An experiment measures quantities $a, b$ and $c$,and quantity $X$ is calculated from $X = ab^2 / c^3$. If the percentage errors in $a, b$ and $c$ are $\pm 1\%, \pm 3\%$ and $\pm 2\%$,respectively,then the percentage error in $X$ will be

In an experiment for the measurement of $g$ using a simple pendulum,the time period was measured with an accuracy of $0.2 \%$ while the length was measured with an accuracy of $0.5 \%$. The percentage accuracy in the value of $g$ thus obtained is: (in $\%$)

The current-voltage relation of a diode is given by $I = (e^{1000V/T} - 1) \text{ mA}$,where the applied voltage $V$ is in volts and the temperature $T$ is in Kelvin. If a student makes an error of $\pm 0.01 \text{ V}$ while measuring the voltage to obtain a current of $5 \text{ mA}$ at $300 \text{ K}$,what will be the error in the value of current in $\text{mA}$?

According to Joule's law of heating,heat produced $H = I^2Rt$,where $I$ is current,$R$ is resistance,and $t$ is time. If the errors in the measurement of $I, R$,and $t$ are $3\%, 4\%$,and $6\%$ respectively,then the error in the measurement of $H$ is:

Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega$ and $R_2 = (500 \pm 4) \,\Omega$ are connected in series. The equivalent resistance of the series combination is

The length of a cylinder is measured with a metre rod having a least count of $0.1 \; cm$. Its diameter is measured with vernier calipers having a least count of $0.01 \; cm$. If the length and diameter of the cylinder are $5.0 \; cm$ and $2.00 \; cm$ respectively,then the percentage error in the calculated value of volume will be (in $\%$)