12th Business Mathematics and Statistics - Book Back Answers - Chapter 3 - English Medium Guides

 

 

Plus Two / 12th Business Mathematics and Statistics - Book Back Answers - Chapter 3 - English Medium

Tamil Nadu Board 12th Standard Business Mathematics and Statistics - Chapter 3: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 3 – Business Mathematics and Statistics from the Tamil Nadu State Board 12th Standard Business Mathematics and Statistics textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Business Mathematics and Statistics  Chapter 3 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 12 students! Prepare well and aim for top scores. Thank you!

Chapter 3:

I. Multiple Choice Questions

1. Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is
(a) $\frac{\mathbf{30}}{\mathbf{3}}$ sq.units 
(b) $\frac{\mathbf{31}}{\mathbf{2}}$ sq.units
(c) $\frac{\mathbf{32}}{\mathbf{3}}$ sq.units 
(d) $\frac{\mathbf{15}}{\mathbf{2}}$ sq.units
Answer Key:
(c) $\frac{\mathbf{32}}{\mathbf{3}}$ sq.units 

 
2. Area bounded by the curve y = ${\mathbf{e}}^{\mathbf{-}\mathbf{2}\mathbf{x}}$ between the limits 0 ≤ x ≤ ∞ is
(a) 1 sq.units 
(b) $\frac{\mathbf{1}}{\mathbf{2}}$ sq.unit
(c) 5 sq.units 
(d) 2 sq.units
Answer Key:
(b) $\frac{\mathbf{1}}{\mathbf{2}}$ sq.unit

 
3. Area bounded by the curve y=$\frac{\mathbf{1}}{\mathbf{x}}$ between the limits 1 and 2 is
(a) log2 sq.units 
(b) log5 sq.units
(c) log3 sq.units 
(d) log 4 sq.units
Answer Key:
(a) log2 sq.units 

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

(b) 1− ${\mathbf{e}}^{\frac{\mathbf{-}\mathbf{x}}{\mathbf{10}}}$
(c) 10$($1− ${\mathbf{e}}^{\frac{\mathbf{-}\mathbf{x}}{\mathbf{10}}}$$)$ 

(d) − ${\mathbf{e}}^{\frac{\mathbf{-}\mathbf{x}}{\mathbf{10\; +10}}}$
Answer Key:
(c) 10$($1− ${\mathbf{e}}^{\frac{\mathbf{-}\mathbf{x}}{\mathbf{10}}}$$)$ 

 
5. If MR and MC denotes the marginal revenue and marginal cost functions, then the profit
functions is
(a) P = $\mathbf{\int }$(MR − MC) dx + k
(b) P = $\mathbf{\int }$(MR + MC) dx + k
(c) P = $\mathbf{\int }$(MR)(MC)dx + k
(d) P = $\mathbf{\int }$(R −C)dx + k
Answer Key:
(a) P = $\mathbf{\int }$(MR − MC) dx + k

 
6. The demand and supply functions are given by D(x)= 16 − ${\mathbf{x}}^{\mathbf{2}}$ and S(x) = 2${\mathbf{x}}^{\mathbf{2}}$ + 4 are
under perfect competition, then the equilibrium price x is
(a) 2 
(b) 3 
(c) 4 
(d) 5
Answer Key:
(a) 2 

 
7. 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) 9${\mathbf{x}}^{\mathbf{2}}$ + 54x 
(b) 9${\mathbf{x}}^{\mathbf{2}}$ − 54x
(c) 54x- $\frac{\mathbf{9}{\mathbf{x}}^{\mathbf{2}}}{\mathbf{2}}$

(d) 54x-$\frac{\mathbf{9}{\mathbf{x}}^{\mathbf{2}}}{\mathbf{2}}$+k 
Answer Key:
(d) 54x-$\frac{\mathbf{9}{\mathbf{x}}^{\mathbf{2}}}{\mathbf{2}}$+k

 
8. 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) $\frac{\mathbf{41}}{\mathbf{2}}$
(c) $\frac{\mathbf{40}}{\mathbf{3}}$
(d) $\frac{\mathbf{41}}{\mathbf{5}}$
Answer Key:
(c) $\frac{\mathbf{40}}{\mathbf{3}}$

$\frac{\mathbf{ }}{}$
9. If the marginal revenue MR = 35 + 7x − 3${\mathbf{x}}^{\mathbf{2}}$, then the average revenue AR is
(a) 35x+$\frac{\mathbf{7}{\mathbf{x}}^{\mathbf{2}}}{\mathbf{2}}\mathbf{-}{\mathbf{x}}^{\mathbf{3}}$  
(b) 35+$\frac{\mathbf{7}\mathbf{x}}{\mathbf{2}}\mathbf{-}{\mathbf{x}}^{\mathbf{2}}$ 
(c)  35+$\frac{\mathbf{7}\mathbf{x}}{\mathbf{2}}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}$
(d) 35 + 7x + ${\mathbf{x}}^{\mathbf{2}}$
Answer Key:
(b) 35+$\frac{\mathbf{7}\mathbf{x}}{\mathbf{2}}\mathbf{-}{\mathbf{x}}^{\mathbf{2}}$ 

 
10. The profit of a function p(x) is maximum when
(a) MC − MR = 0 
(b) MC=0
(c) MR=0 
(d) MC+MR=0
Answer Key:
(a) MC − MR = 0

 
11. 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
Answer Key:
(a) revenue is constant

 
12. The demand function for the marginal function MR = 100 − 9${\mathbf{x}}^{\mathbf{2}}$ is
(a) 100 − 3${\mathbf{x}}^{\mathbf{2}}$
(b)100x − 3${\mathbf{x}}^{\mathbf{2}}$
(c)100x − 9${\mathbf{x}}^{\mathbf{2}}$
(d)100 + 9${\mathbf{x}}^{\mathbf{2}}$
Answer Key:
(a) 100 − 3${\mathbf{x}}^{\mathbf{2}}$

${\mathbf{ }}^{}$
13. When ${\mathbf{x}}_{\mathbf{0}}\mathbf{=}\mathbf{5}$ and ${\mathbf{p}}_{\mathbf{0}}\mathbf{=}\mathbf{3}$ the consumer’s surplus for the demand function ${\mathbf{p}}_{\mathbf{d}}$ = 28 − ${\mathbf{x}}^{\mathbf{2}}$ is
(a) 250 units 
(b) $\frac{250}{3}$ units
(c) $\frac{251}{2}$ units 
(d) $\frac{251}{3}$ Units
Answer Key:
(b) $\frac{250}{3}$ units

 
14. When ${\mathbf{x}}_{\mathbf{0}}\mathbf{=2}$ and ${\mathbf{p}}_{\mathbf{0}}\mathbf{=}$12 the producer’s  surplus for the supply function ${\mathbf{P}}_{\mathbf{s}}$ = 2x2 + 4 is
(a) $\frac{\mathbf{31}}{\mathbf{5}}$ units 
(b) $\frac{\mathbf{31}}{\mathbf{2}}$ units
(c) $\frac{\mathbf{32}}{\mathbf{3}}$ units 
(d) $\frac{\mathbf{30}}{\mathbf{7}}$ Units
Answer Key:
(c) $\frac{\mathbf{32}}{\mathbf{3}}$ units

 
15. Area bounded by y = x between the lines y = 1, y = 2 with y = axis is
(a) $\frac{\mathbf{1}}{\mathbf{2}}$ sq.units 
(b) $\frac{\mathbf{5}}{\mathbf{2}}$ sq.units
(c) $\frac{\mathbf{3}}{\mathbf{2}}$ sq.units 
(d) 1 sq.unit
Answer Key:
(c) $\frac{\mathbf{3}}{\mathbf{2}}$ sq.units

 
16. The producer’s surplus when the supply function for a commodity is P = 3 + x and ${\mathbf{x}}_{\mathbf{0}}$ = 3is
(a) $\frac{\mathbf{5}}{\mathbf{2}}$
(b) $\frac{\mathbf{9}}{\mathbf{2}}$
(c) $\frac{\mathbf{3}}{\mathbf{2}}$
(d) $\frac{\mathbf{7}}{\mathbf{2}}$
Answer Key:
(b) $\frac{\mathbf{9}}{\mathbf{2}}$

$\frac{\mathbf{ }}{}$
17. The marginal cost function is MC = 100 $\sqrt{\mathbf{x}}$. find AC given that TC =0 when the out put is zero is
(a) $\frac{\mathbf{200}}{\mathbf{3}}{\mathbf{x}}^{\frac{\mathbf{1}}{\mathbf{2}}}$
(b) $\frac{\mathbf{200}}{\mathbf{3}}{\mathbf{x}}^{\frac{\mathbf{3}}{\mathbf{2}}}$
(c) $\frac{\mathbf{200}}{\mathbf{3}{\mathbf{x}}^{\frac{\mathbf{3}}{\mathbf{2}}}}$
(d) $\frac{\mathbf{200}}{\mathbf{3}{\mathbf{x}}^{\frac{\mathbf{1}}{\mathbf{2}}}}$
Answer Key:
(a) $\frac{\mathbf{200}}{\mathbf{3}}{\mathbf{x}}^{\frac{\mathbf{1}}{\mathbf{2}}}$

${\frac{\mathbf{ }}{}}^{}$
18. The demand and supply function of a commodity are P(x)= $\mathbf{(}\mathbf{x}\mathbf{-}\mathbf{5}{\mathbf{)}}^{\mathbf{2}}$ and S(x)= ${\mathbf{x}}^{\mathbf{2}}$ + x + 3 then the equilibrium quantity ${\mathbf{x}}_{\mathbf{0}}$ is
(a) 5 
(b) 2 
(c) 3 
(d) 1
Answer Key:
(b) 2 

 
19. The demand and supply function of a commodity are D(x)= 25 − 2x and S(x) = $\frac{\mathbf{10}\mathbf{+}\mathbf{x}}{\mathbf{4}}$+ then the equilibrium price ${\mathbf{p}}_{\mathbf{0}}$ is
(a) 5 
(b) 2 
(c) 3 
(d) 10
Answer Key:
(a) 5 

 
20. If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3${\mathbf{x}}^{\mathbf{2}}$ − 81, then the maximum profit at x is equal to
(a) 3 
(b) 6 
(c) 9 
(d) 5
Answer Key:
(c) 9

 
21. If the marginal revenue of a firm is constant, then the demand function is
(a) MR 
(b) MC 
(c) C(x) 
(d) AC
Answer Key:
(a) MR 

 
22. For a demand function p, if $\int \frac{\mathbf{d}\mathbf{p}}{\mathbf{p}}\mathbf{=}\mathbf{k}\mathbf{\int }\frac{\mathbf{d}\mathbf{x}}{\mathbf{x}}$ then k is equal to
(a) 𝝶d 
(b) −𝝶d 
(c) $\frac{\mathbf{-}\mathbf{1}}{\mathbf{\eta }\mathbf{d}}$
(d) $\frac{\mathbf{1}}{\mathbf{\eta }\mathbf{d}}$
Answer Key:
(c) $\frac{\mathbf{-}\mathbf{1}}{\mathbf{\eta }\mathbf{d}}$

$\frac{\mathbf{ }}{}$
23. Area bounded by y = ${\mathbf{e}}^{\mathbf{x}}$ between the limits 0 to 1 is
(a)( e −1) sq.units 
(b)( e +1) sq.units
(c)$($$\mathbf{1}\mathbf{-}\frac{\mathbf{1}}{\mathbf{e}}$$)$ sq.units 
(d) sq.units
Answer Key:
(a)( e −1) sq.units 

 
24. The area bounded by the parabola y2 = 4x bounded by its latus rectum is
(a) $\frac{\mathbf{16}}{\mathbf{3}}$ sq.units 
(b) $\frac{\mathbf{8}}{\mathbf{3}}$ sq.units
(c) $\frac{\mathbf{72}}{\mathbf{3}}$ sq.units 
(d) $\frac{\mathbf{1}}{\mathbf{3}}$ sq.units
Answer Key:
(b) $\frac{\mathbf{8}}{\mathbf{3}}$ sq.units

 
25. Area bounded by y = |x| between the limits 0 and 2 is
(a) 1 sq.units 
(b) 3 sq.units
(c) 2 sq.units 
(d) 4 sq.units
Answer Key:
(c) 2 sq.units 

 

II. Short answer questions

12th BM

III. Long answer questions

12th BM