If the random error in the arithmetic mean of $50$ observations is $\alpha$, then the random error in the arithmetic mean of $150$ observations would be

A body travels uniformly a distance of $ (13.8 \pm 0.2) m$ in a time $(4.0 \pm 0.3)\, s$. The velocity of the body within error limits is

A physical quantity $P$ is given by $P= \frac{{{A^3}{B^{\frac{1}{2}}}}}{{{C^{ - 4}}{D^{\frac{3}{2}}}}}$. The quantity which brings in the maximum percentage error in $P$ is

The measured value of the length of a simple pendulum is $20 \mathrm{~cm}$ with $2 \mathrm{~mm}$ accuracy. The time for $50$ oscillations was measured to be $40$ seconds with $1$ second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $\mathrm{N} \%$. The value of $\mathrm{N}$ is:

A wire has a mass $0.3 \pm 0.003\,g$, radius $0.5 \pm 0.005\,mm$ and length $6 \pm 0.06\,cm$. The maximum percentage error in the measurement of its density is .......... $\%$

The amount of heat produced in an electric circuit depends upon the current $(I),$ resistance $(R)$ and time $(t).$ If the error made in the measurements of the above quantities are $2\%, 1\%$ and $1\%$ respectively then the maximum possible error in the total heat produced will be  ........... $\%$