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 = e^−2x between the limits 0 ≤ x ≤ ∞ is ________.

(a)

1 sq.units

(b)

\(\frac{1}{2}\) sq.unit

(c)

5 sq.units

(d)

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

If the marginal revenue function of a firm is MR = \({ e }^{ \frac { -x }{ 10 } }\), then revenue is ________.

(a)

\(-10{ e }^{ \frac { -x }{ 10 } }\)

(b)

\(1-{ e }^{ \frac { -x }{ 10 } }\)

(c)

\(10\left( 1-{ e }^{ \frac { -x }{ 10 } } \right) \)

(d)

\({ e }^{ \frac { -x }{ 10 } }+10\)

If MR and MC denotes the marginal revenue and marginal cost functions, then the profit functions is ________.

(a)

P = ഽ(MR − MC) dx + k

(b)

P = ഽ(MR + MC) dx + k

(c)

P = ഽ(MR)(MC)dx + k

(d)

P = ഽ(R −C)dx + k

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

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

The given demand and supply function are given by D(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)

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

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

The profit of a function p(x) is maximum when ________.

(a)

MC − MR = 0

(b)

MC = 0

(c)

MR = 0

(d)

MC + MR = 0

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

The demand function for the marginal function MR = 100 − 9x² is ________.

(a)

100 − 3x²

(b)

100x − 3x²

(c)

100x − 9x²

(d)

100 + 9x²

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

When x₀ = 2 and P₀ = 12 the producer’s surplus for the supply function P_s = 2x² + 4 is ________.

(a)

\(\frac{31}{5}\)units

(b)

\(\frac{31}{2}\) units

(c)

\(\frac{32}{3}\) units

(d)

\(\frac{30}{7}\) units

Area bounded by y = x between the lines y = 1, y = 2 with y = axis is ________.

(a)

\(\frac{1}{2}\) sq.units

(b)

\(\frac{5}{2}\) sq.units

(c)

\(\frac{3}{2}\) sq.units

(d)

1 sq.unit

The producer’s surplus when the supply function for a commodity is P = 3 + x and x₀ = 3 is ________.

(a)

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

(b)

\(\frac{9}{2}\)

(c)

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

(d)

\(\frac{7}{2}\)

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)

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

The demand and supply function of a commodity are P(x) = (x − 5)² and S(x)= x² + x + 3 then the equilibrium quantity x₀ is ________.

(a)

5

(b)

2

(c)

3

(d)

19

The demand and supply function of a commodity are D(x) = 25 − 2x and S(x) = \(\frac { 10+x }{ 4 } \) then the equilibrium price P₀ is ________.

(a)

5

(b)

2

(c)

3

(d)

10

If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x² − 81 , then the maximum profit at x is equal to ________.

(a)

3

(b)

6

(c)

9

(d)

5

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

(a)

MR

(b)

MC

(c)

C(x)

(d)

AC

For a demand function p, if \(\int \frac{d p}{p}=k \int \frac{d x}{x}\) then k is equal to ________.

(a)

\(\eta \)_d

(b)

-\(\eta \)_d

(c)

\(\frac{-1}{\eta_{d}}\)

(d)

\(\frac{1}{\eta_{d}}\)

Area bounded by y = e^x between the limits 0 to 1 is ________.

(a)

( e −1) sq.units

(b)

( e +1) sq.units

(c)

\(\left( 1-\frac { 1 }{ e } \right) \)sq.units

(d)

\(\left( 1+\frac { 1 }{ e } \right) \)sq.units

The area bounded by the parabola y² = 4x bounded by its latus rectum is ________.

(a)

\(\frac { 16 }{ 3 } \) sq.units

(b)

\(\frac { 8 }{ 3 } \) sq.units

(c)

\(\frac { 72 }{ 3 } \) sq.units

(d)

\(\frac { 1 }{ 3 } \) sq.units

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