$Assertion$ : The error in the measurement of radius of the sphere is $0.3\%$. The permissible error in its surface area is $0.6\%$

$Reason$ : The permissible error is calculated by the formula $\frac{{\Delta A}}{A} = \frac{{4\Delta r}}{r}$

The density of a cube is measured by measuring its mass and the length of its sides. If the maximum error in the measurement of mass and length are $3\%$ and $2\%$ respectively, then find the maximum error in the measurement of the density of cube………. $\%$

The random error in the arithmetic mean of $100$ observations is $x$; then random error in the arithmetic mean of $400$ observations would be

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is   …….. $\%$

Find the relative error in $Z,$ if $Z=\frac{A^{4} B^{1 / 3}}{ C D^{3 / 2}}$