Two constant forces F1=2i^-3j^+3k^ N and F2=i^+j^-2k^ N act on a body and displace it from the position r1=i^+2j^-2k^ m to the position r2=7i^+10j^+5k^ m. What is the work done W? [Given : W =F.r]

(A)  9 Joule

(B)  41 Joule

(C)  -3 Joule

(D)  None of these

Subtopic:  Scalar Product |
 62%
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The angle that the vector A=2i^+3j^ makes with the y-axis is:

(1)  tan-1 3/2

(2)  tan-1 2/3

(3)  sin-1 2/3

(4)  cos-1 3/2

Subtopic:  Resultant of Vectors | Scalar Product |
 61%
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A vector A points, vertically upward and, B points towards north. The vector product A×B is -

1.  along west

2.  along east

3.  zero

4.  vertically downward

Subtopic:  Vector Product |
 57%
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The linear velocity of a rotating body is given by v=ω×r, where ω is the angular velocity and r is the radius vector. The angular velocity of a body, ω=i^-2j^+2k^ and their radius vector is  r=4j^-3k^, then value of |v| will be:

1. 29 units

2. 31 units

3. 37 units

4. 41 units

Subtopic:  Vector Product |
 76%
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The displacement of a particle is given by \(y = a+bt+ct^2-dt^4\). The initial velocity and initial acceleration, respectively, are: \(\left(\text{Given:}~ v=\frac{dx}{dt}~\text{and}~a=\frac{d^2x}{dt^2}\right)\)
1. \(b, -4d\)
2. \(-d, 2c\)
3. \(b, 2c\)
4. \(2c, -4d\)

Subtopic:  Differentiation |
 77%
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The momentum is given by p=4t+1, the force at t=2s is-[Given: F=dPdt]

(A)  4 N

(B)  8 N

(C)  10 N

(D)  15 N

Subtopic:  Newton's Laws |
 79%
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If the momentum of a particle is given by P=(180-8t) kg m/s, then its force will be-[Given: F=dPdt]

(1)  Zero

(2)  8 N

(3)  -8 N

(4)  4 N

Subtopic:  Newton's Laws |
 83%
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The maximum value of the function \(7 + 6 x - 9 x^{2}\) is:
1. \(8\)
2. \(-8\)
3. \(4\)
4. \(-4\)

Subtopic:  Differentiation |
 67%
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If \(f \left(x\right) = x^{2} - 2 x + 4\), then \(f(x)\) has:

1. a minimum at \(x=1\).
2. a maximum at \(x=1\).
3. no extreme point.
4. no minimum.
Subtopic:  Differentiation |
 66%
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A particle is moving along x-axis. The velocity v of particle varies with its position x as v=1x. Find velocity of particle as a function of time t given that at t=0, x=1 .

1.  v=2t+1

2.  v=12t+1

3.  v=1t

4.  None of these

Subtopic:  Integration |
 59%
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