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).

$A$ cylindrical wire of mass $(0.4 \pm 0.01) \, g$ has length $(8 \pm 0.04) \, cm$ and radius $(6 \pm 0.03) \, mm$. The maximum error in its density will be $...... \, \%$.

$A$ packet contains silver powder of mass $20.23 \,g \pm 0.01 \,g$. Some of the powder of mass $5.75 \,g \pm 0.01 \,g$ is taken out from it. The mass of the powder left back is ................

$A$ physical quantity $A$ is related to four observables $a, b, c,$ and $d$ as follows: $A = \frac{a^2 b^3}{c \sqrt{d}}$. The percentage errors of measurement in $a, b, c,$ and $d$ are $1\%, 3\%, 2\%,$ and $2\%$ respectively. What is the percentage error in the quantity $A$?

$A$ quantity is measured repeatedly many times with an instrument. The readings are shown in the figures where $T$ represents the true value of the measurement. Which of the following measurements is imprecise but accurate?

The mass of an empty beaker is $(10.1 \pm 0.1) \, g$. When it is completely filled with a liquid,its mass becomes $(17.3 \pm 0.1) \, g$. What is the best value for the mass of the liquid within the possible limits of accuracy?