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Q. No.For \(x \ll 1,\) the approximate value of \((1+x)^2\) is:
1. \(1+x^2\)
2. \(1+x\)
3. \(1+2x\)
4. \(1+2x+x^2\)
1. \(1+x^2\)
2. \(1+x\)
3. \(1+2x\)
4. \(1+2x+x^2\)
Subtopic: Â Differentiation |
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Level 1: 80%+
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The displacement \(x\) of a particle varies with time as \(x=ae^{\alpha t}+be^{\beta t}\) where \(a,b,\alpha,\beta\) are constant and are positives. The velocity of the particle will:
| 1. | drop to zero when \(\alpha=\beta\) |
| 2. | be independent of \(\alpha\) and \(\beta\) |
| 3. | go on increasing with time |
| 4. | go on decreasing with time |
Subtopic: Â Differentiation |
 76%
Level 2: 60%+
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If \(x \ll 1,\) then \((1+x)^{-1}\) is approximately equal to:
1. \(1+x\)
2. \(1-x\)
3. \(1+x^2\)
4. \(1-x^2\)
1. \(1+x\)
2. \(1-x\)
3. \(1+x^2\)
4. \(1-x^2\)
Subtopic: Â Differentiation |
 91%
Level 1: 80%+
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The displacement x of a particle along a straight line at time t is given by . The acceleration of the particle is:
1. \(a_0\)
2. \(a_1\)
3. \(2a_2\)
4. \(a_2\)
Subtopic: Â Differentiation |
 88%
Level 1: 80%+
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The area \(A\) of a metallic disc (in square metres) varies with time \(t\) (in seconds) according to the equation: \(A=5t^2+2t.\)
What is the rate of change of the area with respect to time at \(t=3 ~\text s\text{?}\)
| 1. | \(30~\text{m}^2/\text s\) | 2. | \(32~\text{m}^2/\text s\) |
| 3. | \(\dfrac{51}{3}~\text{m}^2/\text s\) | 4. | \(45~\text{m}^2/\text s\) |
Subtopic: Â Differentiation |
 89%
Level 1: 80%+
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The current in a circuit is given by: \(I=\dfrac{dq}{dt}.\) If the charge flowing through the circuit is described by: \(q=(t^2-3t+4),\) at what time is the current in the circuit equal to zero?
1. \(t=3\) s
2. \(t=2\) s
3. \(t=1.5\) s
4. \(t=15\) s
Subtopic: Â Differentiation |
 87%
Level 1: 80%+
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The derivative of the function; \(y=\sin \left(x^{2}\right)\) with respect to \(x\) is:
1. \(\mathrm{cos}~x^2\)
2. \(\mathrm{sin}~2x\)
3. \(\mathrm{-cos}~x^2\)
4. \(2x~\mathrm{cos}~x^2\)
1. \(\mathrm{cos}~x^2\)
2. \(\mathrm{sin}~2x\)
3. \(\mathrm{-cos}~x^2\)
4. \(2x~\mathrm{cos}~x^2\)
Subtopic: Â Differentiation |
 84%
Level 1: 80%+
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