Momentum of a body moving in a straight line is $\mathrm{p}=\left({\mathrm{t}}^2+2\mathrm{t}+1\right) \mathrm{kg} \mathrm{m}/\mathrm{s}$. Find the force acting on a body at t=2 sec

(1)  6 N

(2)  8 N

(3)  4 N

(4)  2 N

A particle moves along straight line such that at time t its position from a fixed point O on the line is $\mathrm{x}=3{\mathrm{t}}^2-2$. The velocity of the particle when t=2 is:

(A)  $8 {\mathrm{ms}}^{-1}$

(B)  $4 {\mathrm{ms}}^{-1}$

(C)  $12 {\mathrm{ms}}^{-1}$

(D)  $0$

Coordinates of a moving particle are given by $\mathrm{x}={\mathrm{ct}}^2$ and $\mathrm{y}={\mathrm{bt}}^2$. The speed of the particle is given by

(1)  $2\mathrm{t} \left(\mathrm{c}+\mathrm{b}\right)$

(2)  $2\mathrm{t} \sqrt{{\mathrm{c}}^2-{\mathrm{b}}^2}$

(3)  $\mathrm{t} \sqrt{{\mathrm{c}}^2+{\mathrm{b}}^2}$

(4)  $2\mathrm{t} \sqrt{{\mathrm{c}}^2+{\mathrm{b}}^2}$

The x and y components of vector $\overrightarrow{\mathrm{A}}$ are 4m and 6m respectively. The x, y components of vector $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ are 10m and 9m respectively. The length of $\overrightarrow{\mathrm{B}}$ is ______ and angle that $\overrightarrow{\mathrm{B}}$ makes with the x axis is given by _______.

(A)  $\sqrt{0.45}\mathrm{m}, {\tan }^{-1}\left(1/2\right)$

(B)  $\sqrt{4.5}\mathrm{m}, {\tan }^{-1}\left(1/2\right)$

(C)  $\sqrt{45}\mathrm{m}, {\tan }^{-1}\left(1/2\right)$

(D)  $4\sqrt{5}\mathrm{m}, {\tan }^{-1}\left(1/2\right)$

A particle travels with speed $50$ m/s from the point $(3,7)$ in a direction $7\hat i -24 \hat j.$ Find its position vector after $3$ seconds.
1. $151\hat i+45\hat j$
2. $45\hat i-137\hat j$
3. $151\hat i-45\hat j$
4. $4.5\hat i-151\hat j$

If $\overrightarrow{a}$ is a vector and $x$ is a non-zero scalar, then which of the following is correct?

If $\theta$ is the angle between two vectors $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$, and $|\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}|=\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}$, then $\theta$ is equal to:
1. $0^\circ$
2. $180^\circ$
3. $135^\circ$
4. $45^\circ$

The vector $\overrightarrow b$ which is collinear with the vector $\overrightarrow a = \left(2, 1, -1\right)$ and satisfies the condition $\overrightarrow a. \overrightarrow b=3$ is:
1. $\left(1, \frac{1}{2}, \frac{-1}{2}\right)$
2. $\left(\frac{2}{3}, \frac{1}{3}, \frac{-1}{3}\right)$
3. $\left(\frac{1}{2}, \frac{1}{4}, \frac{-1}{4}\right)$
4. $\left(1, 1, 0\right)$

If a, b and c are three non-zero vectors such that $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=0$, then the value of $\overrightarrow{\mathrm{a}}.\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}}.\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}}.\overrightarrow{\mathrm{a}}$ will be: