$A$ physical quantity $p$ is described by the relation $p = a^{1/2} b^2 c^3 d^{-4}$. If the relative errors in the measurement of $a, b, c$ and $d$ are $2\%$,$1\%$,$3\%$ and $5\%$ respectively,then the relative error in $p$ will be ........... $\%$.

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?

$A$ physical quantity $C$ is related to four other quantities $p, q, r$ and $s$ as follows:
$C = \frac{pq^2}{r^3 \sqrt{s}}$
The percentage errors in the measurement of $p, q, r$ and $s$ are $1\%, 2\%, 3\%$ and $2\%$ respectively.
The percentage error in the measurement of $C$ will be . . . . . . $\%$.

The time period of a simple harmonic oscillator is $T = 2 \pi \sqrt{\frac{m}{k}}$. The measured value of mass $(m)$ of the object is $10 \ g$ with an accuracy of $10 \ mg$, and the time for $50$ oscillations of the spring is found to be $60 \ s$ using a watch of $2 \ s$ resolution. The percentage error in the determination of the spring constant $(k)$ is . . . . . . %.

Time intervals measured by a clock give the following readings: $1.25 \; s, 1.24 \; s, 1.27 \; s, 1.21 \; s$,and $1.28 \; s$. What is the percentage relative error of the observations?

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?