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)

\(\frac{31}{2}\)sq.units

(c)

\(\frac{32}{3}\) sq.units

(d)

\(\frac{15}{2}\) sq.units

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

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

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

For the demand function p(x), the elasticity of demand with respect to price is unity then ________.

(a)

revenue is constant

(b)

cost function is constant

(c)

profit is constant

(d)

none of these

When x₀ = 5 and p₀ = 3 the consumer’s surplus for the demand function p_d = 28 − x² is ________.

(a)

250 units

(b)

\(\frac{250}{3}\)units

(c)

\(\frac{251}{2}\) units

(d)

\(\frac{251}{3}\) units

The marginal cost function is MC = 100 \(\sqrt x\). find AC given that TC  = 0 when the out put is zero is ________.

(a)

\(\frac { 200 }{ 3 } { x }^{ \frac { 1 }{ 2 } }\)

(b)

\(\frac { 200 }{ 3 } { x }^{ \frac { 3 }{ 2 } }\)

(c)

\(\frac { 200 }{ { 3x }^{ \frac { 3 }{ 2 } } } \)

(d)

\(\frac { 200 }{ { 3x }^{ \frac { 1 }{ 2 } } } \)

If the marginal revenue of a firm is constant, then the demand function is ________.

(a)

MR

(b)

MC

(c)

C(x)

(d)

AC

Area bounded by y = \(\left| x \right| \) between the limits 0 and 2 is ________.

(a)

1sq.units

(b)

3 sq.units

(c)

2 sq.units

(d)

4 sq.units

The area bounded by y = 2x - x² and X-axis is _________ sq. units

(a)

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

(b)

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

(c)

2

(d)

4