Applications of Differentiation Book Back Questions

11th Standard

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. Average fixed cost of the cost function C(x) = 2x3 +5x2 - 14x +21 is

    (a)

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

    (b)

    \(\frac { 5}{ x } \)

    (c)

    \(\frac { -14 }{ x } \)

    (d)

    \(\frac { 21 }{ x } \)

  2. Marginal revenue of the demand function p= 20–3x is

    (a)

    20–6x

    (b)

    20–3x

    (c)

    20+6x

    (d)

    20+3x

  3. For the cost function C =\(\frac { 1 }{ 25 } { e }^{ 25 }\), the marginal cost is 

    (a)

    \(\frac { 1 }{ 25 } \)

    (b)

    \(\frac { 1 }{ 5 } { e }^{ 5x }\)

    (c)

    \(\frac { 1 }{ 125 } { e }^{ 5x }\)

    (d)

    25e5x

  4. Instantaneous rate of change of y = 2x2 + 5x with respect to x at x = 2 is

    (a)

    4

    (b)

    5

    (c)

    13

    (d)

    9

  5. If the average revenue of a certain firm is Rs 50 and its elasticity of demand is 2, then their marginal revenue is

    (a)

    Rs 50 

    (b)

    Rs 25

    (c)

    Rs 100

    (d)

    Rs 75

  6. 3 x 2 = 6
  7. The cost function of a firm is \(C={1\over3}x^3-3x^2+9x\)Find the level of output (x>0) when average cost is minimum

  8. For the demand function x = \(\frac { 25 }{ { p }^{ 4 } } ,1\le p\le 5\), determine the elasticity of demand

  9. The demand and cost functions of a firm are x = 6000–30p and C = 72000+60x respectively. Find the  level of output and price at which the profit is maximum.

  10. 3 x 3 = 9
  11. Find the interval in which the function f(x)=x2–4x+6 is strictly increasing and strictly decreasing.

  12. If u = log(x2+y2) show that \(\frac { { \partial }^{ 2 }u }{ { \partial x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ \partial { y }^{ 2 } } =0\)

  13. Verify Euler’s theorem for the function \(u=\frac{1}{\sqrt{x^2+y^2}}\)

  14. 2 x 5 = 10
  15. The demand and the cost function of a firm are p = 497-0.2x and C = 25x+10000 respectively. Find the output level and price at which the profit is maximum

  16. A monopolist has a demand curve x = 106 – 2p and average cost curve AC = 5+\(\frac { x }{ 50 } \) where p is the price per unit output and x is the number of units of output. If the total revenue is R = px, determine the most profitable output and the maximum profit.

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