Q. No.If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is:
1. \(90^{\circ}\)
2. \(45^{\circ}\)
3. \(180^{\circ}\)
4. \(0^{\circ}\)
1. \(90^{\circ}\)
2. \(45^{\circ}\)
3. \(180^{\circ}\)
4. \(0^{\circ}\)
Six vectors \(\overrightarrow a ~\text{through}~\overrightarrow f\) have the directions as indicated in the figure. Which of the following statements may be true?
1. \(\overrightarrow b + \overrightarrow c = -\overrightarrow f\)
2. \(\overrightarrow d + \overrightarrow c = \overrightarrow f\)
3. \(\overrightarrow d + \overrightarrow e = \overrightarrow f\)
4. \(\overrightarrow b + \overrightarrow e = \overrightarrow f\)
| Assertion (A): | The graph between \(P\) and \(Q\) is a straight line when \(\frac{P}{Q}\) is constant. |
| Reason (R): | The straight-line graph means that \(P\) is proportional to \(Q\) or \(P\) is equal to a constant multiplied by \(Q\). |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False |
In the given figure
| 1. | Angle between \(\overrightarrow {A}\) and \(\overrightarrow {B}\) is \(110^{\circ}\) |
| 2. | Angle between \(\overrightarrow {C}\) and \(\overrightarrow {D}\) is \(60^{\circ}\) |
| 3. | Angle between \(\overrightarrow {B}\) and \(\overrightarrow {C}\) is \(110^{\circ}\) |
| 4. | Angle between \(\overrightarrow {B}\) and \(\overrightarrow {C}\) is \(70^{\circ}\) |
A child pulls a box with a force of \(200~\text{N}\) at an angle of \(60^{\circ}\)
1. \(100~\text{N}, ~175~\text{N}\)
2. \(86.6~\text{N}, ~100~\text{N}\)
3. \(100~\text{N}, ~86.6~\text{N}\)
4. \(100~\text{N}, ~0~\text{N}\)
The linear velocity of a rotating body is given by , where is the angular velocity and r is the radius vector. The angular velocity of a body, and their radius vector is will be:
1.
2.
3.
4.
A body is moving according to the equation \(x = at +bt^2-ct^3\) where \(x\) represents displacement and \(a, b~\text{and}~c\) are constants. The acceleration of the body is: (\(\text{Given:}~ a=\frac{d^2x}{dt^2}\))
1. \(a+ 2bt\)
2. \(2b+ 6ct\)
3. \(2b- 6ct\)
4. \(3b- 6ct^2\)
If \(\overrightarrow{a}\) is a vector and \(x\) is a non-zero scalar, then which of the following is correct?
| 1. | \(x\overrightarrow{a}\) is a vector in the direction of \(\overrightarrow{a}\). |
| 2. | \(x\overrightarrow{a}\) is a vector collinear to \(\overrightarrow{a}\). |
| 3. | \(x\overrightarrow{a}\) and \(\overrightarrow{a}\) have independent directions. |
| 4. | \(x\overrightarrow{a}\) is a vector perpendicular to \(\overrightarrow{a}\). |
\(\overrightarrow{A}\) and \(\overrightarrow B\) are two vectors and \(\theta\) is the angle between them. If \(\left|\overrightarrow A\times \overrightarrow B\right|= \sqrt{3}\left(\overrightarrow A\cdot \overrightarrow B\right),\) then the value of \(\theta\) will be:
| 1. | \(60^{\circ}\) | 2. | \(45^{\circ}\) |
| 3. | \(30^{\circ}\) | 4. | \(90^{\circ}\) |
1. \(20\) m
2. \(7.2\) m
3. \(5.0\) m
4. \(4.5\) m
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