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.

$A$ scientist performs an experiment in order to measure a certain physical quantity and takes $100$ observations. He repeats the same experiment and takes $400$ observations. By doing so,

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?

In Ohm's experiment,the values of an unknown resistance were found to be $4.12 \; \Omega, 4.08 \; \Omega, 4.22 \; \Omega$,and $4.14 \; \Omega$. Calculate the mean absolute error and relative error in these measurements.

$A$ physical quantity $A$ can be determined by measuring parameters $B, C, D$ and $E$ using the relation $A = \frac{B^\alpha C^\beta}{D^\gamma E^\delta}$. If the maximum percentage errors in the measurement of $B, C, D$ and $E$ are $b\%, c\%, d\%$ and $e\%$ respectively,then the maximum percentage error in the value of $A$ is:

$A$ physical quantity is given by $X = M^a L^b T^c$. The percentage errors in the measurement of $M, L,$ and $T$ are $\alpha, \beta,$ and $\gamma$ respectively. The maximum percentage error in the quantity $X$ is: