The energy of a system as a function of time $t$ is given as $E(t)=A^2 \exp(-\alpha t)$,where $\alpha=0.2 \ s^{-1}$. The measurement of $A$ has an error of $1.25 \%$. If the error in the measurement of time is $1.50 \%$,the percentage error in the value of $E(t)$ at $t=5 \ s$ is

The potential difference across the ends of a conductor is $(30 \pm 0.3) \ V$ and the current through the conductor is $(5 \pm 0.1) \ A$. The error in the determination of the resistance of the conductor is: (in $\%$)

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \text{ g}$, $8.35 \pm 0.05 \text{ mm}$ and $20.20 \pm 0.02 \text{ mm}$, respectively. The calculated percentage fractional error in $\rho$ is . . . . . . . (in $\%$)

$A$ physical quantity $A$ can be determined by measuring parameters $B, C, D$ and $E$ using the relation $A = \frac{B^\alpha C^\beta}{D^\gamma E^\delta}$. If the maximum percentage errors in the measurement of $B, C, D$ and $E$ are $b\%, c\%, d\%$ and $e\%$ respectively,then the maximum percentage error in the value of $A$ is:

In an experiment,the values of refractive indices of glass were found to be $1.54, 1.53, 1.44, 1.54, 1.56$ and $1.45$ in successive measurements. The mean absolute error is:

The voltage across a lamp is $(6.0 \pm 0.3) \text{ V}$ and the current passing through it is $(4.0 \pm 0.1) \text{ A}$. The power consumed in watt will be (using percentage error):