Accuracy of measurement is determined by

Quantity $Z$ varies with $x$ and $y$ , according to given equation $Z = x^2y - xy^2$ , where $x = 3.0 \pm 0.1$ and $y = 2.0 \pm 0.1$ . The value of $Z$ is 

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

Explain Absolute Error, Relative Error and Percentage Error.

The time period of a simple pendulum is given by $T =2 \pi \sqrt{\frac{\ell}{ g }}$. The measured value of the length of pendulum is $10\, cm$ known to a $1\, mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100$ second using a clock of $1s$ resolution. The percentage accuracy in the determination of $'g'$ using this pendulum is $'x'$. The value of $'x'$ to the nearest integer is ...........$\%$

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