Two forces of the same magnitude are acting on a body in the East and North directions, respectively. If the body remains in equilibrium, then the third force should be applied in the direction of:
1. North-East
2. North-West
3. South-West
4. South-East
Given are two vectors, \(\overrightarrow{A} = \left(\right. 2 \hat{i} - 5 \hat{j} + 2 \hat{k} \left.\right)\) and \(\overrightarrow{B} = \left(4 \hat{i} - 10 \hat{j} + c \hat{k} \right).\) What should be the value of \(c\) so that vector \(\overrightarrow A \) and \(\overrightarrow B\) would becomes parallel to each other?
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
If \(\overrightarrow{A} \times \overrightarrow{B} = \overrightarrow{C} + \overrightarrow{D}\), then which of the following statement is correct?
1. | \(\overrightarrow B\) must be perpendicular to \(\overrightarrow C\) |
2. | \(\overrightarrow A\) must be perpendicular to \(\overrightarrow C\) |
3. | Component of \(\overrightarrow C\) along \(\overrightarrow A\) = Component of \(\overrightarrow D\) along \(\overrightarrow A\) |
4. | Component of \(\overrightarrow C\) along \(\overrightarrow A\) = - (Component of \(\overrightarrow D\) along \(\overrightarrow A\)) |
What is the maximum value of \(5\sin\theta-12\cos\theta\)?
1. \(12\)
2. \(17\)
3. \(7\)
4. \(13\)
A block of weight \(W\) is supported by two strings inclined at \(60^{\circ}\) and \(30^{\circ}\) to the vertical. The tensions in the strings are \(T_1\) and \(T_2\) as shown. If these tensions are to be determined in terms of \(W\) using the triangle law of forces, which of these triangles should you draw? (block is in equilibrium):
1. | 2. | ||
3. | 4. |
The magnitude of the resultant of two vectors of magnitude \(3\) units and \(4\) units is \(1\) unit. What is the value of their dot product?
1. \(-12\) units
2. \(-7\) units
3. \(-1\) unit
4. \(0\)
The value of
1. ln (\(x\) + 1) + C
2.
3.
4. ln (\(x\) – 1) + C
If \(\overrightarrow {A} = 2\hat{i} + \hat{j} - \hat{k},\) \(\overrightarrow {B} = \hat{i} + 2\hat{j} + 3\hat{k},\) and \(\overrightarrow {C} = 6 \hat{i} - 2\hat{j} - 6\hat{k},\) then the angle between \(\left(\overrightarrow {A} + \overrightarrow{B}\right)\) and \(\overrightarrow{C}\) will be:
1. \(30^{\circ}\)
2. \(45^{\circ}\)
3. \(60^{\circ}\)
4. \(90^{\circ}\)
The maximum or the minimum value of the function \(y= 25x^{2}-10x +5\) is:
1. \(y_{\text{min}}= 4\)
2. \(y_{\text{max}}= 8\)
3. \(y_{\text{min}}= 8\)
4. \(y_{\text{max}}= 4\)
The unit vector perpendicular to vectors \(\overrightarrow a= \left(3 \hat{i}+\hat{j}\right) \) and \(\overrightarrow B = \left(2\hat i - \hat j -5\hat k\right)\) is:
1. \(\pm \frac{\left(\right. \hat{i} - 3 \hat{j} + \hat{k} \left.\right)}{\sqrt{11}}\)
2. \(\pm \frac{\left(3 \hat{i} + \hat{j}\right)}{\sqrt{11}}\)
3. \(\pm \frac{\left(\right. 2 \hat{i} - \hat{j} - 5 \hat{k} \left.\right)}{\sqrt{30}}\)
4. None of these