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)

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

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

(a)

20–6x

(b)

20–3x

(c)

20+6x

(d)

20+3x

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

Relationship among MR, AR and η_d is ______.

(a)

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

(b)

η_d =  AR - MR

(c)

MR = AR = η_d

(d)

\(AR=\frac { MR }{ {ηd } } \)

For the cost function C =\(\frac { 1 }{ 25 } { e }^{ 5x }\), the marginal cost is _________.

(a)

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

(b)

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

(c)

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

(d)

25e^5x

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

(a)

4

(b)

5

(c)

13

(d)

9

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

Profit P(x) is maximum when ________.

(a)

MR = MC

(b)

MR = 0

(c)

MC = AC

(d)

TR = AC

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

(a)

1

(b)

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

(c)

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

(d)

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

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