The error in the measurement of the length and the breadth of a rectangular table is $1 \%$. If the length and breadth of the table are $1 \ m$ and $50 \ cm$ respectively, then the area of the table including error is

$A$ student performs an experiment for the determination of $g = \frac{4 \pi^{2} \ell}{T^{2}}$. Given $\ell = 1 \, m$,the student commits an error of $\Delta \ell$. For $T$,the student measures the time of $n$ oscillations using a stopwatch with a least count of $\Delta T$ and commits a human error of $0.1 \, s$. For which of the following data will the measurement of $g$ be the most accurate?

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:

Using the expression $2 d \sin \theta = \lambda$,one calculates the values of $d$ by measuring the corresponding angles $\theta$ in the range $0^{\circ}$ to $90^{\circ}$. The wavelength $\lambda$ is exactly known and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from $0^{\circ}$:

The resistance $R = V / I$ where $V = (100 \pm 5) \; V$ and $I = (10 \pm 0.2) \; A$. Find the percentage error in $R$. (in $\%$)

Which of the following comes under the category of random errors?