Class 11 Mathematics Set MCQs Set A

Question. A – (B ∪ C) is
(a) (A – B) ∪ (A – C)
(b) A – B – C
(c) (A – B) ∩ (A – C)
(d) A – (B ∩ C)’

Answer: C

Question. In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?
(a) 19
(b) 41
(c) 47
(d) 21
(e) 57

Answer: C

Question. In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects?
(a) 5%
(b) 15%
(c) 0%
(d) 25%

Answer: A

Question. The number of elements in the Power set P(S) of the set S = [ [ Φ] , 1, [ 2, 3 ]] is
(a) 4
(b) 8
(c) 2
(d) None of the options

Answer: B

Question. Among 200 ppl, 56% like strawberry, 44% like apple, and 40% like raspberry. IF 30% of people like both strawberry and apple, what is the LARGEST possible number of people who like raspberry but do not like either strawberry or apple?
(a) 20
(b) 60
(c) 80
(d) 89

Answer: B

Question. The number of elements in the power set of the set {{a, b}, c} is
(a) 8
(b) 4
(c) 3
(d) 7

Answer: C

Question. There are 230 students. 80 play football, 42 play soccer and 12 play rugby. 32 play exactly 2 sports and 4 play all three. How many students play none?
(a) 132
(b) 136
(c) 140
(d) 94

Answer: A

Question. From 50 students taking examination in Mathematics, Physics and Chemistry, each of the students has passed in at least 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. Then, the largest numbers that could have passed all three examinations, are
(a) 12
(b) 14
(c) 15
(d) 16

Answer: B

Question. Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total 64 played both basketball and hockey, 80 played cricket and basketball and 40 played cricket and hockey, 24 played all the three games. The number of boys who did not play any game is :
(a) 128
(b) 216
(c) 240
(d) 160

Answer: D

Question. Let S be an infinite set and S1, S2, S3, …, Sn be sets such that S1 ∪S2 ∪ S3∪….Sn = S then
(a) atleast one of the sets Si is a finite set
(b) not more than one of the set Si can be infinite
(c) atleast one of the sets Si is an infinite set
(d) None of the options

Answer: C

Question. In a language survey of students it is found that 80 students know English, 60 know French, 50 know German, 30 known English and French, 20 know French and German, 15 know English and German and 10 students know all the three languages. How many students know at least one language?
(a) 135
(b) 30
(c) 10
(d) 45

Answer: A

Question. Number of subsets of a set of order three is
(a) 3
(b) 6
(c) 8
(d) 9

Answer: C

Question. The set of all Equivalence classes of a set A of cardinality
(a) has the same cardinality as A
(b) forms a partition of A
(c) is of cardinality 2C
(d) is of cardinality C²

Answer: C

Question. A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
(a) 40
(b) 30
(c) 20
(d) 15

Answer: D

Question. The set { 1/2, 2/3, 3/4 ,4/5, 5/6, 6/7} in the set-builder form is
(a) x : x = /n+1 , where n ∈ N and 1 < n < 6
(b) x : x = /n+1 , where n ∈ N and 1 ≤ n < 6
(c) x : x = /n+1 , where n ∈ N and 1 ≤ n ≤ 6
(d) None of the options

Answer: C

Question. In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person like at least one of the two drinks. How many like both coffee and tea?
(a) 30
(b) 15
(c) 14
(d) 9

Answer: D

Question. In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 persons speak both English and Hindi, 11 persons speak both Hindi and Kannada where as 13 person speak both Kannada and English. How+ many people speak all the three languages?
(a) 6
(b) 7
(c) 8
(d) 9

Answer: A

Question. Total number of different partitions of a set having four elements is
(a) 16
(b) 8
(c) 15
(d) 4

Answer: C

Question. Let A, B, C be finite sets. Suppose that n (A) = 10, n (B) = 15, n (C) = 20, n (A∩B) = 8 and n (B∩C) = 9. Then the possible value of n (A ∪ B ∪ C) is
(a) 26
(b) 27
(c) 28
(d) Any of the three values 26, 27, 28 is possible

Answer: D

Question. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5},
B = {2, 4, 6, 7} and C = {2, 3, 4, 8}, then which of the following is true?
(a) (B ∪ C)’ = {1, 5, 9, 10}
(b) (C – A)’ = {1, 2, 3, 5, 6, 7, 9, 10}
(c) Both (a) and (b)
(d) None of the options

Answer: C

Question. Which of the following sets are null sets?
(a) {0}
(b) Ø
(c) { }
(d) Both (b) & (c)

Answer: D

Question. Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?
(a) 0
(b) 20
(c) 10
(d) 18

Answer: C

Question. In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
(a) 30
(b) 10
(c) 18
(d) 28

Answer: C

Question. If a set is denoted as B = Φ, then the number of element in B is
(a) 3
(b) 2
(c) 1
(d) 0

Answer: D

Question. If A be a finite set of size n, then number of elements in the power set of A x A
(a) 2 2n
(b) 2 n²
(c) (2n)2
(d) None of the options

Answer: B

Question. Let n(A) denotes the number of elements in set (a) If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ?
(a) p²
(b) p x q
(c) p + q
(d) 2 pq

Answer: B

Question. If A and B are non-empty subsets of a set, then (A – B) ∪ (B – A) equals to
(a) (A ∩ B) ∪ (A ∪ B)
(b) (A ∪ B) – (A – B)
(c) (A ∪ B) – (A ∩ B)
(d) (A ∪ B) – B

Answer: C

Question. If the sets A and B are given by A = {1, 2, 3, 4},
B = {2, 4, 6, 8, 10} and the universal set
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then
(a) (A∪B)= {5, 7, 9}
(b) (A∩B)= {1, 3, 5, 6, 7}
(c) (A∩B) = {1, 3, 5, 6, 7, 8}
(d) None of the options

Answer: A

Question. In a competition, a school awarded medals in different categories, 36 medals in dance, 12 medals in dramatics and 18 in musi(c) If these medals went to a total of 45 students and only 4 students got medals in all the three categories, How many did receive medals in exactly two of the categories?
(a) 10
(b) 8
(c) 7
(d) 3

Answer: D

Question. In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. (b) 10 voted for both and 6 did not vote for either. How many experts were there in all?
(a) 18
(b) 36
(c) 24
(d) None of the options

Answer: B

Question. A market research group conducted a survey of 2000 consumers and reported that 1720 consumers like product P1 and 1450 consumers like product P2. What is the least number that must have liked both the products?
(a) 1150
(b) 2000
(c) 1170
(d) 2500

Answer: C

Question. If A and B are sets and A∪ B= A ∩ B, then
(a) A= Φ
(b) B= Φ
(c) A=B
(d) None of the options

Answer: C

Question. Consider:
X = Set of all students in your school.
Y = Set of all students in your class.
Then, which of the following is true?
(a) Every element of Y is also an element of X
(b) Every element of X is also an element of Y
(c) Every element of Y is not an element of X
(d) Every element of X is not an element of Y

Answer: A

Question. Order of the power set of a set of order n is
(a) n
(b) 2n
(c) n²
(d) 2n

Answer: D

Statement and Questions

Question. Which of the following are correct?
I. A – B = A – (A ∩ B).
II. A = (A ∩ B) ∪ (A – B).
III. A – (B ∪ C) = (A – B) ∪ (A – C).
(a) I and II
(b) II and III
(c) I, II and III
(d) None of the options

Answer: A

Question. Consider the following statements
I. The vowels in the English alphabet.
II. The collection of books.
III. The rivers of India.
IV. The collection of most talented batsmen of India. Which of the following is/are well-defined collections?
(a) I and II
(b) Only I
(c) I and III
(d) I and IV

Answer: C

Question. Statement – I : The set D = {x : x is a prime number which is a divisor of 60} in roster form is {1, 2, 3, 4, 5}.
Statement – II : The set E = the set of all letters in the word ‘TRIGONOMETRY’, in the roster form is {T, R, I, G, O, N, M, E, Y}.
(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. n(S ∪ T) is maximum when n (S ∩ T) is least.
II. If n(U) = 1000, n(S) = 720, n(T) = 450, then least value of n(S ∩ T) = 170.
(a) Only I is true
(b) Only II is true
(c) Both I and II are true
(d) Both I and II are false

Answer: C

Question. Statement-I : If A = {1, 2, 3, 4, 5}, B = {2, 4, 6}, C = {3, 4, 6}, then (A ∪ B) ∩ C = {3, 4, 6}
Statement-II : (A ∪ B)’ = A’ ∩ B’
(a) Only I is true
(b) Only II is true
(c) Both I and II are true.
(d) Both I and II are false.

Answer: C