Application Of Calculus Chapter Important Questions Class 12 ISC
Here we provide Class 12 Maths important questions,board questions and predicted questions with Answers for chapter Application Of Calculus. These important notes,board questions and predicted questions are based on ISC board curriculum and correspond to the most recent Class 12 Maths syllabus. By practising these Class 12 materials, students will be able to quickly review all of the ideas covered in the chapter and prepare for the Class 12 Board examinations.
Q1
A television manufacturer finds that total cost for the production and marketing x number of
television sets is :
C(x) = 300x2 + 4200x + 13500.
Each product is sold for Rs 8400. Determine the breakeven points.
Solution
Q2
A company sells its products at the rate of Rs 6 per unit. The variable costs are estimated
to run 25% of the total revenue received. If the fixed costs for the product are Rs 4500, find
(i) the total revenue function
(ii) the total cost function
(iii) the profit function
(iv) the breakeven point
(v) the number of units the company must sell to cover its fixed cost.
Solution
Q3 The price of selling one unit of a product when x units are demanded is given by the equation p = 4000 - 2x. The fixed costs of the product are Rs 20000 and Rs 1484 per unit are paid for the product to place in a store. Find the level of sales at which the company can expect to cover its costs.
Solution
Q4
A company sells pens at Rs 5 per unit.
The fixed cost for the company is Rs 3200 and variable cost is estimated to run 25% of the total
revenue. Determine :
(i) the total revenue function
(ii) the total cost function
(iii) the breakeven point, and
(iv) the quantity the company must sell to cover its fixed cost.
Solution
Q5 A company sells x packets of noodles each day at Rs 20 a packet. The cost of production is Rs 15 per packet plus a fixed daily overhead cost of Rs 1200. Determine the profit function What is the profit if 1000 packets are produce and sold everyday? 500 packets ? 200 packets ?
Solution
Q6
The demand x of a commodity in terms of price p is given by x = 1/9(245 - 7p). The average cost is
Rs 20 per unit. Find in terms of p:
(i) the cost function
(ii) the revenue function
(iii) the profit function
(iv) the price and level of output at which profit is zero.
Solution
Q7
The average cost function AC for a commodity is given by AC = x + 5 + 36/x in terms of
output x. Find
(i) the total cost and the marginal cost as the functions of x.
(ii) the output for which AC increases.
Solution
Q8
Given the total cost function for x units of a commodity as
C(x) = (1/3)x3 + x2 - 8x + 5, find :
(i) the marginal cost function
(ii) average cost function
(iii) slope of average cost function.
Solution
Q9 If the cost function of a production unit is C(x) = 40 - 20x + 10 x2, find the average cost function and the output x where average cost is minimum. Verify that the average cost is equal to the marginal cost at this level of output.
Solution
Q10
The demand function of a monopolist is P(x) = 300 - x2. Find
(i) the revenue function
(ii) the marginal revenue function
(iii) the output x when revenue is maximum.
Solution
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