Class 11 Mathematics Set Theory MCQs Set 02

Question: In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. The number of people speak atleast one of these two languages is
a) 150
b) 60
c) 155
d) None of the options
Answer: b

Question: If A = {x : x² = 1} and B = {x : x⁴ =1 } , then A Δ B is equal to
a) {i, – i}
b) {- 1, 1}
c) {- 1, 1, i, – 1}
d) None of the options
Answer: a

Question: In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then, the number of persons who read neither is
a) 210
b) 290
c) 180
d) 260
Answer: b

Question: Let S = set of points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then,
a) S ∩T ∩C =Φ
b) S ∪T ∪C = S
c) S ∪T ∪C = C
d) S ∪T = S ∩C
Answer: c

Question: Let X be the universal set for sets A and B. If n a) = 200, nb) = 300 and n (A∩B) = 100, then n (A’ ∩ B’) is equal to 300 provided n (X) is equal to a) 600
b) 700
c) 800
d) 900
Answer: b

Question: The set (A∩B’ )’∪(B∩C) is equal to
a) A∪B ∪C
b) A’∪ B
c) A∪ C’
d) A’∩ B
Answer: b

Question: 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) atleast 30
b) atmost 20
c) exactly 25
d) None of the options
Answer: c

Question: If A ={(x, y): y= e^2x,X∈ R} and B={(x,y): y=e -2x,x∈ R},then
a) A ∩ B =Φ
b) A ∩B ≠Φ
c) A ∩ B is a singleton set
d) None of the options
Answer: c

Question: If A ={x,Y):Y=4/X,0≠X∈R} and B = {(x, y) : y = x, x > 0,x ∈R}
a) A ∩ B =Φ
b) A ∩ B is singleton set
c) A ∩ B ≠ 0
d) A ∩ B has two elements
Answer: b

Question: Let S = {x : x is a positivemultiple of 3 less than 100} P = {x : x is a prime number less than 20}. Then, n(S) + n(P) is
a) 34
b) 41
c) 33
d) 30
Answer: b

Question: If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6}, then A ∩ Bconsists of allmultiples of
a) 16
b) 12
c) 8
d) 4
Answer: b

Question: In a class of 60 students, 25 students play Cricket and 20 students play Tennis, and 10 students play both the games. Then, the number of students who play neither is
a) 0
b) 25
c) 35
d) 45
Answer: b

Question: If A = {x : x is an odd natural number} and B = {x : x is a prime number}, then A ∩ B is
a) odd number
b) prime number
c) odd prime number
d) None of the options
Answer: c

Question: If ∪{1, 2} = {1, 2, 3, 5, 9}, then
a) the smallest set X is {3, 5, 9}
b) the smallest set X is {2, 3, 5, 9}
c) the largest set X is {1, 2, 3, 5, 9}
d) the largest set X is {2, 3, 4, 9}
Answer: a

Question: Consider the following relations
I. A – B = A – (A ∩ B)
II. A = (A ∩ B) ∪(A – B)
III. A – (B ∪ C) = (A – B) ∪(A – C)
Which of these is/are correct?
a) I and III
b) Only II
c) II and III
d) I and II
Answer: d 

Question: If aN = {an : n ∈N} and bN ∩ cN = dN, where a, b, c ∈N and b, c are coprime, then
a) b = cd
b) c = bd
c) d = bc
d) None of the options
Answer: c

Question: If A, Band C are three sets such that A ∩ B = A ∩ C and A υ B = A υC, then
a) A = C2
b) B = C
c) A ∩ B = f
d) A = B
Answer: b

Question: From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in atleast one of the subject, 37 passed Mathematics, 24 Physics and 43 Chemistry. Atmost 19 passed Mathematics and Physics, atmost 29 Mathematics and Chemistry and atmost 20 Physics and Chemistry. The largest possible number that could have passed all three examination is
a) 14
b) 15
c) 13
d) 20
Answer: a

Question: In a group of 52 persons, 16 drink tea but not coffee, while 33 drink tea. How many persons drink coffee but not tea ?
a) 17
b) 36
c) 23
d) 19
Answer: d

Question: If A and B are non-empty sets, then Pa) ∪ Pb) is equal to
a) P(A ∪ B)
b) P(A ∩ B)
c) Pa) = Pb)
d) None of the options
Answer: d

Question: If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}, then A – B is equal to
a) A ∩ B
b) A ∩ B
c) A ∩ B
d) A ∩ B
Answer: b

Question: If A = {x : x is a multiple of 4} and B = {x : x is a multiple of 6}, then A ∩ B consists of all multiples of
a) 16
b) 12
c) 8
d) 4
Answer: b

Question: If X = {1, 2, 3, …, 10} and ‘a’ represents any element of X, then the set containing all the elements satisfy a + 2 = 6, a ∈ X is
a) {4}
b) {3}
c) {2}
d) {5}
Answer: a

Question: If na) = 8 and n (A ∩ B) = 2, then n[(A ∩ B)’ ∩ A] is equal to
a) 8
b) 6
c) 4
d) 2
Answer: b

Question: If A is the set of the divisors of the number 15, B is the set of prime numbers smaller than 10 and C is the set of even numbers smaller than 9, then (A ∪ C) ∩ B is the set
a) {1, 3, 5}
b) {1, 2, 3}
c) {2, 3, 5}
d) {2, 5}
Answer: c

Question: Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is
a) 7
b) 5
c) 10
d) 4
Answer: b 

STATEMENT TYPE QUESTIONS

Question: Which of the following is/are true?
I. If A is a subset of the universal set U, then its complement A’ is also a subset of U.
II. If U = {1, 2, 3, ….., 10} and A = {1, 3, 5, 7, 9}, then (A’)’ = A.
a) Only I is true
b) Only II is true
c) Both I and II are true
d) None of the options
Answer: c

Question: Consider the following sets.
I. A = {1, 2, 3}
II. B = {x ∈ R : x² – 2x + 1 = 0}
III. C = {1, 2, 2, 3}
IV. D = {x ∈ R : x³ – 6x² + 11x – 6 = 0}
Which of the following are equal?
a) A = B = C
b) A = C = D
c) A = B = D
d) B = C = D
Answer: b

Question: Select the infinite set from the following:
I. The set of lines which are parallel to the X-axis.
II. The set of numbers which are multiples of 5.
III. The set of letters in the English alphabet.
a) I and II
b) II and III
c) I and III
d) None of the options
Answer: a

Question: Statement-I : Let U be the universal set and A be the subset of U. Then, complement of A is the set of element of A.
Statement-II : The complement of a set A can be represented by A . ‘
a) Statement I is true
b) Statement II is true
c) Both are true
d) Both are false
Answer: b

Question: Which of the following is correct?
I. Three sets A, B, C are such that A = B ∩ C and B = C ∩ A, then A = B.
II. If A = {a, b}, then A ∩ Pa) = A
a) Only I is true
b) Only II is true
c) Both are true
d) Both are false
Answer: a

Question: Suppose A₁, A₂,  , , . . .,A₃₀ are thirty sets each having 3 elements and B₁ B₂,   , . . ., B_n,are n sets each having 3 elements. Let 

and each elements of S belongs to exactly 10 of Ai ’ s and exactly 9 of Bj ’ s. The value of n is equal to 
a) 15
b) 3
c) 45
d) None of the options
Answer: c

Question: The interval represented by 

a) (a, b)
b) [a, b]
c) [a, b)
d) (a, b] 
Answer: b

Question: Match the following sets in column -I with the intervals in column -II.  

Codes:
    A B C D
a) 4 1 2 3
b) 2 3 4 1
c) 1 2 3 4
d) 3 4 2 1
Answer: d

Assertion and Reason

Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
c) Statement I is true, Statement II is false.
d) Statement I is false, Statement II is true.

Question: Suppose A be a non-empty set, then the collection ofall possible subsets of set A is a power set Pa).
Statement I Pa) ∩ Pb) = P(A ∩B)
Statement II Pa) υ Pb) = P(A υ B)
Answer: c

Question: In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers.
Statement I The number of people who read exactly one newspaper is 30.
Statement II Exactly one of the newspaper read is
n(H) + n(T) + n(I ) – 2{n(H Ç I ) + n(H ÇT) + n(T ÇI )} + 3n(H ÇT ÇI )
Answer: a

Question: Suppose, A, Band C are three arbitrary sets andUis a universal set.
Statement I If B = U – A, then nb) = n(U) – na).
Statement II If C = A – B, then nc) = na) – nb). C
Answer: c