Applications of Differentiation questions with solutions

Showing 1–10 of 100 questions

• MCQeasyMathematical tools and vectorApplications of Differentiation

  Find the maximum value of sin x cos x.

  Options

  • Option A

    √2/2

  • Option B

    1/2

  • Option C

    1

  • Option D

    1/4

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• MatchmediumMathematical tools and vectorApplications of Differentiation

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

  List 1

  1. cubic local maximum

  2. cubic local minimum

  3. potential-energy minimum

  4. potential-energy maximum

  List 2

  1. stable equilibrium

  2. unstable equilibrium

  3. f''<0

  4. f''>0

  Options

  • Option A

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

  • Option B

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

  • Option C

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

  • Option D

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

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• MatchmediumMathematical tools and vectorApplications of Differentiation

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

  List 1

  1. θ=45°

  2. tanθ=μ

  3. x=R/√2

  4. R=r

  List 2

  1. max ring field

  2. max load power

  3. max projectile range

  4. min rough-surface pull

  Options

  • Option A

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

  • Option B

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

  • Option C

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

  • Option D

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

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• MCQmediumMathematical tools and vectorApplications of Differentiation

  A cone of height 12 cm has radius increasing at 0.5 cm s⁻¹ while height remains constant. Find dV/dt when r = 3 cm.

  Options

  • Option A

    12π cm³ s⁻¹

  • Option B

    9π cm³ s⁻¹

  • Option C

    18π cm³ s⁻¹

  • Option D

    24π cm³ 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

  For a cone, radius and height always satisfy h = 2r. If r increases at 1 cm s⁻¹, find dV/dt at r = 3 cm.

  Options

  • Option A

    9π cm³ s⁻¹

  • Option B

    27π cm³ s⁻¹

  • Option C

    36π cm³ s⁻¹

  • Option D

    18π cm³ s⁻¹

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• MCQeasyMathematical tools and vectorApplications of Differentiation

  A projectile has range R=u²sin2θ/g. For fixed u, range is maximum at:

  Options

  • Option A

    θ=30°

  • Option B

    θ=60°

  • Option C

    θ=90°

  • Option D

    θ=45°

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• MCQeasyMathematical tools and vectorApplications of Differentiation

  Find the maximum value of sin x + cos x.

  Options

  • Option A

    2

  • Option B

    1/√2

  • Option C

    √2

  • Option D

    1

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• MCQeasyMathematical tools and vectorApplications of Differentiation

  A projectile trajectory is y = 2x - x²/10. Find the slope at x=5 m.

  Options

  • Option A

    0

  • Option B

    2

  • Option C

    1/2

  • Option D

    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. projectile range

  2. minimum pull force

  3. ring electric field

  4. load power from cell

  List 2

  1. tanθ=μ

  2. x=R/√2

  3. θ=45°

  4. R=r

  Options

  • Option A

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

  • Option B

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

  • Option C

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

  • Option D

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

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