A particle moves from position null to \(\left(11\hat i + 11\hat j + 15\hat k \right)\) due to a uniform force of \(\left(4\hat i + \hat j + 3\hat k\right)\)N. If the displacement is in m, then the work done will be: (Given: \(W=\overrightarrow {F}.\overrightarrow {S}\))
1. \(100~\text{J}\)
2. \(200~\text{J}\)
3. \(300~\text{J}\)
4. \(250~\text{J}\)

If for two vectors \(\overrightarrow{A}\) and \(\overrightarrow {B}\), \(\overrightarrow {A}\times \overrightarrow {B}=0\), then the vectors:

When $\overrightarrow{\mathrm{A}}.\overrightarrow{\mathrm{B}}=-\left|\mathrm{A}\right|\left|\mathrm{B}\right|$, then

1. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are perpendicular to each other

2. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ act in the same direction

3. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ act in the opposite direction

4. $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ can act in any direction

The dot product of two mutual perpendicular vector is:

1. \(0\)

2. \(1\)

3. \(\infty\)

4. None of the above

Current in a circuit is given by $i =3t^2+2t$. Find charge that crosses a cross-section from time t=0 to t=2 sec.

1. 12 C

2. 10 C

3. 8 C

4. 2 C

Let \(\theta\) be the angle between vectors \(\overrightarrow A\) and \(\overrightarrow {B}\). Which of the following figures correctly represents the angle \(\theta\)?

1.		2.
3.		4.

A plane is revolving around the earth with a speed of 100 km/hr at a constant height from the surface of the earth. The change in the velocity as it travels half-circle is:

1. 200 km/hr

2. 150 km/hr

3. $100\sqrt{2}$ km/hr

4. 0

If vectors $\hat{\mathrm{i}}-3\hat{\mathrm{j}}+5\hat{\mathrm{k}}$ and $\hat{\mathrm{i}}-3\hat{\mathrm{j}}-\mathrm{\alpha }\hat{\mathrm{k}}$ are equal vectors, then the value of $\mathrm{\alpha }$ is:

1. -5

2. 2

3. -3

4. 4

If a particle moves from point P(2,3,5) to point Q(3,4,5). Its displacement vector be

1. $\hat{\mathrm{i}}+\hat{\mathrm{j}}+10\hat{\mathrm{k}}$

2. $\hat{\mathrm{i}}+\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

3. $\hat{\mathrm{i}}+\hat{\mathrm{j}}$

4. $2\hat{\mathrm{i}}+4\hat{\mathrm{j}}+6\hat{\mathrm{k}}$

If $\overrightarrow{\mathrm{A}}=4\hat{\mathrm{i}}-3\hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=6\hat{\mathrm{i}}+8\hat{\mathrm{j}}$ then magnitude and direction of $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$ will be

1. $5, {\tan }^{-1}(3/4)$

2. $5\sqrt{5}, {\tan }^{-1}(1/2)$

3. $10, {\tan }^{-1}\left(5\right)$

4. $25, {\tan }^{-1}(3/4)$