The percentage errors in the measurement of mass and speed are $2\%$ and $3\%$ respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed  ......... $\%$

A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is  $90\;s$ ,$91\;s $, $95\;s$ and $92\;s$. If the minimum division in the  measuring clock is $1\;s$, then the reported mean time should be

In an experiment, the values of refractive indices of glass were found to be $1.54, 1.53,$$1.44,1.54,1.56$ and $1.45$ in successive measurements, then Mean absolute error is 

A student uses a simple pendulum of exactly $1 \mathrm{~m}$ length to determine $\mathrm{g}$, the acceleration due to gravity. He uses a stop watch with the least count of $1 \mathrm{sec}$ for this and records $40$ seconds for $20$ oscillations. For this observation, which of the following statement$(s)$ is (are) true?

$(A)$ Error $\Delta T$ in measuring $T$, the time period, is $0.05$ seconds

$(B)$ Error $\Delta \mathrm{T}$ in measuring $\mathrm{T}$, the time period, is $1$ second

$(C)$ Percentage error in the determination of $g$ is $5 \%$

$(D)$ Percentage error in the determination of $g$ is $2.5 \%$

An optical bench has $1.5 m$ long scale having four equal divisions in each $cm$. While measuring the focal length of a convex lens, the lens is kept at $75 cm$ mark of the scale and the object pin is kept at $45 cm$ mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at $135 cm$ mark. In this experiment, the percentage error in the measurement of the focal length of the lens is. . . . .

According to Joule's law of heating, heat produced $H = {I^2}\,Rt$, where I is current, $R$ is resistance and $t$ is time. If the errors in the measurement of $I, R$ and t are $3\%, 4\% $ and $6\% $ respectively then error in the measurement of $H$ is