# If two forces of 5 N each are acting along X and Y axes, then the magnitude and direction of resultant is  (1) $5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /3$ (2) $5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /4$ (3) $-5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /3$ (4) $-5\sqrt{2},\text{\hspace{0.17em}\hspace{0.17em}}\pi /4$

Subtopic:  Resultant of Vectors |
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Two forces are such that the sum of their magnitudes is 18 N and their resultant is perpendicular to the smaller force and the magnitude of the resultant is 12 N. Then the magnitudes of the forces will be:

1. 12 N, 6 N

2. 13 N, 5N

3. 10 N, 8 N

4. 16 N, 2 N

Subtopic:  Resultant of Vectors |
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Two forces with equal magnitudes F act on a body and the magnitude of the resultant force is F/3. The angle between the two forces is

(1) ${\mathrm{cos}}^{-1}\left(-\frac{17}{18}\right)$

(2) ${\mathrm{cos}}^{-1}\left(-\frac{1}{3}\right)$

(3) ${\mathrm{cos}}^{-1}\left(\frac{2}{3}\right)$

(4) ${\mathrm{cos}}^{-1}\left(\frac{8}{9}\right)$

Subtopic:  Resultant of Vectors |
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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°

Subtopic:  Resultant of Vectors |
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If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is:

Subtopic:  Resultant of Vectors |
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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°

2. 45°

3. 180°

4. 0°

Subtopic:  Resultant of Vectors |
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If vectors A = cosωt $\stackrel{^}{i}$ + sinωt $\stackrel{^}{j}$ and B = (cosωt/2) $\stackrel{^}{i}$ + (sinωt/2) $\stackrel{^}{j}$ are functions of time, then the value of t at which they are orthogonal to each other

1. t=$\mathrm{\pi }$/4ω
2. t=$\mathrm{\pi }$/2ω
3. t=$\mathrm{\pi }$
4. t=0

Subtopic:  Scalar Product |
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Six vectors  have the directions as indicated in the figure. Which of the following statements may be true?

1. $\stackrel{\to }{b}+\stackrel{\to }{c}=\stackrel{\to }{-f}$
2. $\stackrel{\to }{d}+\stackrel{\to }{c}=\stackrel{\to }{f}$
3. $\stackrel{\to }{d}+\stackrel{\to }{e}=\stackrel{\to }{f}$
4. $\stackrel{\to }{b}+\stackrel{\to }{e}=\stackrel{\to }{f}$

Subtopic:  Resultant of Vectors |
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Assertion: The graph between P and Q is a straight line when P/Q is constant.
Reason: The straight-line graph means that P is proportional to Q or P is equal to a constant multiplied by Q.

Which one, of the following statements, is correct?
1. If both the assertion and the reason are true, and the reason is the correct explanation of the assertion.
2. If both the assertion and the reason are true but the reason is not the correct explanation of the assertion.
3. If the assertion is true but the reason is false.
4. If the assertion and reason are both false

Subtopic:  Co-ordinate geometry |
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Two forces A and B have a resultant ${R}_{1}$. If B is doubled, the new resultant ${R}_{2}$ is perpendicular to A. Then

1. ${R}_{1}=A$

2. ${R}_{1}=B$

3. ${R}_{2}=A$

4. ${R}_{2}=B$

Subtopic:  Resultant of Vectors |
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