100$ observations. He repeats the same experiment and takes $400$ observations. By doing so,

We can reduce random errors by

The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{\ell}{g}}$. The measured value of the length of the pendulum is $10 \ cm$ known to a $1 \ mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100 \ s$ using a clock of $1 \ s$ resolution. The percentage accuracy in the determination of $g$ using this pendulum is $x$. The value of $x$ to the nearest integer is ...........$\%$

The error in the measurement of the length and the breadth of a rectangular table is $1 \%$. If the length and breadth of the table are $1 \ m$ and $50 \ cm$ respectively, then the area of the table including error is

The resistance $R = \frac{V}{I}$,where $V = 100 \pm 5 \, \text{volts}$ and $I = 10 \pm 0.2 \, \text{amperes}$. What is the total percentage error in $R$?

State the rule for the error in the result due to multiplication and division of two physical quantities.