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   ........ $\%$

A torque meter is calibrated to reference standards of mass, length and time each with $5 \%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of$............\%$

Two resistance are measured in $Ohm$ and is given as

$R_1 = 3 \Omega \pm 1\%$  and  $R_2 = 6 \Omega \pm 2\%$ When they are connected  in parallel, the percentage error in equivalent resistance is.......... $\%$

The dimensions of a cone are measured using a scale with a least count of $2 mm$. The diameter of the base and the height are both measured to be $20.0 cm$. The maximum percentage error in the determination of the volume is. . . . .

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

The percentage errors in quantities $P, Q, R$  and $S$  are $0.5\%,\,1\%,\,3\%$  and  $1 .5\%$ respectively in the  measurement of a physical quantity $A\, = \,\frac{{{P^3}{Q^2}}}{{\sqrt {R}\,S }}$ . the maximum percentage error in the value of $A$  will be ........... $\%$