AIIMS UG 2013 Mock Test

In an experiment, four quantities $a,b,c$ and $d$ are measured with percentage error $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows: $P=\frac{a^3{b}^2}{cd}$. The percentage error in $P$ is:

The velocity of a projectile at the initial point $A$ is $(2\hat{i}+3\hat{j})\text{m/s}$. Its velocity (in $\text{m/s}$) at point $B$ (the end of the trajectory on the same horizontal plane) is:

A stone falls freely under gravity. It covers distances $h_1,h_2$ and $h_3$ in the first $5\text{seconds}$, the next $5\text{seconds}$ and the next $5\text{seconds}$ respectively. The relation between $h_1,h_2$ and $h_3$ is:

Three blocks with masses $m,2m$ and $3m$ are connected by strings, as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward at constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by: