Measure of two quantities along with the precision of respective measuring instrument $A = 2.5\,m{s^{ - 1}} \pm 0.5\,m{s^{ - 1}}$, $B = 0.10\,s \pm 0.01\,s$ The value of $AB$ will be
$\left( {0.25 \pm 0.08} \right)\,m$
$\left( {0.25 \pm 0.5} \right)\,m$
$\left( {0.25 \pm 0.05} \right)\,m$
$\left( {0.25 \pm 0.135} \right)\,m$
The acceleration due to gravity is measured on the surface of earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively, then percentage error in the measurement of acceleration due to gravity is
A student performs an experiment to determine the Young's modulus of a wire, exactly $2 \mathrm{~m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.8 \mathrm{~mm}$ with an uncertainty of $\pm 0.05 \mathrm{~mm}$ at a load of exactly $1.0 \mathrm{~kg}$. The student also measures the diameter of the wire to be $0.4 \mathrm{~mm}$ with an uncertainty of $\pm 0.01 \mathrm{~mm}$. Take $g=9.8 \mathrm{~m} / \mathrm{s}^2$ (exact). The Young's modulus obtained from the reading is
The values of a number of quantities are used in a mathematical formula. The quantity that should be most precise and accurate in measurement is the one
A public park, in the form of a square, has an area of $(100 \pm 0.2)\; m ^2$. The side of park is ............ $m$
A packet contains silver powder of mass $20.23 \,g \pm 0.01 \,g$. Some of the powder of mass $5.75 \,g \pm 0.01 \,g$ is taken out from it. The mass of the powder left back is ................