The temperatures of two bodies measured by a thermometer are $t_1 = 20^{\circ}C \pm 0.5^{\circ}C$ and $t_2 = 50^{\circ}C \pm 0.5^{\circ}C$. The temperature difference and the error therein are:

The error in the measurement of resistance, when $(10 \pm 0.5) \text{ A}$ current passing through it produces a potential difference of $(100 \pm 6) \text{ V}$ across it, is (in $\%$)

If $P = \frac{A^3}{B^{5/2}}$ and $\Delta A$ is the absolute error in $A$ and $\Delta B$ is the absolute error in $B$,then the absolute error $\Delta P$ in $P$ is:

The length and width of a rectangular room are measured to be $3.95 \pm 0.05 \,m$ and $3.05 \pm 0.05 \,m$,respectively. The area of the floor is .................... $m^2$

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 $11 \%$

$A$ physical quantity $X$ is given by $X = \frac{2k^3l^2}{m\sqrt{n}}$. The percentage errors in the measurements of $k, l, m$ and $n$ are $1\%, 2\%, 3\%$ and $4\%$ respectively. The value of $X$ is uncertain by .......... $\%$