The measurements of two quantities along with the precision of their respective measuring instruments are $A = 2.5 \, m/s \pm 0.5 \, m/s$ and $B = 0.10 \, s \pm 0.01 \, s$. The value of $AB$ will be:

For $z = a^{2} x^{3} y^{1/2}$,where $a$ is a constant. If the percentage error in the measurement of $x$ and $y$ are $4\%$ and $12\%$,respectively,then the percentage error for $z$ will be $........... \%$.

$A$ student performs an experiment for the determination of $g = \frac{4 \pi^{2} \ell}{T^{2}}$. Given $\ell = 1 \, m$,the student commits an error of $\Delta \ell$. For $T$,the student measures the time of $n$ oscillations using a stopwatch with a least count of $\Delta T$ and commits a human error of $0.1 \, s$. For which of the following data will the measurement of $g$ be the most accurate?

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its moment of inertia $(I = M R^2)$ about its geometric axis. (in $\%$)

If $x = 10.0 \pm 0.1$ and $y = 10.0 \pm 0.1$,then $2x - 2y$ is equal to

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 $\%$)