Quantity $Z$ varies with $x$ and $y$ according to the equation $Z = x^2y - xy^2$,where $x = 3.0 \pm 0.1$ and $y = 2.0 \pm 0.1$. The value of $Z$ is:

The percentage error in the measurement of mass and velocity are $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is (in $\%$)

Two students $P$ and $Q$ perform an experiment to verify Ohm's law for a conductor with resistance $R$. They use a current source and a voltmeter with least counts of $0.1 \, mA$ and $0.1 \, mV$,respectively. The plots of the variation of voltage drop $V$ across $R$ with current $I$ for both are shown below. Which statement is most likely to be correct?

The resistance $R = \frac{V}{I}$,where $V = (50 \pm 2) \; V$ and $I = (20 \pm 0.2) \; A$. The percentage error in $R$ is $x\%$. The value of $x$ to the nearest integer is .........

In an experiment, the coefficient of viscosity (in $mPa \cdot s$) of a liquid was determined as $2.62, 2.68, 2.58, 2.57, 2.54$ and $2.55$. The mean absolute error in the determination of the coefficient of viscosity of the liquid is

The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of its volume is