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#### Integral Calculus – II Two Marks Questions

12th Standard EM

Reg.No. :
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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. The marginal cost function is MC = 300 ${ x }^{ \frac { 2 }{ 5 } }$ and fixed cost is zero. Find out the total cost and average cost functions.

2. If the marginal cost function of x units of output is $\frac { a }{ \sqrt { ax+b } }$ and if the cost of output is zero. Find the total cost as a function of x.

3. If the marginal cost (MC) of a production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is Rs. 5,000 and the cost of producing 50 units is Rs. 5,625.

4. The demand function p = 85 − 5x and supply function p = 3x − 35. Calculate the equilibrium price and quantity demanded .Also calculate consumer’s surplus.

5. The demand and supply functions under perfect competition are p= 1600 − x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus.

6. Under perfect competition for a commodity the demand and supply laws are Pd  =  $\frac { 8 }{ x+1 } -2$ and P$\frac { x-3 }{ 2 }$ respectively. Find the consumer’s and producer’s surplus.

7. For the marginal revenue function MR = 6 − 3x2 − x3 , Find the revenue function and demand function.

8. The marginal cost of production of a firm is given by C'(x) = 20 + $\frac { x }{ 20 }$ the marginal revenue is given by R'(x) = 30 and the fixed cost is Rs. 100. Find the profit function

9. Find the area of the region bounded by the curve between the parabola y = 8x2 − 4x + 6 the y-axis and the ordinate at x = 2.

10. Find the area of the region bounded by the curve y2 = 27x3 and the lines x = 0, y = 1 and y = 2.

11. Find the area of the region bounded by the parabola x2 = 4y, Y = 2, Y = 4 and the y-axis.

12. Find the area under the curve y = 4x2 - 8x + 6 bounded by the Y-axis, X-axis and the ordinate at x = 2.

13. If the marginal revenue for a commodity is MR = 9 - 6x2 + 2x, find the total revenue function.

14. The marginal cost at a production level of x units is given by C '(x) = 85+$\frac{375}{x^2}$. Find the cost of producing 10 in elemental units after 15 units have been produced?

15. Find the producer's surplus for the supply function p =r +x2 + 3 when xo =4