CBSE Class 11 Mathematics HOTs Sets

Question. If A and B are non-empty sets such that A ⊃ B, then
(a) B' – A' = A – B
(b) B' – A' = B – A
(c) A' – B' = A – B
(d) A' ⋂ B' = B – A
Answer : A

Question. In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newpapers is
(a) at least 30
(b) at most 20
(c) exactly 25
(d) None of these
Answer : C

Question. Let A and B be two sets then (A⋃B)'⋃(A'⋂B) is equal to
(a) A′
(b) A
(c) B′
(d) None of these
Answer : A

Question. The set (A \ B) ⋃ (B \ A) is equal to
(a) [A\ (A⋂B)]⋂[B \ (A⋂B)]
(b) (A⋃B) \ (A⋂B)
(c) A\ (A⋂B)
(d) A⋂B \ A⋃B
Answer : B

Question. Let A = {x : x∈R, | x | < 1}
B = { x : x∈R, | x – 1| ≥1} and A⋃B = R – D, then the set D is :
(a) { x : 1< x ≤ 2}
(b) {x : 1≤ x < 2}
(c) {x : – 2 ≤ x ≤ 2}
(d) None of these
Answer : B

Question. If aN = {ax : x Î N} and bN ⋂ cN = dN, where b, c ∈ N are relatively prime, then
(a) d = bc
(b) c = bd
(c) b = cd
(d) None of these
Answer : A

Question. Let U be the universal set and A ⋃ B ⋃ C = U.
Then {(A – B) ⋃ (B – C) ⋃ (C – A)}′ is equal to:
(a) A ⋃ B ⋃ C
(b) A ⋃ (B ⋂ C)
(c) A ⋂ B ⋂ C
(d) A ⋂ (B ⋃ C)
Answer : C

Question. At a certain conference of 100 people, there are 29 Indian women and 23 Indian men. Of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors.
How many foreigners and women doctors are attending the conference?
(a) 48, 1
(b) 34, 3
(c) 46, 4
(d) 42, 2
Answer : A

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

Question. The set (A ⋃ B ⋃ C) ⋃ (A ⋂ B' ⋂ C')' ⋂ C' is equal to
(a) B ⋂ C'
(b) A ⋂ C
(c) B' ⋂ C'
(d) None of these
Answer : A

Question. Let A = {θ : sin(θ) = tan(θ)} and B = {θ : cos(θ) = 1} be two sets. Then :
(a) A = B
(b) A ⊄ B
(c) B ⊄ A
(d) A ⊂ B and B - A ≠ Φ
Answer : B

Question. In a school 80 students like chocolate, 40 like coffee if the number of students doesn’t like any of them is equal to the number of students who like both of them then what is the total number of students in the school?
(a) 115
(b) 90
(c) 120
(d) None of these
Answer : A

Question. If n(A) = 1000, n(B) = 500 and if n(A ⋂ B) ≥ 1 and n(A ⋃ B) = p, then
(a) 500 ≤ p ≤ 1000
(b) 1001 ≤ p ≤ 1498
(c) 1000 ≤ p ≤ 1498
(d) 1000 ≤ p ≤ 1499
Answer : D

Question. In a battle 70% of the combatants lost one eye, 80% an ear, 75% an arm, 85% a leg, x % lost all the four limbs. The minimum value of x is
(a) 10
(b) 12
(c) 15
(d) None of these
Answer : A

Question. A set S contains 3 elements, the number of subsets of which of following sets is 256.
(a) S
(b) P(S)
(c) P(P(S))
(d) None of these
Answer : C

Question. In a school there are 100 students 60 of them don’t like Chocolate and 50 don’t like Biscuit and 10 of them like none then how many of them like both?
(a) 20
(b) 30
(c) 40
(d) None of these
Answer : D

Question. In a market research project, 20% opted for 'Nirma' detergent whereas 60% opted for 'Surf blue' detergent. The remaining individuals were not certain. If the difference between those who opted for 'Surf blue' and those who were uncertain was 720, how many respondents were covered in the survey
(a) 1100
(b) 1150
(c) 1800
(d) None of these
Answer : C

Question. A dinner party is to be fixed for a group of 100 persons. In this party, 50 persons do not prefer fish, 60 prefer chicken and 10 do not prefer either chicken or fish. The number of persons who prefer both fish and chicken is
(a) 20
(b) 22
(c) 25
(d) None of these
Answer : A

Question. The number of students who take both the subjects mathematics and chemistry is 30. This represents 10% of the enrolment in mathematics and 12% of the enrolment in chemistry. How many students take at least one of these two subjects?
(a) 520
(b) 490
(c) 560
(d) 480
Answer : A

Question. A survey was conducted of 100 people whether they have read recent issues of ‘Golmal', a monthly magazine. Summarized information is presented below:
Only September: 18
September but not August: 23
September and July: 8
September: 28
July: 48
July and August:10
None of the three months: 24
What is the number of surveyed people who have read exactly for two consecutive months?
(a) 7
(b) 9
(c) 12
(d) 14
Answer : B

Numeric Value Answer

Question. In a class of 80 students numbered 1 to 80, all odd numbered students opt of Cricket, students whose numbers are divisible by 5 opt for Football and those whose numbers are divisible by 7 opt for Hockey. If the number of students who do not opt any of the three games is n, then n/4 is equal to
Answer : 7

Question. An investigator interviewed 100 students to determine their preferences for the three drinks : milk (M), coffee (C) and tea (T). He reported the following : 10 students had all the three drinks M, C and T; 20 had M and C; 30 had C and T; 25 had M and T; 12 had M only; 5 had C only; and 8 had T only. If number of students who did not take any of the three drinks is n, then n/5 is
Answer : 4

Question. If n(A) = 4 and n(B) = 7, then the difference between maximum and minimum value of n(A ⋃ B) is
Answer : 4

Question. A survey shows that 61%, 46% and 29% of the people watched “3 idiots”, “Rajneeti” and “Avatar” respectively. 25% people watched exactly two of the three movies and 3% watched none. What percentage of people watched all the three movies?
Answer : 7

Question. Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that of the second set. The value of m – n is
Answer : 3