Q. No.If vectors A = cosωt + sinωt and B = (cosωt/2) + (sinωt/2) are functions of time, then the value of t at which they are orthogonal to each other
1. t=/4ω
2. t=/2ω
3. t=/ω
4. t=0
1. t=/4ω
2. t=/2ω
3. t=/ω
4. t=0
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. \(\overrightarrow b + \overrightarrow e = \overrightarrow f\)
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. \(0^{\circ}\)
2. \(90^{\circ}\)
3. \(45^{\circ}\)
4. \(180^{\circ} \)
If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is
1.
2.
3.
4.
Two forces are such that the sum of their magnitudes is \(18~\text{N}\) and their resultant is perpendicular to the smaller force and the magnitude of the resultant is \(12~\text{N}\). Then the magnitudes of the forces will be:
1. \(12~\text{N}, 6~\text{N}\)
2. \(13~\text{N}, 5~\text{N}\)
3. \(10~\text{N}, 8~\text{N}\)
4. \(16~\text{N}, 2~\text{N}\)
Two forces with equal magnitudes \(F\) act on a body and the magnitude of the resultant force is \(\frac{F}{3}\). The angle between the two forces is:
1. \(\cos^{- 1} \left(- \frac{17}{18}\right)\)
2. \(\cos^{- 1} \left(- \frac{1}{3}\right)\)
3. \(\cos^{- 1} \left(\frac{2}{3}\right)\)
4. \(\cos^{- 1} \left(\frac{8}{9}\right)\)
Two forces of magnitude F have a resultant of the same magnitude F. The angle between the two forces is
1. 45°
2 120°
3. 150°
4. 60°
| 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 |
Two forces A and B have a resultant . If B is doubled, the new resultant is perpendicular to A. Then
1.
2.
3.
4.
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