Class 11 Mathematics · Chapter 13 · Test 3
Differentiation Applications
37 MCQs Covers velocity and acceleration, stress, profit and marginal profit, investment growth and cost minimisation (Ex 13.3).
37 questions · 30 min · 37 marks
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Sample questions
The first 5 of 37. Try each one, then tap to see the answer.
Question 1
A car's position is s(t) = 5t³ − 3t² + t. Its velocity is
- A5t² − 3t + 1
- B15t² − 6t + 1
- C15t³ − 6t² + t
- D15t² − 6t
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Answer: B
v = ds/dt = 15t² − 6t + 1.
Question 2
For s(t) = 5t³ − 3t² + t, the velocity at t = 2 is
- A60
- B41
- C25
- D49
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Answer: D
15(4) − 12 + 1 = 49.
Question 3
Acceleration is the derivative of
- Avelocity with respect to time
- Bposition with respect to distance
- Cacceleration with respect to time
- Dvelocity with respect to distance
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Answer: A
a = dv/dt = d²s/dt².
Question 4
Structural stress is S(x) = 100 − 5x². The rate of change dS/dx is
- A10x
- B100 − 10x
- C−10x
- D−5x
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Answer: C
S′ = −10x.
Question 5
S(x) = 100 − 5x² is maximum at x =
- A10
- B0
- C√20
- D−10
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Answer: B
S′ = −10x = 0 gives x = 0, and S″ = −10 < 0.
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