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

A force of 5N acts on a particle along a direction making an angle of $60°$ with vertical. Its vertical component will be:

1. 10 N

2. 3 N

3. 4 N

4. 2.5 N

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. \(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}~\text{and}~\frac{5}{\sqrt{45}}\)

The vector that must be added to the vector $\hat{\mathrm{i}}-3\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and $3\hat{\mathrm{i}}+6\hat{\mathrm{j}}-7\hat{\mathrm{k}}$ so that the resultant vector is a unit vecotr along the y-axis is

1. $4\hat{\mathrm{i}}+2\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

2. $-4\hat{\mathrm{i}}-2\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

3. $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

4. Null vector

Surface area is:

1. Scalar

2. Vector

3. Neither scalar nor vector

4. Both scalar and vector

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. \(F , \frac{F}{\sqrt{2}}\)

Angular momentum is

1. A scalar

2. A polar vector

3. An axial-vector

4. None of these

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. \(\overrightarrow {P}+ \overrightarrow {Q}= \widehat{P}+ \widehat{Q}\)