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 |
 60%
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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 |
 58%
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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 |
 68%
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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 |
 80%
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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 |
 60%
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Consider east as positive x-axis, north as positive y-axis and vertically upward direction as z-axis. A helicopter first rises up to an altitude of 100 m than flies straight in north 500 m and then suddenly takes a turn towards east and travels 1000 m east. What is position vector of helicopter. (Take starting point as origin)

(1)  1000 i^-500 j^+100 k^

(2)  1000 i^+500 j^-100 k^

(3)  1000 i^+500 j^+100 k^

(4)  -1000 i^+500 j^+100 k^

Subtopic:  Resolution of Vectors |
 77%
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A force F=6i^-8j^+10k^ Newton produces acceleration 1 m/s2 in a body. The mass of the body is (in kg)

(1)  6i^-8j^+10k^

(2)  100

(3)  102

(4)  10

Subtopic:  Newton's Laws |
 75%
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Given the vectors

                         A=2i^+3j^-k^
                         B=3i^-2j^-2k^
&                      C=pi^+pj^+2pk^

Find the angle between A-B & C

(A)  θ=cos-123

(B)  θ=cos-132

(C)  θ=cos-123

(D)  none of these

Subtopic:  Scalar Product |
 52%
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The vector having a magnitude of 10 and perpendicular to the vector 3i^-4j^ is- 

1. 4i^-3j^

2. 52 i^-52 j^

3. 8i^+6j^

4.  8i^-6j^

Subtopic:  Scalar Product |
 62%
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