Integral Calculus – II Important Questions

12th Standard EM

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    10 x 1 = 10
  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. The demand and supply functions are given by D(x)= 16 − x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    5

  3. The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is

    (a)

    9x2 + 54x

    (b)

    9x2 − 54x

    (c)

    54x - \(\frac { { 9x }^{ 2 } }{ 2 } \)

    (d)

    54x - \(\frac { { 9x }^{ 2 } }{ 2 } \) + k

  4. 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)

    \(\frac{41}{5}\)

  5. The area unded by the curves y = 2x, x = 0 anx=2 is________sq.units.

    (a)

    loge2

    (b)

    3loge2

    (c)

    \(\frac{3}{log_e2}\)

    (d)

    2loge3

  6. 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)

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

  7. The area enclosed by the curve y = cos2x in [0,\(\pi\)] the lines x=0, x=\(\pi\) and the X-axis is ________sq.units.

    (a)

    2\(\pi\)

    (b)

    2\(\pi\)

    (c)

    \(\frac{2}{\pi}\)

    (d)

    \(\frac{\pi}{2}\)

  8. 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)

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

  9. The area of the region bounded by the curve y2 = 2y - x and the y-axis _____ sq. units

    (a)

    \(\frac{4}{3}\)

    (b)

    \(\frac{2}{3}\)

    (c)

    4

    (d)

    \(\frac{16}{3}\)

  10. The area bounded by the curve y = 4ax and the lines y2 = 2a and Y-axis is _______ sq. units.

    (a)

    \(\frac{2a}{3}\)

    (b)

    2a2

    (c)

    \(\frac{a^2}{3}\)

    (d)

    \(\frac{2a^2}{3}\)

  11. 5 x 1 = 5
  12. \(\int _{ 0 }^{ t }{ 20,000t\quad dt } \)

  13. (1)

    2x+5ex+k

  14. \(\int _{ 0 }^{ t }{ f(t)dt } \)

  15. (2)

    55

  16. \(\int _{ 0 }^{ t }{(100-90x)dx } \)

  17. (3)

    MR-MC

  18. ഽ(2+5ex)dx

  19. (4)

    10,000t2

  20. \(\frac{dp}{dx}\)

  21. (5)

    F(t)

    5 x 2 = 10
  22. Calculate the area bounded by the parabola y2 = 4ax and its latusrectum.

  23. Find the area of the region lying in the first quadrant bounded by the region y = 4x2 , x = 0, y = 0 and y = 4

  24. Find the demand function for which the elasticity of demand is 1

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

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

  27. 5 x 3 = 15
  28. The demand function of a commodity is y = 36 − x2. Find the consumer’s surplus for y0 = 11

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

  30. Find the area of the region bounded by the line y = x - 5, the x-axis and between the ordinates x=3and x=7

  31. The Marginal revenue for a commodity is MR=\(\frac { { e }^{ x } }{ 100 } +x+{ x }^{ 2 }\), find the revenue function.

  32. The marginal revenue function is given by \(R'(x)=\frac { 3 }{ { x }^{ 2 } } -\frac { 2 }{ x } \). Find the revenue function and demand function if R(1)=6

  33. 2 x 5 = 10
  34. 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.

  35. Sketch the graph of y = Ix - 5|. Evaluate \(\int _{ 0 }^{ 1 }{ |4x-5|dx } \)

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