$A$ physical quantity $P$ is related to four observables $a, b, c$ and $d$ as $P = \frac{\sqrt{a b} \cdot d^\alpha}{\sqrt{c}}$ (where $\alpha$ is a constant). The percentage errors in $a, b, c$ and $d$ are $0.5 \%$ each. If the percentage error in $P$ is $2 \%$,then the value of $\alpha$ is:

In an experiment for the measurement of $g$ using a simple pendulum,the time period was measured with an accuracy of $0.2 \%$ while the length was measured with an accuracy of $0.5 \%$. The percentage accuracy in the value of $g$ thus obtained is: (in $\%$)

The distance $s$ travelled by a particle in time $t$ is $s = ut - \frac{1}{2} gt^2$. The initial velocity of the particle was measured to be $u = 1.11 \pm 0.01 \, m/s$ and the time interval of the experiment was $t = 1.01 \pm 0.1 \, s$. The acceleration was taken to be $g = 9.8 \pm 0.1 \, m/s^2$. With these measurements,the student estimates the total distance travelled. How should the student report the result?

Two clocks are being tested against a standard clock located in a national laboratory. At $12:00:00$ noon by the standard clock,the readings of the two clocks are

Day	Clock $1$	Clock $2$
Monday	$12:00:05$	$10:15:06$
Tuesday	$12:01:15$	$10:14:59$
Wednesday	$11:59:08$	$10:15:18$
Thursday	$12:01:50$	$10:15:07$
Friday	$11:59:15$	$10:14:53$
Saturday	$12:01:30$	$10:15:24$
Sunday	$12:01:19$	$10:15:11$

If you are doing an experiment that requires precision time interval measurements,which of the two clocks will you prefer?

The length and breadth of a rectangle are $(5.7 \pm 0.1) \text{ cm}$ and $(3.4 \pm 0.2) \text{ cm}$,respectively. Calculate the area of the rectangle with error limits.

The resistance $R = \frac{V}{I}$,where $V = 100 \pm 5 \, \text{volts}$ and $I = 10 \pm 0.2 \, \text{amperes}$. What is the total percentage error in $R$?