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#### Integral Calculus – II Book Back Questions

12th Standard EM

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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

(a)

$\frac{30}{3}$ sq.units

(b)

$\frac{31}{3}$sq.units

(c)

$\frac{32}{3}$ sq.units

(d)

$\frac{15}{2}$ sq.units

2. Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

(a)

1 sq.units

(b)

$\frac{1}{2}$ sq.unit

(c)

5 sq.units

(d)

2 sq.units

3. The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

(a)

40

(b)

$\frac{41}{2}$

(c)

$\frac{40}{3}$

(d)

$\frac{41}{5}$

4. The profit of a function p(x) is maximum when

(a)

MC − MR = 0

(b)

MC = 0

(c)

MR = 0

(d)

MC + MR = 0

5. When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 − x2 is

(a)

250 units

(b)

$\frac{250}{3}$units

(c)

$\frac{251}{2}$ units

(d)

$\frac{251}{3}$ units

6. 3 x 2 = 6
7. The cost of over haul of an engine is Rs. 10,000 The operating cost per hour is at the rate of 2x − 240 where the engine has run x km. Find out the total cost if the engine run for 300 hours after overhaul.

8. A company receives a shipment of 500 scooters every 30 days. From experience it is known that the inventory on hand is related to the number of days x. Since the shipment, I (x) = 500 − 0.03x2 , the daily holding cost per scooter is Rs. 0.3. Determine the total cost for maintaining inventory for 30 days.

9. If MR = 20 − 5x + 3x2, find total revenue function.

10. 3 x 3 = 9
11. The demand function of a commodity is y = 36 − x2. Find the consumer’s surplus for y0 = 11

12. Find the producer’s surplus defined by the supply curve g(x) = 4x + 8 when xo= 5.

13. The demand and supply function of a commodity are pd = 18− 2x − x2 and ps = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.

14. 2 x 5 = 10
15. The rate of new product is given by f (x) = 100 − 90 e−x where x is the number of days the product is on the market. Find the total sale during the first four days. (e–4 = 0.018)

16. In year 2000 world gold production was 2547 metric tons and it was growing exponentially at the rate of 0.6% per year. If the growth continues at this rate, how many tons of gold will be produced from 2000 to 2013? [e0.078 = 1.0811)