In an experiment four quantities $a, b, c$ and $d $ are measured with percentage error $1\%, 2\%, 3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{{{a^3}{b^2}}}{{cd}}$. $ \%$ error in $P$ is ........ $\%$

A metal wire has mass $(0.4 \pm 0.002)\,g$, radius $(0.3 \pm 0.001)\,mm$ and length $(5 \pm 0.02) \,cm$. The maximum possible percentage error in the measurement of density will nearly be $.......\%$

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 period of oscillation of a simple pendulum is $T=2 \pi \sqrt{L / g}$ Measured value of $L$ is $20.0 \;cm$ known to $1\; mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90 \;s$ using a wrist watch of $1\; s$ resolution. What is the accuracy in the determination of $g in \% ?$

$Assertion$: In the measurement of physical quantities direct and indirect methods are used.

$Reason$ : The accuracy and precision of measuring instruments along with errors in measurements should be taken into account, while expressing the result.

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are $3\%$ each, then error in the value of resistance of the wire is ........ $\%$