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

A physical quantity $X$ is related to four measurable quantities $a,\, b,\, c$ and $d$ as follows $X = a^2b^3c^{\frac {5}{2}}d^{-2}$. The percentange error in the measurement of $a,\, b,\, c$ and $d$ are $1\,\%$, $2\,\%$, $3\,\%$ and $4\,\%$ respectively. What is the percentage error in quantity $X$ ? If the value of $X$ calculated on the basis of the above relation is $2.763$, to what value should you round off the result.

If $Q= \frac{X^n}{Y^m}$ and $\Delta X$ is absolute error in the measurement of $X,$ $\Delta Y$ is absolute error in the measurement of $Y,$ then absolute error $\Delta Q$ in $Q$ is 

The temperatures of two bodies measured by a thermometer are $t_{1}=20^{\circ} C \pm 0.5^{\circ} C$ and $t_{2}=50^{\circ} C \pm 0.5^{\circ} C$ Calculate the temperature difference and the error theirin.

The mass of the body is $10.000\,g$ and its volume is $10.00\,cm^3$. If the measured values are expressed upto the correct significant figures, the maximum error in the measurement of density is