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CBSE Class 12 Mathematics 2026 Main Paper 65/5/2 · Q263 Marksrelated_rates

CBSE Class 12 Mathematics 2026 Main Paper 65/5/2 · Question 26 (Applications Of Derivatives)

The area enclosed by a circular wire increases at constant rate k. Prove that the circumference rate is inversely proportional to radius.

✅ Step-by-Step Solution

Final Answer: dC/dt=k/r.
  1. Use A=πr² and C=2πr.
  2. The chain rule gives k=2πr dr/dt and dC/dt=2π dr/dt.
  3. Eliminate dr/dt to get k/r.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Use A=πr² and C=2πr.
  • [2 marks] The chain rule gives k=2πr dr/dt and dC/dt=2π dr/dt.
  • [0.5 marks] Eliminate dr/dt to get k/r.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/5/2

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