In the measurement of a physical quantity $X = \frac{A^2 B}{C^{1/3} D^3}$, the percentage errors introduced in the measurements of the quantities $A, B, C$, and $D$ are $2 \%, 2 \%, 4 \%$, and $5 \%$, respectively. Then, the minimum amount of percentage error in the measurement of $X$ is contributed by:

$A$ 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:

Explain least count and least count error. Write a note on least count error.

The percentage error in the measurement of mass and speed of a particular body is $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is (in $\%$)

An experiment measures quantities $a, b$ and $c$,and quantity $X$ is calculated from $X = ab^2 / c^3$. If the percentage errors in $a, b$ and $c$ are $\pm 1\%, \pm 3\%$ and $\pm 2\%$,respectively,then the percentage error in $X$ will be

The length of a uniform rod is $100.0 \,cm$ and radius is $1.00 \,cm$. If length is measured with a meter rod having least count $1 \,mm$ and radius is measured with vernier callipers having least count $0.1 \,mm$,the percentage error in calculated volume of cylinder is ............. $\%$