Exercise 6.6 - Chapter 6 - Application of Differentiation - 11th Business Maths Guide Samacheer Kalvi Solutions

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Exercise 6.6

Text Book Back Questions and Answers

Choose the correct answer.

Question 1.
Average fixed cost of the cost function C(x) = 2x³ + 5x² – 14x + 21 is:

Answer:

Question 2.
Marginal revenue of the demand function p = 20 – 3x is:
(a) 20 – 6x
(b) 20 – 3x
(c) 20 + 6x
(d) 20 + 3x
Answer:
(a) 20 – 6x
Hint:
p = 20 – 3x
Revenue, R = px = (20 – 3x)x = 20x – 3x²

Marginal revenue

Question 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
Answer:
(b) x² – 7
Hint:
Profit = Revenue – Cost
= (2 – x)x – (-2x² + 2x + 7)
= 2x – x² + 2x² – 2x – 7
= x² – 7

Question 4.
If the demand function is said to be inelastic, then:
(a) |η_d| > 1
(b) |η_d| = 1
(c) |η_d| < 1
(d) |η_d| = 0
Answer:
(a) |η_d| > 1

Question 5.
The elasticity of demand for the demand function  is

(a) 0
(b) 1

(d) ∞
Answer:
(b) 1
Hint:

Question 6.
Relationship among MR, AR and ηd is:

(b) η_d = AR – MR
(c) MR = AR = η_d

Question 7.
For the cost function  the marginal cost is:

Answer:

Question 8.
Instantaneous rate of change of y = 2x² + 5x with respect to x at x = 2 is:
(a) 4
(b) 5
(c) 13
(d) 9
Answer:
(c) 13
Hint:
y = 2x² + 5x

Question 9.
If the average revenue of a certain firm is ₹ 50 and its elasticity of demand is 2, then their marginal revenue is:
(a) 50
(b) 25
(c) 100
(d) 75
Answer:
(b) 25
Hint:

Question 10.
Profit P(x) is maximum when:
(a) MR = MC
(b) MR = 0
(c) MC = AC
(d) TR = AC
Answer:
(a) MR = MC

Question 11.
The maximum value of f(x) = sin x is:
(a) 1

Answer:
(a) 1
Hint:
When   sin x is maximum.
Maximum value is

Question 12.
If f(x, y) is a homogeneous function of degree n, then  

is equal to:
(a) (n – 1)f
(b) n(n – 1)f
(c) nf
(d) f
Answers:
(c) nf

Question 13.
If u = 4x² + 4xy + y² + 4x + 32y + 16, then   
 is equal to:
(a) 8x + 4y + 4
(b) 4
(c) 2y + 32
(d) 0
Answer:
(b) 4
Hint:
u = 4x² + 4xy + y² + 4x + 32y + 16

Question 14.
If u = x³ + 3xy² + y³ then    is:
(a) 3
(b) 6y
(c) 6x
(d) 2
Answer:
(b) 6y
Hint:
u = x³ + 3xy² + y³

Question 15.

Question 16.
Average cost is minimum when:
(a) Marginal cost = marginal revenue
(b) Average cost = marginal cost
(c) Average cost = Marginal revenue
(d) Average Revenue = Marginal cost
Answer:
(b) Average cost = marginal cost

Question 17.
A company begins to earn profit at:
(a) Maximum point
(b) Breakeven point
(c) Stationary point
(d) Even point
Answer:
(b) Breakeven point

Question 18.
The demand function is always:
(a) Increasing function
(b) Decreasing function
(c) Non-decreasing function
(d) Undefined function
Answer:
(b) Decreasing function

Question 19.
If q = 1000 + 8p₁ – p₂ then,  is

(a) -1
(b) 8
(c) 1000
(d) 1000 – p₂
Answer:
(b) 8
Hint:
q = 1000 + 8p₁ – p₂

Question 20.
If R = 5000 units/year, C₁ = 20 paise, C₃ =  20 then EOQ is:
(a) 5000
(b) 100
(c) 1000
(d) 200
Answer:
(c) 1000
Hint: