If $∆ABC$ is right-angled at C, then the value of cos (A + B) is

                               

1.  0

2.  1

3.  $\frac{1}{2}$

4.  $\frac{\sqrt{3}}{2}$

Which of the following is not possible?
1. sin θ = \(3\over5\)
2. sec θ = 100
3. cosec θ = 0.14
4. None of the above

Figure shows the orientation of two vectors u and v in the XY plane.

$\text{ If }\mathrm{u}=\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}}\text{ and }\mathrm{v}=\mathrm{p}\hat{\mathrm{i}}+\mathrm{q}\hat{\mathrm{j}}$

Which of the following is correct?

1. a and p are positive while b and q are negative

2. a, p, and b are positive while q is negative

3. a, q, and b are positive while p is negative

4. a, b, p, and q are all positive

The component of a vector r along the X-axis will have the maximum value if-

1. r is oriented along the positive Y-axis

2. 3r is oriented along the positive X-axis.

3. r makes an angle of 45^o with the X-axis

4. r is along the negative Y-axis

If the angle between the vector $\overrightarrow{\mathrm{A}}\text{ and }\overrightarrow{\mathrm{B}}$ is θ, the value of the product $(\overrightarrow{\mathrm{B}}\times \overrightarrow{\mathrm{A}})\cdot \overrightarrow{\mathrm{A}}$ is equal to:

1. zero

2. BA²sinθcosθ

3. BA²cosθ

4. BA²sinθ

$\begin{array}{l}\text{ If }|\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}|=\sqrt{3}\overrightarrow{\mathrm{A}}\cdot \overrightarrow{\mathrm{B}}\text{, then the value of }\\ |\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\text{ is: }\end{array}$

1. ${({\mathrm{A}}^2+{\mathrm{B}}^2+\frac{\mathrm{AB}}{\sqrt{3}})}^{1/2}$

2. A+B

3. ${({\mathrm{A}}^2+{\mathrm{B}}^2+\sqrt{3}\mathrm{AB})}^{1/2}$

4. ${({\mathrm{A}}^2+{\mathrm{B}}^2+\mathrm{AB})}^{1/2}$

When vector $\overrightarrow{\mathrm{A}} = \sqrt{3}\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + 2\hat{\mathrm{k}}$ intersects the Y-axis, it forms an angle of

1.  ${\sin }^{-1}\left(\frac{3}{\sqrt{14}}\right)$

2.  ${\sin }^{-1}\left(\frac{\sqrt{7}}{4}\right)$

3.  ${\cos }^{-1}\left(\frac{4}{3}\right)$

4.  ${\cos }^{-1}\left(\frac{3}{5}\right)$

The scalar and vector product of two vectors, $\overrightarrow{\mathrm{a}} = \left(3\hat{\mathrm{i}}-4\hat{\mathrm{j}}+5\hat{\mathrm{k}}\right)$ and $\overrightarrow{\mathrm{b}} = \left(-2\hat{\mathrm{i}}+\hat{\mathrm{j}}-3\hat{\mathrm{k}}\right)$ is equal to:

1.  -25 & $\left(7\hat{\mathrm{i}}-\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right)$

2.  25 & $\left(-7\hat{\mathrm{i}}+\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right)$

3.  0 & $\left(-7\hat{\mathrm{i}}+\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)$

4.  -25 & $\left(-7\hat{\mathrm{i}}+\hat{\mathrm{j}}+5\hat{\mathrm{k}}\right)$

Three vectors A, B, and C add up to zero. Then:

The incorrect statement/s is/are:

1. (b, d)
2. (a, c)
3. (b, c, d)
4. (a, b)

The vector sum of two forces is perpendicular to their vector difference. In that case, the forces:

1. are not equal to each other in magnitude.

2. cannot be predicted.

3. are equal to each other.

4. are equal to each other in magnitude.