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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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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A vector A is directed along 30° west of north direction and another vector B along 15° south of east. Their resultant cannot be in ____________ direction.

(1)  North

(2)  East

(3)  North-East

(4)  South

Subtopic:  Resultant of Vectors |
 59%
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ABCD is a quadrilateral. Forces BA, BC, CD & DA act at a point. Their resultant is 

(A)  2 AB

(B)  2 DA

(C)  zero vector

(D)  2 BA

Subtopic:  Resultant of Vectors |
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The maximum and minimum magnitude of the resultant of two vectors are 17 units and 7 units respectively. Then the magnitude of resultant of the vectors when they act perpendicular to each other is:

(1)  14

(2)  16

(3)  18

(4)  13

Subtopic:  Resultant of Vectors |
 69%
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A vector A makes an angle of 20° and B makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the magnitude of the resultant.

(A)  1

(B)  52

(C)  5

(D)  7

Subtopic:  Resultant of Vectors |
 81%
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A particle is moving westward with a velocity vi=5 m/s. Its velocity changed to vf=5m/s northward. The change in velocity vector V=vf-vi is:

(1)  52 m/s  towards north east

(2)  5 m/s  towards north west

(3)  zero

(4)  52 m/s towards north west

Subtopic:  Resultant of Vectors |
 61%
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