Integral Calculus – II Book Back Questions

12th Standard EM

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Business Maths

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)

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