A particle moves in the XY plane and at time t is at the point whose coordinates are (t2, . Then at what instant of time, will its velocity and acceleration vectors be perpendicular to each other?
(1) 1/3 sec
(2) 2/3 sec
(3) 3/2 sec
(4) never
The maximum value of the function 7 + 6 x - 9 x^{2} is:
1. 8
2. -8
3. 4
4. -4
A motor boat of mass m moving along a lake with velocity . At t=0, the engine of the boat is shut down. Magnitude of resistance force offered to the boat is equal to rV. (V is instantaneous speed). What is the total distance covered till it stops completely?
(1)
(2)
(3)
(4)
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 = is (shaded region):
1. 1 unit
2. 2 units
3. 3 units
4. 4 units
The dimension of is
(1)
(2)
(3)
(4) None of these
Component of perpendicular to and in the same plane as that of is:
1.
2.
3.
4.
If two force vectors of the same magnitude are arranged in the following manner, the magnitude of resultant is maximum for?
(1) (I)
(2) (II)
(3) Both (II) & (III)
(4) Both (I) & (II)
If vector and have magnitude 5, 12 and 13 units and , then the angle between and will be:
1.
2.
3.
4.
A particle travels with speed 50 m/s from the point (3,7) in a direction 7\hat i -24 \hat j. Find its position vector after 3 seconds.
1. 151\hat i+45\hat j
2. 45\hat i-137\hat j
3. 151\hat i-45\hat j
4. 4.5\hat i-151\hat j
Two forces A and B have a resultant . If B is doubled, the new resultant is perpendicular to A. Then
1.
2.
3.
4.