Applications of Differentiation questions with solutions

Showing 1–10 of 100 questions

• MCQmediumMathematical tools and vectorApplications of Differentiation

  The volume of a sphere increases at 36π cm³ s⁻¹. Find dr/dt when r=3 cm.

  Options

  • Option A

    1 cm s⁻¹

  • Option B

    2 cm s⁻¹

  • Option C

    1/2 cm s⁻¹

  • Option D

    3 cm s⁻¹

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• MatchmediumMathematical tools and vectorApplications of Differentiation

  Match List I with List II and choose the correct option.

  List 1

  1. x=5t² at t=2

  2. v=3t² at t=2

  3. I=4t+1 at t=3

  4. A=πr², r=2, dr/dt=3

  List 2

  1. 12 A s⁻¹

  2. 20 m s⁻¹

  3. 12 m s⁻²

  4. 12π cm² s⁻¹

  Options

  • Option A

    P-1, Q-2, R-3, S-4

  • Option B

    P-2, Q-4, R-1, S-3

  • Option C

    P-3, Q-1, R-4, S-2

  • Option D

    P-2, Q-3, R-1, S-4

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• MCQmediumMathematical tools and vectorApplications of Differentiation

  The side of a cube changes so that dV/dt = 96 cm³ s⁻¹ when a=4 cm. Find da/dt.

  Options

  • Option A

    1 cm s⁻¹

  • Option B

    3 cm s⁻¹

  • Option C

    4 cm s⁻¹

  • Option D

    2 cm s⁻¹

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• MCQeasyMathematical tools and vectorApplications of Differentiation

  A velocity-time curve is v=t³-3t²+2t. Find its slope at t=1 s.

  Options

  • Option A

    -1 m s⁻²

  • Option B

    1 m s⁻²

  • Option C

    0

  • Option D

    2 m s⁻²

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• MCQmediumMathematical tools and vectorApplications of Differentiation

  A curve has slope -√3. In the range 0°<θ<180°, tangent angle is:

  Options

  • Option A

    120°

  • Option B

    60°

  • Option C

    30°

  • Option D

    150°

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• MCQmediumMathematical tools and vectorApplications of Differentiation

  A closed cylinder of fixed volume has minimum surface area when:

  Options

  • Option A

    h=4r

  • Option B

    h=r/2

  • Option C

    h=2r

  • Option D

    h=r

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• MatchmediumMathematical tools and vectorApplications of Differentiation

  Match List I with List II and choose the correct option.

  List 1

  1. y=log(sinx)

  2. y=sin(logx)

  3. y=√(x²+1)

  4. y=x sinx

  List 2

  1. sinx+xcosx

  2. x/√(x²+1)

  3. cotx

  4. cos(logx)/x

  Options

  • Option A

    P-1, Q-2, R-3, S-4

  • Option B

    P-2, Q-4, R-1, S-3

  • Option C

    P-3, Q-1, R-4, S-2

  • Option D

    P-3, Q-4, R-2, S-1

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• MCQeasyMathematical tools and vectorApplications of Differentiation

  The radius of a circle increases at 3 cm s⁻¹. Find the rate of increase of its area when r = 4 cm.

  Options

  • Option A

    48π cm² s⁻¹

  • Option B

    24π cm² s⁻¹

  • Option C

    12π cm² s⁻¹

  • Option D

    16π cm² s⁻¹

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• MCQmediumMathematical tools and vectorApplications of Differentiation

  A rectangular field is fenced on three sides with total fence length L, the fourth side along a river. Maximum area is:

  Options

  • Option A

    L²/2

  • Option B

    L²/8

  • Option C

    L²/4

  • Option D

    L²/16

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• MCQeasyMathematical tools and vectorApplications of Differentiation

  Find the slope of y = log x at x = 2.

  Options

  • Option A

    1/2

  • Option B

    2

  • Option C

    1

  • Option D

    1/4

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