The length $l$,breadth $b$,and thickness $t$ of a block of wood were measured with the help of a measuring scale. The results with permissible errors are $l = 15.12 \pm 0.01 \; cm$,$b = 10.15 \pm 0.01 \; cm$,and $t = 5.28 \pm 0.01 \; cm$. The percentage error in volume up to proper significant figures is: (in $\%$)

In an experiment to determine the acceleration due to gravity $g$,the formula used for the time period of a periodic motion is $T=2 \pi \sqrt{\frac{7(R-r)}{5 g}}$. The values of $R$ and $r$ are measured to be $(60 \pm 1) \text{ mm}$ and $(10 \pm 1) \text{ mm}$,respectively. In five successive measurements,the time period is found to be $0.52 \text{ s}, 0.56 \text{ s}, 0.57 \text{ s}, 0.54 \text{ s}$ and $0.59 \text{ s}$. The least count of the watch used for the measurement of time period is $0.01 \text{ s}$. Which of the following statement$(s)$ is(are) true?
$(A)$ The error in the measurement of $r$ is $10 \%$
$(B)$ The error in the measurement of $T$ is $3.57 \%$
$(C)$ The error in the measurement of $T$ is $2 \%$
$(D)$ The error in the determined value of $g$ is $11 \%$

The values of a number of quantities are used in a mathematical formula. The quantity that should be most precise and accurate in measurement is the one

Four students measure the height of a tower. Each student uses a different method and each measures the height many different times. The data for each are plotted below. The measurement with the highest precision is

If the error in the measurement of the surface area of a sphere is $1.2 \%$,then the error in the determination of the volume of the sphere is (in $\%$)

The formula for the physical quantity is $P = \frac{x^3 y}{z^2}$ and the percentage error in the determination of physical quantities $x, y, z$ are $0.6 \%$,$3 \%$,and $1.3 \%$ respectively. The percentage error in the measurement of $P$ is (in $\%$)