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 ........... $\%$

The error in the measurement of resistance,when $(10 \pm 0.5) \text{ A}$ current passing through it produces a potential difference of $(100 \pm 6) \text{ V}$ across it,is (in $\%$)

In an experiment,the mass of an object is measured by applying a known force on it and then measuring its acceleration. If in the experiment,the measured values of applied force and the measured acceleration are $F = 10.0 \pm 0.2 \, N$ and $a = 1.00 \pm 0.01 \, m/s^2$,respectively,then the mass of the object is ............... $kg$.

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 $........... \%$.

Accuracy of measurement is determined by

$Assertion$ : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$.
$Reason$ : The permissible error is calculated by the formula $\frac{\Delta A}{A} = \frac{4\Delta r}{r}$.