## (d) data is not sufficient to find

1. Chapter 6 Class 12 Application of Derivatives (Term 1)
2. Serial order wise
3. Case Based Questions (MCQ)

Transcript

Question P(x) = ใโ5๐ฅใ^2+125๐ฅ+37500 is the total profit function of a company, where x is the production of the company. Question 1 What will be the production when the profit is maximum? (a) 37500 (b) 12.5 (c) โ12.5 (d) โ37500 Given P(x) = โ5x2 + 125x + 37500 Differentiating w.r.t x Pโ(x) = d(ใโ5๐ฅใ^2 + 125๐ฅ + 37500)/๐๐ฅ Pโ(x) = โ5 ร 2x + 125 Pโ(x) = โ10x + 125 Putting Pโ(x) = 0 โ10x + 125 = 0 โ10x = --125 x = (โ125)/(โ10) x = 12.5 Finding Pโโ(x) Pโโ(x) = d(โ10๐ฅ + 125)/๐๐ฅ Pโโ(x) = โ10 < 0 Since Pโโ(๐) < 0 at ๐ฅ = 12.5 โด ๐ฅ = 12.5 is point of maxima Thus, P(๐ฅ) is maximum when ๐ = 12.5 So, the correct answer is (b) Question 2 What will be the maximum profit? (a) Rs 38,28,125 (b) Rs 38281.25 (c) Rs 39,000 (d) None Putting x = 12.5 in P(x) P(x) = โ5x2 + 125x + 37500 = โ5(12.5)2 + 125(12.5) + 37500 = โ5(156.25) + 1562.5 + 37500 = โ781.25 + 1562.5 + 37500 = 781.25 + 37500 = Rs 38281.25 So, the correct answer is (b) Question 3 Check in which interval the profit is strictly increasing . (a) (12.5, โ) (b) for all real numbers (c) for all positive real numbers (d) (0, 12.5) Profit is strictly increasing where Pโ(x) > 0 โ10x + 125 > 0 125 > 10x 10x < 125 x < 12.5 So, profit is strictly increasing for x โ (0, 12.5) So, the correct answer is (d) Question 4 When the production is 2 units, what will be the profit of the company? (a) 37,500 (b) 37,730 (c) 37,770 (d) None Putting x = 2 in P(x) P(x) = โ5x2 + 125x + 37500 = โ5(2)2 + 125(2) + 37500 = โ5(4) + 250 + 37500 = โ20 + 250 + 37500 = 230 + 37500 = Rs 37730 So, the correct answer is (b) Question 5 What will be production of the company when the profit is Rs 38,250? (a) 15 (b) 30 (c) 2 (d) data is not sufficient to find Putting P(x) = 38250 in formula of P(x) P(x) = โ5x2 + 125x + 37500 38250 = โ5x2 + 125x + 37500 5x2 โ 125x โ 37500 + 38250 = 0 5x2 โ 125x + 750 = 0 Dividing both sides by 5 x2 โ 25x + 150 = 0 x2 โ 10x โ 15x + 150 = 0 x(x โ 10) โ 15(x โ 10) = 0 (x โ 10) (x โ 15) = 0 โด x = 10, 15 Since x = 15 is in the options So, the correct answer is (a)

Case Based Questions (MCQ)