The best method to reduce random error 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 ........ $\%$

$A$ quantity $P$ is related as $P = X^{-2}Y^{-3/2}Z^{2/5}$, where $X, Y, Z$ are independent parameters which have fractional errors of $0.1, 0.2$ and $0.5$ respectively in measurement. The maximum fractional error in $P$ is

The period of oscillation of a simple pendulum is $T = 2 \pi \sqrt{\frac{L}{g}}$. The measured value of $L$ is $1.0 \text{ m}$ using a meter scale with a minimum division of $1 \text{ mm}$,and the time for one complete oscillation is $1.95 \text{ s}$ measured using a stopwatch with a resolution of $0.01 \text{ s}$. The percentage error in the determination of $g$ will be ..... $\%$.

If the length of rod $A$ is $3.25 \pm 0.01 \,cm$ and that of rod $B$ is $4.19 \pm 0.01 \,cm$,then the rod $B$ is longer than rod $A$ by:

$A$ torque meter is calibrated to reference standards of mass,length,and time,each with $5 \%$ accuracy. After calibration,the measured torque with this torque meter will have a net accuracy of $............\%$.