$A$ physical quantity $x$ is calculated from the relation $x = \frac{a^2 b^3}{c \sqrt{d}}$. If the percentage errors in $a, b, c,$ and $d$ are $2\%, 1\%, 3\%,$ and $4\%$ respectively,what is the percentage error in $x$?

$A$ wire has a mass $0.3 \pm 0.003 \text{ g}$,radius $0.5 \pm 0.005 \text{ mm}$ and length $6 \pm 0.06 \text{ cm}$. The maximum percentage error in the measurement of its density is (in $\%$)

Students $A, B$ and $C$ measure the length of a room using a $25 \,m$ long measuring tape of least count $0.5 \,cm$,a meter-scale of least count $0.1 \,cm$,and a foot-scale of least count $0.05 \,cm$,respectively. If the actual length of the room is $9.5 \,m$,which of the following students will report the lowest relative error in the measured length?

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

In an experiment for determination of the focal length of a thin convex lens,the distance of the object from the lens is $10 \pm 0.1 \text{ cm}$ and the distance of its real image from the lens is $20 \pm 0.2 \text{ cm}$. The error in the determination of focal length of the lens is $n \%$. The value of $n$ is. . . . . . .

$A$ student uses a simple pendulum of exactly $1 \ m$ length to determine $g$,the acceleration due to gravity. He uses a stopwatch with a least count of $1 \ s$ for this and records $40 \ s$ 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 $0.05 \ s$
$(B)$ Error $\Delta T$ in measuring $T$,the time period,is $1 \ s$
$(C)$ Percentage error in the determination of $g$ is $5 \%$
$(D)$ Percentage error in the determination of $g$ is $2.5 \%$