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Question Bank No: 1

1. N(A) = 10, n(B) = 6, n(C) = 5 for three disjoint sets A, B and C then n(A $\cup$ B $\cup$ C) =

a)		21
b)		11
c)		1
d)		9

2. Two finite sets have m and n elements. The number of elements in the power set of the first is 48 more than the number of elements in the power set of the second. Then the value of m and n are

a)		7, 6
b)		6, 3
c)		6, 4
d)		3, 7

3. If A = {x : $x^{2}$ – 5x + 6 = 0}, B = {2, 4}, C = {4, 5}, then A × (B ∩ C) is

a)		{(2, 4), (3, 4)}
b)		{(4, 2), (4, 3)}
c)		{(2, 4), (3, 4), (4, 4)}
d)		{(2, 2), (3, 3), (4, 4), (5, 5)}

4. In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then the persons travelling by car or bus is

a)		80%
b)		40%
c)		60%
d)		70%

5. In Z, the set of integers, inverse of ‘-7’ w.r.t ‘*’ defined by a * b = a + b + 7 for all a, b $\in$ Z, is

a)		-14
b)		7
c)		14
d)		-7

6. The binary operation ‘*’ defined on the set of integers as a * b = $| a - b |$ - 1 is

a)		Not commutative
b)		commutative
c)		associative
d)		none of the above

7. In the set N of natural numbers, the binary operation '*' is defined as follows : m * n = $\frac{mn}{p}$ , where p is a fixed number, then the identity element of * is

a)		A prime number
b)		p + m + n
c)		p – 1
d)		p

8. On the power set P of a non-empty set A, we define an operation $Δ$ by X $Δ$ Y = (X $\cap$ $Y^{'}$ ) $\cup$ ( $X^{'}$ $\cap$ Y) Then which one of the statements is true about (P, $Δ$ ).

a)		Commutative and associative without identity
b)		Connutative but not associative with an identity
c)		Associative but not commutative without an identity
d)		Commutative and associative with an identity

9. Let Y = {1, 2, 3, 4, 5}, A = {1, 2}, B = {3, 4, 5} and $φ$ denotes nulls et. If A $\times$ B denotes the cartesian product of the sets A and B then (Y x A) ∩ (Y ×B) is

a)		Y
b)		A
c)		B
d)		$φ$

10. Let A = {x : x is a digit in the number 3591}, B = {x : x $\in$ N, x < 10}. Which of the following is false?

a)		A $\cap$ B = {1, 3, 5, 9}
b)		A – B = $φ$
c)		B – A = {2, 4, 6, 7, 8}
d)		A $\cup$ B = {1, 2, 3, 5, 9}

11. Of the number of three atheletic teams in a school, 21 arer in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the games. The total number of members is

a)		42
b)		43
c)		45
d)		None of these

12. A town has total population 25,000 out of which 13,000 read "The Hindustan Times" and 10,500 read "The Indian Express" and 2,500 read both papers. The percentage of poulation who read neither of these newspaper is

a)		10%
b)		16%
c)		27%
d)		30%

13. Which of the following does not have a proper subset

a)		${x : x \in Q}$
b)		${x : x \in N, 3 < x < 4}$
c)		${x : x \in Q, 3 < x < 4}$
d)		None of these

14. If for two sets A and B, A $\cup$ B = A $\cap$ B = A, then we have

a)		A – B $\neq$ $φ$
b)		B – A $\neq$ $φ$
c)		A = B
d)		None of these

15. If n(A) = 4 and n (B)= 7, then the minimum and maximum valuses of n (A $\cup$ B) are respectively

a)		4, 11
b)		4, 7
c)		7, 11
d)		None of these

16. If A= ${2, 3, 4, 8, 10}$ , B = ${3, 4, 5, 10, 12}$ and C = ${4, 5, 6, 12, 14}$ , then (A $\cup B$ ) $\cap (A \cup C)$ is equal to

a)		${2, 3, 4, 5, 10, 12}$
b)		${2, 3, 4, 5, 8, 19, 12}$
c)		${2, 3, 4, 10, 12}$
d)		None of these

17. If A $\times$ B = ${(5, 5), (5, 6), (5, 7), (8, 6), (8, 7), (8, 5)}$ , then A is equal to

a)		${5, 6, 7}$
b)		${5, 8}$
c)		${5, 6, 8}$
d)		None of these

18. In n (A) = 115, n (B) = 326, n (A-B) = 47, then n (A $\cup$ B) is equal to

a)		373
b)		165
c)		370
d)		None of these

19. If A= ${1, 2, 5}$ and B = ${3, 4, 5, 9}$ , then A $Δ$ B is equal to

a)		${1, 2, 5, 9}$
b)		${1, 2, 3, 4, 9}$
c)		${1, 2, 3, 4, 5, 9}$
d)		None of these

20. Let n(U) = 700 n(A) = 200 n(B) = 300 n(A $\cap B) = 100$ then n $(A^{'} \cap B^{'})$ is equal to

a)		400
b)		600
c)		300
d)		None of these

21. If A = ${1, 2, 3}$ B = ${4, 5, 6}$ Then (A $- B) \times (A \cap C)$ is equal to

a)		${(1, 3), (1, 5}$
b)		${(2, 1), (2, 2), (2, 3)}$
c)		${(1, 2), (1, 3), (1, 5)}$
d)		None of these

22. If A and B are two sets then A $\cap {(A \cup B)}^{'}$ equals

a)		A
b)		B
c)		$φ$
d)		None of these

23. Set A and B have 5 and 7 elements respectively. What can be the minimum number of elements in A $\cup B$ ?

a)		5
b)		7
c)		12
d)		35

24. If a set A has n elements, then the total number of subset of A is

a)		n
b)		$n^{2}$
c)		$2^{n}$
d)		2n

25. In the group (Z, *) of all integers, where a x b=a+b+1 for al a,b, $ϵ$ Z, the inverse of -2 is

a)		– 2
b)		0
c)		– 4
d)		2

26. The set of all non-zero real numbers with the operation * defined on it by a*b = $\frac{ab}{2}$ is an abelian group. The identity of the group is

a)		1
b)		2
c)		$\frac{1}{2}$
d)		$\frac{1}{3}$ *

27. If A and B are two sets, then A $⋂$ (A $⋃$ B)' is equal to;

a)		A
b)		B
c)		$\emptyset$
d)		none of these

28. Two sets A, B are disjoint if:

a)		A U B = $\emptyset$
b)		A $⋂$ B $\neq$ $\emptyset$
c)		A $⋂$ B = $\emptyset$
d)		A - B = A

29. If A = ${2, 3, 4, 5, 10}$ , B = ${3, 4, 5, 10, 12}$ , C = ${4, 5, 10, 12, 14}$ } then (A $⋃$ B) $⋂$ ( A $⋃$ C ) is equal to;

a)		{ 2, 3, 4, 5, 8, 10, 12}
b)		{ 2, 4, 8, 10, 12}
c)		{ 3, 8, 10, 12}
d)		{ 2, 8, 10}

30. If A and B are disjoint, then n (A $⋃$ B ) is equal to;

a)		n (A)
b)		n (B)
c)		n (A) + n (B)
d)		n (A) . n (B)

31. Let S = { 0, 1, 5, 4, 7}. Then the total number of subsets of S is;

a)		64
b)		32
c)		40
d)		20

32. Let A and B be two sets such that n(A) = 70, n(B) = 60, and n(A $⋃$ B) = 110. Then n(A $⋂$ B) is equal to;

a)		240
b)		20
c)		100
d)		120

33. If Q = { x:x= $\frac{1}{y}$ , where y $ε$ N}, then

a)		0 $ε$ Q
b)		1 $ε$ Q
c)		2 $ε$ Q
d)		$\frac{2}{3}$ $ε$ Q

34. Let ƒ: X $\to$ Y be a given function, then $f^{- 1}$ exists (or ƒ is invertible) if;

a)		ƒ is one-one
b)		ƒ is onto
c)		ƒ is one-one but not onto
d)		ƒ is one-one and onto

35. Let ƒ = { (1,5), (2,6), (3,4)}, g = { (4,7), (5,8), (6,9) } then gof is;

a)		{ (4,7), (5,8), (6,9), (1,5), (2,6), (3,4) }
b)		{ }
c)		{ (1,8), (2,9), (3,7) }
d)		none of these

36. If A = { 1, 2, 3 }, B = { x, y }, then the number of functions that can be defined from A into B is;

a)		3
b)		6
c)		8
d)		12

37. If n $\geq$ 2, then the number of onto mappings or surjections that can be defined from { 1,2,3,…..,n} onto { 1, 2} is;

a)		$n^{2}$
b)		$2^{n}$
c)		$n^{2}$ - 2
d)		$2^{n 2}$ - 2

38. Let n(A) = 4 and n(B) = 5. The number of all possible injections from A to B is;

a)		9
b)		24
c)		120
d)		none of these

39. If ƒ : A $\to$ B is bijection, then;

a)		$\leq$ n(B)
b)		n(A) = n(B)
c)		n(A) $\geq$ n(B)
d)		none of these

40. Sets of A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A $⋃$ B?

a)		3
b)		6
c)		9
d)		18

41. In a college of 300 students, every student reads 5 newspaper and every newspaper is read by 60 students. The number of newspaper is;

a)		at least 30
b)		at most 20
c)		exactly 25
d)		none of these

42. The set of intelligent students in a class is ;

a)		a null set
b)		a singleton set
c)		a finite set
d)		not a well defined collection

43. Which of the following is the empty set?

a)		{ x : x is a real number $x^{2}$ - 1 = 0}
b)		{ x : x is a real number $x^{2}$ + 1 = 0}
c)		{ x : x is a real number $x^{2}$ - 9 = 0}
d)		{ x : x is a real number $x^{2}$ = x + 2}

44. If the set A has p elements, B has q elements, then the number of elements in A x B is;

a)		p + q
b)		p + q + 1
c)		pq
d)		p²

45. $| x - y |$ = $| x |$ - $| y |$ is true.

a)		for no real x and y
b)		for those real x and y such that x y $<$ 0
c)		for those real x and y such that x y $>$ 0
d)		none of these

46. $π$  and e are

a)		natural numbers
b)		integers
c)		rational numbers
d)		irrational numbers