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Integral Calculus – II Model Question Paper

12th Standard

    Reg.No. :
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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. 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

  2. Area bounded by the curve y = \(\frac{1}{x}\) between the limits 1 and 2 is ________.

    (a)

    log 2 sq.units

    (b)

    log 5 sq.units

    (c)

    log 3 sq.units

    (d)

    log 4 sq.units

  3. If the marginal revenue MR = 35 + 7x − 3x2, then the average revenue AR is ________.

    (a)

    35x + \(\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 3 }\)

    (b)

    35x + \(\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 2 }\)

    (c)

    35 +\(\frac { 7{ x }^{ 2 } }{ 2 } +{ x }^{ 2 }\)

    (d)

    35 + 7x + x2

  4. The area of the region bounded by the line 2y = -x + 8, X - axis and the lines x = 2 and x = 4 is ________ sq.units.

    (a)

    \(\frac{1}{5}\)

    (b)

    \(\frac{2}{5}\)

    (c)

    5

    (d)

    \(\frac{5}{2}\)

  5. The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.

    (a)

    \(\frac{13}{3}\)

    (b)

    13

    (c)

    \(\frac{26}{3}\)

    (d)

    \(\frac{3}{13}\)

  6. 5 x 2 = 10
  7. Elasticity of a function \(\frac{Ey}{Ex}\) is given by \(\frac{Ey}{Ex}\) = \(​​\frac { -7x }{ (1-2x)(2+3x) } \). Find the function when x = 2, y = \(\frac{3}{8}\)

  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 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.

  10. Find the consumer's surplus for the demand function p = 25 - x -x2 when Po = 19

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

  12. 5 x 3 = 15
  13. Using integration find the area of the region bounded between the line x = 4 and the parabola y2 = 16x.

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

  15. 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.

  16. Find the area bounded by one arc of the curve y = sin ax and the x-axis.

  17. A company determines that the marginal cost of producing x units is C'(x) = 10.6x. The fixed cost is Rs. 50. The selling price per unit is Rs.5. Find the profit function.

  18. 4 x 5 = 20
  19. The price of a machine is 6,40,000 if the rate of cost saving is represented by the function f(t) = 20,000 t. Find out the number of years required to recoup the cost of the function.

  20. The marginal cost C'(x) and marginal revenue R'(x) are given by C'(x) = 50 + \(\frac{x}{50}\) and R'(x) = 60. The fixed cost is Rs. 200. Determine the maximum profit

  21. The marginal cost function of a commodity in a firm is 2 + e3x where X is the output. Find the total cost and average cost function if the fixed cost is Rs. 500.

  22. Find the area bounded by the curve y = sin x between x = 0 and x = 2π

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