$A$ student measures the distance traversed in free fall of a body,initially at rest,in a given time. He uses this data to estimate $g$,the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively,the percentage error in the estimation of $g$ is:

$A$ particle covers a distance of $(13.8 \pm 0.2) \ m$ in $(4 \pm 0.3) \ s$. Its velocity under error limits will be

Which of the following comes under the category of random errors?

$A$ physical quantity $P$ is related to four observables $a, b, c$ and $d$ as follows: $P = \frac{a^3 b^2}{\sqrt{c} d}$. The percentage errors of measurement in $a, b, c$ and $d$ are $1 \%, 3 \%, 4 \%$ and $2 \%$ respectively. What is the percentage error in the quantity $P$? If the value of $P$ calculated using the above relation turns out to be $3.763$,to what value should you round off the result?

$A$ projectile is thrown with velocity $U = 20 \ m/s \pm 5\%$ at an angle $60^{\circ}.$ If the projectile falls back on the ground at the same level,then which of the following values in $m$ cannot be a possible answer for the range?

The error in the measurement of length and mass is $3 \%$ and $4 \%$ respectively. The error in the measurement of density will be (in $\%$)