A scalar quantity is one that:

1.	is conserved in a process.
2.	will never accept negative values.
3.	must be dimensionless.
4.	has the same value for observers with different orientations of axes.

The position of a particle in a rectangular co-ordinate system is \((3, 2, 5)\). Then its position vector will be:
1. \(5\hat i + 6\hat j + 2\hat k\)
2. \(3\hat i + 2\hat j + 5\hat k\)
3. \(5\hat i + 3\hat j + 2\hat k\)
4. None of these

If \(\overrightarrow {A}= 2\hat i + 4\hat j- 5\hat k,\) then the direction cosines of the vector are:

(direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three \(+\)ve coordinate axes.)
1. \(\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}~\text{and}~\frac{-5}{\sqrt{45}}\)
2. \(\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{3}{\sqrt{45}}\)
3. \(\frac{4}{\sqrt{45}}, 0~\text{and}~\frac{4}{\sqrt{45}}\)
4. \(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{5}{\sqrt{45}}\)

A force \(F\) applied at a \(30^\circ\) angle to the \(x \)-axis has the following \(X\) and \(Y\) components:
1. \(\frac{F}{\sqrt{2}}, F\)
2. \(\frac{F}{2}, \frac{\sqrt{3}}{2}F\)
3. \(\frac{\sqrt{3}}{2}F, \frac{1}{2}F\)
4. \(F , \frac{F}{\sqrt{2}}\)

If \(\overrightarrow {P}= \overrightarrow {Q}\), then which of the following is NOT correct?
1. \(\widehat{P}= \widehat{Q}\)
2. \(\left|\overrightarrow {P}\right|= \left|\overrightarrow {Q}\right|\)
3. \(P\widehat{Q}= Q\widehat{P}\)
4. \(\overrightarrow {P}+ \overrightarrow {Q}= \widehat{P}+ \widehat{Q}\)

There are two force vectors, one of \(5~\text{N}\) and the other of \(12~\text{N}\). At what angle should the two vectors be added to get the resultant vector of \(17~\text{N}, 7~\text{N},\) and \(13~\text{N}\) respectively:
1. \(0^{\circ}, 180^{\circ}~\text{and}~90^{\circ}\)
2. \(0^{\circ}, 90^{\circ}~\text{and}~180^{\circ}\)
3. \(0^{\circ}, 90^{\circ}~\text{and}~90^{\circ}\)
4. \(180^{\circ}, 0^{\circ}~\text{and}~90^{\circ}\)

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:

The angle between vectors $\left(\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}\right)$ and $\left(\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{A}}\right)$ is:
1. zero
2. $\mathrm{\pi }$
3. $\mathrm{\pi }/4$
4. $\mathrm{\pi }/2$