When two resistors of resistances $R_1=(200 \pm 2) \Omega$ and $R_2=(400 \pm 4) \Omega$ are connected in series,then the equivalent resistance of the combination is

What is the difference between a mistake and an error in the context of physical measurements?

An experiment measures quantities $a, b$ and $c$,and quantity $X$ is calculated from $X = ab^2 / c^3$. If the percentage errors in $a, b$ and $c$ are $\pm 1\%, \pm 3\%$ and $\pm 2\%$,respectively,then the percentage error in $X$ will be

Two resistances are measured in $\Omega$ and are 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 period of oscillation of a simple pendulum is $T = 2\pi(L/g)^{1/2}$. Measured value of $L$ is $10 \text{ cm}$ known to $1 \text{ mm}$ accuracy and time for $100$ oscillations is $50 \text{ s}$, using a watch of $1 \text{ s}$ resolution. The percentage error in the measurement of $g$ is (in $\%$)

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