Applications of Differentiation One Mark Questions

11th Standard

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Business Maths

Time : 00:30:00 Hrs
Total Marks : 10
    10 x 1 = 10
  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. If demand and the cost function of a firm are p= 2–x and c = 2x2 +2x +7 then its profit function is

    (a)

    x2 + 7

    (b)

    x2 - 7

    (c)

    - x2 + 7

    (d)

    - x2 - 7

  4. Relationship among MR, AR and ηd is

    (a)

    \({ n }_{ d }=\frac { AR }{ AR-MR } \)

    (b)

    n4 =  AR - MR

    (c)

    MR = AR = n4

    (d)

    \(AR=\frac { MR }{ { n }_{ 4 } } \)

  5. 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

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

    (a)

    4

    (b)

    5

    (c)

    13

    (d)

    9

  7. 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

  8. Profit P(x) is maximum when 

    (a)

    MR = MC

    (b)

    MR = 0

    (c)

    MC = AC

    (d)

    TR = AC

  9. The maximum value of f(x)= sinx is

    (a)

    1

    (b)

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

    (c)

    \(\frac { 1 }{ \sqrt { 2 } } \)

    (d)

    \(-\frac { 1 }{ \sqrt { 2 } } \)

  10. If f(x,y) is a homogeneous function of degree n, then \(x\frac { \partial f }{ \partial x } +y\frac { \partial f }{ \partial y } \) is equal to

    (a)

    (n–1)f

    (b)

    n(n–1)f

    (c)

    nf

    (d)

    f

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