A curve is governed by the equation y=sinx, then what is the area enclosed by the curve and x-axis between x =0 and x =π is (shaded region)

       

1. 1 units

2. 2 units

3. 3 units

4. 4 units

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Calculate the area of disk of radius 'a' using integration

1. πa22

2. πa2

3. 32πa2

4. 2πa2

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The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. Find the velocity of the particle at time instant t.

1. αt2+βt

2. αt2+βt2

3. αt22+βt

4. 2αt2+βt

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The displacement of particle is zero at t=0 and at t=t it is x. It starts moving in the x direction with velocity, which varies as v=kx, where k is constant. The velocity-

1. varies with time

2. is independent to time

3. inversely proportional to time

4. inversely proportional to acceleration

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The acceleration of a particle is given as a=3x2. At t=0, v=0, x=0, the velocity at t =2 sec will be-

1.  0.05 m/s

2. 0.5 m/s

3. 5 m/s

4. 50 m/s 

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The acceleration of a particle is given by a=3t and at t=0, v=0, x=0. The velocity and displacement at t = 2 sec will be-

1. 6 m/s, 4 m

2. 4 m/s, 6 m

3. 3 m/s, 2 m

4. 2 m/s, 3 m

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The 9 kg block is moving to the right with a velocity of 0.6 m/s on a horizontal surface when a force F, whose time variation is shown in the graph, is applied to it at time t = 0. Calculate the velocity v of the block when t= 0.4s. The coefficient of kinetic fricton is μk=0.3[ This question is only for Dropper and XII batch]

1. 0.6 m/s

2. 1.2 m/s

3. 1.8 m/s

4. 2.4 m/s

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A 10 kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x=0 to x=8 cm [This question is only for Dropper and XII batch]

1. 6×10-2 J

2. 7×10-2 J

3. 8×10-2 J

4. 9×10-2 J

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The relationship between force and position is shown in the figure given (in one dimensional case). Find the work done by the force in displaying a body from x= 1 cm to x= 5cm is   [This question is only for Dropper and XII batch]

1. 10 erg

2. 20 erg

3. 30 erg

4. 40 erg

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The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and initial velocity is 2 m/s. When the distance covered by the body is 4 m, its kinetic energy would be    [This question is only for Dropper and XII batch]

1. 50 J

2. 40 J

3. 20 J

4. 10 J

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