FUNDAMENTALS OF BUSINESS MATHEMATICS MCQs

FUNDAMENTALS OF BUSINESS MATHEMATICS MCQs

                        Fundamentals of Business Mathematics is a crucial subject for anyone involved in business, finance, or economics. It involves applying mathematical concepts to solve problems related to various aspects of business, such as accounting, financial analysis, investments, and statistics. MCQs (Multiple Choice Questions) are a common form of assessment used to test students' understanding of the subject.

MCQs in Fundamentals of Business Mathematics cover a wide range of topics, including basic arithmetic, algebra, statistics, financial ratios, and forecasting. They often present a problem or scenario and ask students to select the most appropriate solution from a list of options.

UNIT 1 SET THEORY

1. If A = {1, 2, 3, 4, 5}, then the number of proper subsets of A is
a) 120
b) 30
c) 31
d) 32
ANS. c) 31




2. In a set – builder method, the null set is represented by
a) { }
b) Φ
c) { x : x ≠ x}
d) { x : x = x}
ANS. c) { x : x ≠ x}




3. Two finite sets have n and m elements. The number of elements in the power set of first set is
48 more than the total number of elements in power set of the second set. Then the values of
m and n are
a) 6, 4
b) 7, 6
c) 6, 3
d) 7, 4
ANS. a) 6, 4




4. A set consisting of a definite number of elements is called a
a) Null set
b) Singleton set
c) Infinite set
d) Finite set
ANS. d) Finite set




5. If the set has p elements, b has q elements, the no of elements in A x B is
a) p + q
b) p + q + 1
c) pq
d) p²
ANS. c) pq




6. In a class of 200 students, 70 played cricket, 60 played hockey and 80 played football. 30
played cricket and football, 30 played hockey and football, 40 played cricket and hockey.
Find the maximum number of people playing all three games and also the minimum number
of people playing at least one game.
a) 200, 100
b) 30,110
c) 30, 120
d) None of these
ANS. b) 30, 110

7. A survey showed that 63 % of the Americans like cheese whereas 76 % like apples. If x % of
Americans like both cheese and apples, then find the range of x?
a) 0 ≤ x ≤ 23 %
b) 0 ≤ x ≤ 39 %
c) 4 ≤ x ≤ 35 %
d) 6 ≤ x ≤ 33 %
ANS. b

8. If a class with n students is organized into four groups keeping the following conditions :
• Each student belongs to exactly two groups
• Each pair of groups has exactly one student in common, what is the value of n?
a) n = 11
b) n = 7
c) n = 9
d) None of these
ANS. d

9. In a club, all the members are free to vote for one, two, or three of the candidates. 20 % of the
members did not vote, 38 % of the total members voted for at least 2 candidates. What % of
the members voted for either 1 or 3 candidates, If 10 % of the total members voted for all 3
candidates?
a) 40 %
b) None of these
c) 44 %
d) 36 %
ANS. b

10. In a survey conducted in Patna, it was found that 3/4ths of town owns color T.V., 85 % of the
people own refrigerators and every 4 in 5 in the town own music systems, what is the
minimum percentage of people who have all the three?
a) 30 %
b) 55 %
c) 40 %
d) None of these
ANS. c

11. In a recent survey conducted by cable T.V., among the people who watch DD, ZEE and
STAR TV., it is found that 80 % of the people watched DD, 22% watched Star TV, and 15 %
o watched Zee. What is the maximum percentage of people, who can watch all the three
channels?
a) 12.5 %
b) 8.5 %
c) 15 %
d) Data insufficient
ANS. c

12. If f : Q → Q is defined as f(x) = x², then (9) =
a) 3
b) – 3
c) {-3, 3}
d) Π
ANS. c

13. If x ≠ 1, and f(x) = x + 1 / x – 1 is a real function, then f(f(f(2))) is
a) 1
b) 2
c) 3
d) 4
ANS. c

14. If f(x) = Log [(1 + x)/(1-x), then f (2x )/(1 + x²) is equal to
a) 2 f (x)
b) {f(x)}²
c) {f(x)}³
d) 3 f(x)
ANS. a

15. The range of the function f(x) = x / │x│ is
a) R - {0}
b) R – {-1, 1}
c) {-1, 1}
d) None of these
ANS. c

16. The range of the function f(x) = │x - 1│ is
a) (- ∞, 0)
b) [0, ∞)
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c) (0, - ∞)
d) R
ANS. b

17. Let f(x) = x / x+ 3, then f (x + 1) =
a) 3x + 2/ x+ 2
b) x + 1 / x + 4
c) (x + 1) / (x + 3)
d) 2 x + 3 / (x + 3)
ANS. b

18. A function f(x) is such that f(x) + f(y) = f(xy). Which of the following could be f (x).
a)
b)
c) x²
d) log ax
ANS. d

19. If f(x) = c.x +1 and g(x)= 3x+2. If f(g(x)) = g(f(x))then what is the value of c?
a) 1
b) 2
c) 3
d) 4
ANS. b

20. If f(x) = - then the value of 2(f(x))- 5f(x-1) + 2f(x-2) is
a) 1
b) -3
c) 15
d) None of these
ANS. d

21. If f(x) = + , then f(x) is
a) An odd function
b) An even function
c) Neither odd nor even
d) None of the above
ANS. b

22. If b = f(a) and f(a) = (a – 1) / (a + 1), which of the following is true?
a) f(2a) = f(a) + 1
b) f(1/a) = -f(a)
c) a = f(b) + f(1/a)
d) a = f(b)
ANS. b

23. Find the domain of the function y = f(x) which is defined as f(x) = (1 / √{x- [x]}) [x] is the
greatest integer function
a) X is any real number other than an integer
b) And real value of x
c) All natural numbers
d) None of these
ANS. a

24. f(x) = │x│+ │y│ g(x) = max (x + y) (x – y) h(x) = min (x + y, x – y)
(i) g(x) ≥ f(x) (ii) g(x) + h(x) ≥ f(x) (iii) g(x) > f(x).
Which of the following are not necessarily true?

a) i and ii
b) i and iii
c) ii and iii
d) i, ii and iii
ANS. d

25. Evaluate f(1) + f(2) + f(3) + … + f(25)
a) -26
b) None of these
c) -24
d) -22
ANS. b

26. If A = {1, 2, 4} B = {2, 4, 5}, C = {2, 5} then (A – B) x (B – C)
a) {(1, 2), (1, 5), (2, 5) }
b) {(1, 4)}
c) (1, 4)
d) None of these.
ANS. b

27. If A = {1, 2, 3}, B = {1,4,6, 9} and R is a relation from A to B defined by x is greater than y.
The range of R is
a) {1, 4, 6, 9}
b) {4, 6, 9}
c) {1}
d) None of these
ANS. c

28. Find the range for the relation : {(3, 5), (2, 5), (2, 6), (3, 7)
a) {2, 3}
b) {5, 6, 7}
c) {3, 2, 6}
d) {2, 3, 5}
ANS. b

29. The range of the real function f defined by f (x) = √(x -1) =
a) (1,∞)
b) (0,1)
c) [0,∞)
d) (∞,0]
ANS. c

30. Let f = {(x, x² /1+x² ): x € R } be a function from R into R . range of x is
a) negative real numbers.
b) non negative real numbers.
c) positive real numbers.
d) any positive real number x such that 0≤ x <1
Ans. d

31. Solve f(x) = √9-x² the range is
a) {x: 3< x <0}
b) {x: 0≤ x ≤ 3}
c) {x: 0< x < 3}
d) {x: 3≤ x ≤ 0}
Ans. b

31. Let R be a relation N define by x + 2y = 8 . The domain of R is
a) {2,4,8}
b) {2,4,6,8}
c) {2,4,6}
d) {1,2,3,4}
Ans. c

32. If R is a relation on a finite set having a elements , then the number of relations on A is
a) 2a
b) 2a2
c) a²
d) aª
Ans: b
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33. { (a, b) : a² +b² = 1} on the set S has the following relation
a) symmetric
b) reflexive and transitive
c) none
d) reflexive
Ans. a

34. If A and B are two sets containing respectively m and n distinct elements. How many
different relations can be defined for A and B?
a) 2mn
b) 2m+n
c) 2m-n
d) 2m/n
Ans. a

35. If R is the relation “is greater than” from A ={1,2,3,4,5}to B={1,3,4} , Than R-1 is
a) {(1,2) ,(1,3),(1,4),(1,5)}
b) {(3,4),(4,5),(3,5)}
c) {(1,2), (1,3), (1,4), (3,4), (1,5), (3,5), (4,5)}
d) {(2,1), (3,1), (4,1),(4,3), (5,1), (5,3), (5,4)}
Ans. c

36. A relation R ={(1,1), (1,2)}ON a ={1,2,3}. A minimum number of elements required in R so
that the enlarged relation becomes an equilance relationis
a) {(2,2), (3,3)}
b) {(2,1) , (3,1), (3,3)}
c) {(2,2), (2,1), }
d) {(2,2), (3,3), (2,1)}
Ans. d

37. Let A ={1,2,3} and R= {(1,2), (1,1), (2,3)}be a relation on A.What minimum number of
elements may be adjoined with the elements of R so that it becomes transitive.
a) (1,2)
b) (1,3)
c) (2,3)
d) (1,1)
Ans. b

38. Let R= {(x,y) :x, y belong to N, 2x+y =41}. The range is of the relation R is
a) {(2n +1):n belongs to N , 1≤ n≤ 20}
b) {2n: n belongs to N, 1< n< 20}
c) {(2n-1) : n belongs to N, 1≤ n≤ 20}
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d) { (2n+2) : n belongs to N, 1< n <20}
Ans. c

39. If R is a relation from a finite set A having m elements to a finite set B having n elements,
then the number of relations from A to B is
a) 2mn
b) 2mn -1
c) 2mn
d) Mn
Ans. a

40. A set is known by its _______.
a) Values
b) Elements
c) Letters
d) Members
Ans. b