The length,breadth,and thickness of a strip are $(10.0 \pm 0.1) \; cm$,$(1.00 \pm 0.01) \; cm$,and $(0.100 \pm 0.001) \; cm$ respectively. The most probable error in its volume will be?

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 $\%$)

The percentage errors in measurements of mass and speed of a body are $2 \%$ and $3 \%$ respectively. What is the percentage error in kinetic energy of the body (in $\%$)?

The resistance $R = \frac{V}{I}$ where $V = (200 \pm 5) \ V$ and $I = (20 \pm 0.2) \ A$. The percentage error in the measurement of $R$ is: (in $\%$)

The percentage error in the measurement of a physical quantity $m$ given by $m = \pi \tan \theta$ is minimum when $\theta = \dots \dots \dots \dots \dots ^\circ$ (Assume that the error in $\theta$ remains constant).

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