Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega$ and $R_2 = (500 \pm 4) \,\Omega$ are connected in series. The equivalent resistance of the series combination is

The time period of a simple pendulum is given by $T = 2 \pi \sqrt{\frac{\ell}{g}}$. The measured value of the length of the pendulum is $10 \ cm$ known to a $1 \ mm$ accuracy. The time for $200$ oscillations of the pendulum is found to be $100 \ s$ using a clock of $1 \ s$ resolution. The percentage accuracy in the determination of $g$ using this pendulum is $x$. The value of $x$ to the nearest integer is ...........$\%$

$A$ simple pendulum is being used to determine the value of gravitational acceleration $g$ at a certain place. The length of the pendulum is $25.0 \; cm$ and a stopwatch with $1 \; s$ resolution measures the time taken for $40$ oscillations to be $50 \; s$. The accuracy in $g$ is ....... $\%$ (in $.40$)

The relative density of the material of a body is found by weighing it first in air and then in water. If the weight in air is $(5.00 \pm 0.05) \ N$ and the weight in water is $(4.00 \pm 0.05) \ N$,then the relative density along with the maximum permissible percentage error is:

Error in volume of a sphere is $6\%$. Error in its radius will be .......... $\%$

The initial and final temperatures of water as recorded by an observer are $(40.6 \pm 0.2)^{\circ}C$ and $(78.9 \pm 0.3)^{\circ}C$. Calculate the rise in temperature with proper error limits.