bba-fundamentals of business mathematics

45 Pages·2013·0.13 MB·English

MGU-BBA-First Semester-FUNDAMENTALS OF BUSINESS MATHEMATICS
MCQs
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

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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

2
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)
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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)
5
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

UNIT 2 NUMBER SYSTEMS AND PROGRESSION
41. Find the sum of 17 terms of the A.P. 5, 9, 13, 17, …
a) 623
b) 580
c) 629
d) 650

ANS. c

42. Find the sum of the series 2+5+8+ … +182
a) 5520
b) 5612
c) 5623
d) 5418

ANS. b

43. Insert A.M.’s (Arithmetic Mean) between 7 and 71 in such a way that the 5th A.M. is 27. The
number of A.M.s are
a) 12
b) 17
c) 15
d) 51
8
ANS. b

44. Find the 5th term from the end of the G.P. 3, 6, 12, 24, …, 12,288
a) 384
b) 192
c) 1536
d) 768

ANS. d

45. Find the Harmonic Mean between 2/3 and -4/3.
a) 8/3
b) 16/3
c) -8/3
d) -16/3

ANS. a

46. If z = (2-3i) and z²-4z+13 = 0 and hence find the value of (4z³-3z²+169)
a) 0
b) -1
c) 10
d) 9

ANS. a

47. Write the modulus of 2+ √-3.
a) √ 7
b) √ 5
c) √ 13
d) √8

ANS. a

48. A car travels 432 km on 48 litres of petrol. How far will it travel on 20 litres of petrol?
a) 18
b) 9
c) 34
d) 180

ANS. d

49. If x and y vary inversely as each other, x = 10 when y = 6. Find y when x=15.
a) 25
b) 4
c) 90
9
d) 60

ANS. b

50. 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?
a) 84 cows
b) 34 cows
c) 88 cows
d) 44 cows

ANS. b

51. Solve log √8/log 8 is the same as
a) 1/√8
b) 1/8
c) ¼
d) ½

ANS. d

52. If log 27 = 1.431, then the value of log 9 is:
a) 0.934
b) 0.958
c) 0.945
d) 0.954

ANS. d

53. If log 2 = 0.3010, then log 10 is equal to:
10 2
a) 0.6990
b) 1000/301
c) 699/301
d) 0.3010

ANS. b

54. A private taxi charges a fare of Rs. 260 for a journey of 200 km. How much would it travel
for Rs 279.50?
a) 215
b) 363.35
c) 186
d) 240

ANS. a

55. Log 36 / log 6
a) 5
b) 8
10