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12th Business Maths Weekly Test - 4 ( Integral Calculus – II )

St. Britto Hr. Sec. School - Madurai

12th Business Maths Weekly Test - 4 ( Integral Calculus – II )-Aug 2020

Time : 12.45 Hours

Part - A

Multiple Choice Question - Answer All Question

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

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

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

5
2
3
10

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

9x² + 54x
9x² − 54x
54x - \(\frac { { 9x }^{ 2 } }{ 2 } \)
54x - \(\frac { { 9x }^{ 2 } }{ 2 } \) + k

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

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

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

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

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

revenue is constant
cost function is constant
profit is constant
none of these

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

5
2
3
19

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

3
6
9
5

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

MC − MR = 0
MC = 0
MR = 0
MC + MR = 0

Area bounded by the curve y = e^−2x between the limits 0 ≤ x ≤ ∞ is

1 sq.units
\(\frac{1}{2}\) sq.unit
5 sq.units
2 sq.units

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

250 units
\(\frac{250}{3}\)units
\(\frac{251}{2}\) units
\(\frac{251}{3}\) units

Area bounded by the curve y = \(\frac{1}{x}\) between the limits 1 and 2 is

log2 sq.units
log5 sq.units
log3 sq.units
log 4 sq.units

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

40
\(\frac{41}{2}\)
\(\frac{40}{3}\)
\(\frac{41}{5}\)

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

1sq.units
3 sq.units
2 sq.units
4 sq.units

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

MR
MC
C(x)
AC

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

\(\frac{1}{2}\)sq.units
\(\frac{5}{2}\)sq.units
\(\frac{3}{2}\)sq.units
1 sq.unit

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

2
3
4
5

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

P = ഽ(MR − MC) dx + k
P = ഽ(MR + MC) dx + k
P = ഽ(MR)(MC)dx + k
P = ഽ(R −C)dx + k

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

\(\frac{31}{5}\)units
\(\frac{31}{2}\) units
\(\frac{32}{3}\) units
\(\frac{30}{7}\) units

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

100 − 3x²
100x − 3x²
100x − 9x²
100 + 9x²

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