Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The resultant force acting on particle is:

(A)  2i^+5j^+4k^

(B)  2i^-5j^-4k^

(C)  i^-3j^-2k^

(D)  i^-j^-k^

Subtopic:  Resultant of Vectors |
 84%
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A=4i+4j-4k and B=3i+j+4k, then angle between vectors A and B is:

(1)  180°

(2)  90°

(3)  45°

(4)  0°

Subtopic:  Resultant of Vectors |
 77%
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If vectors \(\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}\) and \(\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}\) are functions of time. Then, at what value of \(t\) are they orthogonal to one another?
1. \(t = \frac{\pi}{4\omega}\)
2. \(t = \frac{\pi}{2\omega}\)
3. \(t = \frac{\pi}{\omega}\)
4. \(t = 0\)

Subtopic:  Scalar Product |
 59%
From NCERT
NEET - 2015
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Six vectors a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true? 

1. b+c=f

2. d+c=f

3. d+e=f

4. b+e=f

Subtopic:  Resultant of Vectors |
 74%
From NCERT
AIPMT - 2010
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A and B are two vectors and θ is the angle between them. If A×B=3A.B, then the value of θ will be:

1. 60o

2. 45o

3. 30o

4. 90o

Subtopic:  Scalar Product | Vector Product |
 80%
From NCERT
AIPMT - 2007
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If a curve is governed by the equation y=sinx, then the area enclosed by the curve and x-axis between x =0 and x =π is (shaded region) :

              

1. 1 unit

2. 2 units

3. 3 units

4. 4 units

Subtopic:  Integration |
 58%
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The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. The velocity of the particle at time instant t is: (\(Here, a=\frac{dv}{dt}\))

1. αt2+βt

2. αt2+βt2

3. αt22+βt

4. 2αt2+βt

Subtopic:  Integration |
 85%
From NCERT
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The displacement of the particle is zero at t=0 and at t=t it is x. It starts moving in the x-direction with a velocity that varies as v=kx, where k is constant. The velocity will : (Here, \(v=\frac{dx}{dt}\))

1. vary with time.

2. be independent of time.

3. be inversely proportional to time.

4. be inversely proportional to acceleration.

Subtopic:  Integration |
 51%
From NCERT
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The acceleration of a particle is given as a=3x2.  At t = 0, v = 0 and x = 0. It can then be concluded that the velocity at t = 2 sec will be: (Here, \(a=v\frac{dv}{dx}\))

1.  0.05 m/s

2. 0.5 m/s

3. 5 m/s

4. 50 m/s 

Subtopic:  Integration |
 62%
From NCERT
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The acceleration of a particle is given by a=3t  at t=0, v=0, x=0. The velocity and displacement at t = 2 sec will be: (\(Here, a=\frac{dv}{dt}~ and~v=\frac{dx}{dt}\))

1. 6 m/s, 4 m

2. 4 m/s, 6 m

3. 3 m/s, 2 m

4. 2 m/s, 3 m

Subtopic:  Integration |
 85%
From NCERT
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