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CA Foundation · Quantitative Aptitude · Differential and Integral Calculus

The marginal cost of a firm is MC = 6x + 10 (in ₹), where x is output in units. If the fixed cost is ₹200, the total cost of producing 5 units is:

The total cost of 5 units is ₹325. Integrating marginal cost gives 3x² + 10x plus a constant equal to the fixed cost of ₹200. At x = 5 this is 75 + 50 + 200, which equals ₹325.

  1. A₹325Correct
  2. B₹275
  3. C₹125
  4. D₹300

Explanation

C(x) = ∫(6x + 10)dx = 3x² + 10x + K. With C(0) = 200, K = 200. At x = 5: 3(25) + 50 + 200 = 75 + 50 + 200 = ₹325. Omitting fixed cost gives ₹125, which is wrong because fixed cost must be added.

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