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Two men $P$ and $Q$ are standing at corners $A$ and $B$ of a square $ABCD$ of side $8~\text m.$ They start moving along the track with a constant speed $2~\text{m/s}$ and $10~\text {m/s}$ respectively. The time when they will meet for the first time is equal to:
       
1. $2~\text{sec}$
2. $3~\text{sec}$
3. $1~\text{sec}$
4. $6~\text{sec}$ 

The sum and difference of two perpendicular vectors of equal length are:
1. Perpendicular to each other and of equal length
2. Perpendicular to each other and of different lengths
3. Of equal length and have an obtuse angle between them
4. Of equal length and have an acute angle between them

A vector perpendicular to $\hat{i}+\hat{j}+\hat{k}$ is
1. $\hat{i}-\hat{j}+\hat{k}$
2. $\hat{i}-\hat{j}-\hat{k}$
3. $-\hat{i}-\hat{j}-\hat{k}$
4. $3\hat{i}+2\hat{j}-5\hat{k}$

Out of the following set of forces, the resultant of which cannot be zero?
1. 10, 10, 10
2. 10, 10, 20
3. 10, 20, 20
4. 10, 20, 40

Two forces, each equal to F, act as shown in the figure. Their resultant is:

1. F/2
2. F
3. $\sqrt{3}$F
4. $\sqrt{5}$F

What is the angle betweem two vector forces of equal magnitude such that their resultant is one-third of either of the original forces?
1. ${\cos }^{-1}\left(-\frac{17}{18}\right)$
2. ${\cos }^{-1}\left(-\frac{1}{3}\right)$
3. 45$°$
4. 120$°$

The projection of a vector $\overrightarrow{r}=3\hat{i}+\hat{j}+2\hat{k}$ on the x-y plane has magnitude
1. 3
2. 4
3. $\sqrt{14}$
4. $\sqrt{10}$

Given $\overrightarrow{A}=2\hat{i}+p\hat{j}+q\hat{k} and \overrightarrow{B}=5\hat{i}+7\hat{j}+3\hat{k}$. If $\overrightarrow{A}\parallel \overrightarrow{B}$, then the values of p and q are, respectively,
1. $\frac{14}{5} and \frac{6}{5}$
2. $\frac{14}{3} and \frac{6}{5}$
4. $\frac{6}{5} and \frac{1}{3}$
4. $\frac{3}{4}~and~\frac{1}{4}$

The magnitude of displacement is equal to the distance covered in a given interval of time if the particle
1. Moves with consatant acceleration along any path
2. Moves with constant speed
3. Moves in same direction with constant velocity or with variable velocity
4. Moves with constant velocity

The distance travelled by a particle in a straight line motion is directly proportional to $t^{1/2}$, where t is the time elapsed. What is the nature of motion?
1. Increasing acceleration
2. Decreasing acceleration
3. Increasing retardation
4. Decreasing retardation

The position x of a particle varies with time (t) as $x= a{t}^2-b{t}^3$. The acceleration at time t of the particle will be equal to zero, where t is equal to
1. $\frac{2a}{3b}$
2. $\frac{a}{b}$
3. $\frac{a}{3b}$
4. zero

A particel is moving along the x-axis whose instantaneous speed is given by $v^2=108-9x^2$. The acceleration of the particle is
1. -9x m ${\mathrm{s}}^{-2}$
2. -18x m ${\mathrm{s}}^{-2}$
3. $\frac{-9\mathrm{x}}{2}\mathrm{m} {\mathrm{s}}^{-2}$
4. None of these

A ball is released from the top of a tower of height h. It takes time T to  reach the ground. What is the position of the ball (from ground) after time T/3?
1. h/9 m
2. 7h/9 m
3. 8h/9 m
4. 17h/19 m

When the speed of a car is $u,$ the minimum distance over which it can be stopped is $s.$ If the speed becomes $nu,$ what will be the minimum distance over which it can be stopped?
1. $\frac{s}{n}$
2. $ns$
3. $\frac{s}{n^{2}}$
4. $n^{2}s$

The relation between time t and distance x is $\alpha x^2+\beta x$ where $\alpha and \beta$ are constants. The retardation is
1. $2\alpha v^3$
2. $2\beta v^3$
3. $2\alpha \beta v^3$
4. $2b^2{v}^3$

$B_1,B_2 and B_3$ are three balloons ascending with velocities v, 2v and 3v, respectively. If a bomb is dropped from each when they are at the same height, then
1. Bomb from $B_1$ reaches ground first
2. Bomb from $B_2$ reaches ground first
3. Bomb from $B_3$ reaches ground first
4. They reach the ground simultaneously

A particle is dropped from rest from a large height. Assume g to be constant throughout the motion. The time taken by it to fall through successive distances of 1 m each will be
1. All equal, being equal to $\sqrt{2/g}$ second
2. In the ratio of the square roots of the integers 1, 2, 3,....
3. In the ratio of the difference in the square roots of the integers i.e., $\sqrt{1},(\sqrt{2}-\sqrt{1}),(\sqrt{3}-\sqrt{2}),(\sqrt{4}-\sqrt{3}),....$
4. In the ratio of the reciprocals of the square roots of the integers, i.e., $\frac{1}{\sqrt{1}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}},....$

If a particles travels n equal distances with speeds $v_1. v_2,....v_n,$ then the average speed $\overline{V}$ of the particle will be such that 
1. $\overline{V}=\frac{v_1+v_2+...+v_n}{n}$
2. $\overline{V}=\frac{n{v}_1{v}_2+v_n}{v_1+v_2+v_3+..v_n}$
3. $\frac{1}{\overline{V}}=\frac{1}{n}\left(\frac{1}{v_1}+\frac{1}{v_2}+....+\frac{1}{v_n}\right)$
4. $\overline{V}=\sqrt{v_1^2+v_2^2+..+v_n^2}$

For acceleration of a particle varies with time as shown in the figure. Find an expression for velocity in terms of t. Assume that v=0 at t=0.

1. $t^2-2t$
2. $2t$
3. $t^2$
4. $t^2+2t$

For acceleration of a particle varies with time as shown in the figure. Calculate the displacement of the particle in the time interval from t=2 s to t=4 s.

1. $\frac{20}{3}m$
2. 20 m
3. 10 m
4. $\frac{10}{3}m$

Referring to a-s diagram as shown in the figure. Find the velocity of the particle when the particle just covers 20 m $({\mathrm{v}}_0=\sqrt{50}\mathrm{m} {\mathrm{s}}^{-1})$.

1. $\sqrt{350}m s^{-1}$
2. $\sqrt{300}m s^{-1}$
3. $\sqrt{100}m s^{-1}$
4. $10m s^{-1}$

The velocity-time graph of a body is shown in figure. The displacement of the body for 8 s is

1. 9 m
2. 12 m
3. 10 m
4. 28 m

The deceleration experienced by a moving motor boat, after its engine is cut-off is given by dv/dt=$-{\mathrm{kv}}^3$, where k is constant. If $v_0$ is the magnitude of the velocity at cut-off, the magnitude of the velocity at time t after the cut-off is
1. $v_0/2$
2. v
3. $v_0{e}^{-kt}$
4. $\frac{v_0}{\sqrt{2v_0^2kt+1}}$

From the velocity-time graph, given in figure of a particle moving in a straight line,  one can conclude that

1. Its average velocity during the 12 s interval is 27/7 $\mathrm{m} {\mathrm{s}}^{-1}$.
2. Its velocity for the first 3 s is uniform and is equal to 4 $\mathrm{m} {\mathrm{s}}^{-1}$.
3. The body has a constant acceleration between t= 3 s and t= 10 s
4. The body has a uniform retardation from t= 8 s to t= 12 s.

An object is vertically thrown upwards. Then the displacement-time graph for the motion is as shown in 
1. 
2. 
3. 
4.