A particle starts rotating from rest and its angular displacement is given by θ=t240+t5. Then, the angular velocity ω=dt at the end of 10 s will be :

1. 0.7

2. 0.6

3. 0.5

4. 0

Subtopic:  Differentiation |
 81%
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The value of x=x=RGMmx2 dx is

1. GMmR

2. 2GMmR

3. -GMmR

4. -2GMmR

Subtopic:  Integration |
 71%
From NCERT
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0QqCdq, where C is a constant, can be expressed as:

1. Q2C

2. -Q22C

3. -Q2C

4. Q22C

Subtopic:  Integration |
 82%
From NCERT
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If the force on an object as a function of displacement is F(x)=3x2+x, what is work as a function of displacement w(x) W=(fdx). Assume W(0)=0 and force is in the direction of the object's motion.

1. 3x32+x2

2. x3+x22

3. 6x+1

4. 3x2+x

Subtopic:  Integration |
 85%
From NCERT
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The velocity of a rocket, in metres per second, t seconds after it was launched is modelled by \(v(t)=2\sqrt{t}\). What is the total distance travelled by the rocket during the first four seconds of its launch?

1. 163 m

2. 32 m

3. 323 m

4. 16 m

Subtopic:  Integration |
 73%
From NCERT
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The work done by gravity exerting an acceleration of -10 m/s2 for a 10 kg block down 5 m from its original position with no initial velocity is:

(Fgrav=mass ×acceleration and W=abF(x)dx)

1. 250 J

2. 500 J

3. 100 J

4. 1000 J

Subtopic:  Integration |
 80%
From NCERT
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Water flows into a container of 1000 L at a rate of (180+3t) gal/min for an hour, where t is measured in minutes. Find the amount of water that flows into the pool during the first 20 minutes.

1. 4000 gal

2. 2800 gal

3. 4200 gal

4. 3800 gal

Subtopic:  Integration |
 74%
From NCERT
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If v(t)=3t-1 and x(2)=1, then the original position function is: 
Hint: v(t)=dsdt

1. 32t2-t-3

2. 12t2-t-3

3. 32t2-2t-3

4. None of the above

Subtopic:  Integration |
 75%
From NCERT
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If charge flown through a wire is given by q=3sin(3t), then-current flown through the wire at t=π9 seconds is: i=dqdt

1. 4.5 Amp

2. 4.53 Amp

3. 32 Amp

4. 9 Amp

Subtopic:  Differentiation |
 71%
From NCERT
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A weight hanging from a spring is stretched down 3 cm beyond its rest position and released at time t=0 to bob up and down. Its position at any later time t is s=3cos(t). Then its velocity at time t is velocity =dsdt

(1) cost

(2) 3cost

(3) 3sint

(4) -3sint

Subtopic:  Differentiation |
 81%
From NCERT
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