DR. B. R.

AMBEDKAR
SCHOOL OF SPECIALIZED EXCELLENCE, DESU COLONY
TYPE – B
TOPIC: SETS
2. Match the following sets for all sets A, B and C
CLASS XI (PCM – GROUP) – 2025 – 26
MATHEMATICS COLUMN 1 COLUMN 2
A (( A  B) – A) P  A – B
TYPE – A B
[ B   B – A ] Q A
1. Fill in the blanks in each of the following :
(a) If A and B are two finite sets, then n  A   n  B  is equal to ________ .
C
 A – B – B – C  R B
(b) If A is a finite set containing 6 element, then number of subsets of A is ____.
(c) The set { x : x  , 1  x  2} can be written as ______________ .
D
 A – B   C – B  S
A  C – B
 d  When A  {}   , then number of elements in P  A  is ______________ . 3. Let S = {1, 2, 3, ..., 10}, then Match the following:
 e  When A  {}   , then number of elements in P(P  A  ) is __________ .
COLUMN 1 COLUMN 2
 f  When A  {}   , then number of elements in P  P(P  A  )  is _________ . A The number of subsets  x , y , z of S so that P 15
 g  When A  {}   , then number of elements in P(P  P(P  A  ))  is _______ .
(h) If A and B are finite sets such that A  B , then n( A  B )  ___________ . x, y , z are in A.P.
(i ) If A and B are finite sets such that A  B, then n( A  B )  ___________ . B
The number of subsets  x, y , z of S so that Q 20
( j ) If A and B are finite sets such that A  B, then n( A  B )  ___________ .
no two of them are consecutive
(k ) Power set of the set A  s, o, e is ______________ .
 l  For A  1, 3, 5 ,B  2, 4, 6 and C  0, 2, 4, 6, 8 , The universal set of
C
The number of subsets  x, y of S so that R 24

all the three sets A, B and C can be ______________ . x 3  y 3 is divisible by 3

 m  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  i  ( B  C )  _____  ii  C – A   = ______ .
D
The number of subsets  x, y of S so that S 56

T 30
(n) Cardinality of set A   x : x 2  5 | x | 6  0, x   is ______________ . x 2  y 2 is divisible by 3
(o) Cardinality of set A   x : x 2025  2025 x 2023 , x   is ______________ .
( p ) Cardinality of set A   x : x 2026  2025 x 2024 , x   is ______________ .
TYPE – C
(q ) Cardinality of power set of set A   x : x 4  3x 2  4, x   is _______ . For Question 4 to 10, choose the correct alternative out of given four options:
4. In a city 20% of the population travels by car, 50% travels by bus and 10 % travels by
both car and bus. Then persons travelling by car or bus is
(a) 80 % (b) 40 % (c) 60 % (d) 70 %
(PREPARED BY SHASHANK VOHRA (LECT. MATHEMATICS – DOE, DELHI) (PREPARED BY SHASHANK VOHRA (LECT. MATHEMATICS – DOE, DELHI)
5. 20 teachers of a school either teach mathematics or physics. 12 of them teach (b) Given A = { 1, 2, 3, 4}, B = {3, 4, 5, 6} and C = {1, 3, 5}, verify that
mathematics while 4 teach both the subjects. Then the number of teachers teaching A - (B U C) = (A – B) U (A – C) and A U (B ∩ C) = (A U B) ∩ (A U C)
physics only is
(a) 12 (b) 8 (c) 16 (d) None of these 16. Let A and B be two sets having 3 and 6 elements respectively. Write the
(a) minimum & maximum number of elements that A U B can have.
(b) minimum & maximum number of elements that A ∩ B can have.
6. Which of the following is the empty set
(a) {x : x is a real number and x2 = 1} (b) {x : x is a real number and x2 + 1 = 0}
17. Write the following sets by Roaster method.
(c) {x : x is a real number and x2 - 9 = 0} (d) {x : x is a real number and x2 = x + 2}
(a) The set of all natural number ‘x’ such that 4x + 9 < 50.
7. The smallest set A such that A U {1, 2} = {1, 2, 3, 5, 9} is (b) The set of all integers ‘x’ such that x2 + 5x + 6 = 0
(a) {2, 3, 5} (b) {3, 5, 9} (c) {1, 2, 5, 9} (d) None of these (c) The set of all natural numbers ‘x’ such that |x| ≤ 4.
(d) The set of all integers ‘x’ such that x2 ≤ 36.
8. 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 : 1 x 2} (d) None of these (e) The set of all two digit number such that the sum of its digits is at most 5.
(f) The set of all two digit number such that the sum of its digits is at least 16.
(g) The set of all two digit number such that the sum of its digits is 10.
9. In a college of 300 students, every student reads 5 newspapers and every newspaper
is read by 60 students. The number of newspaper is- 18. Describe the following sets by Set-Builder method (Property Method):
(a) at least 30 (b) at most 20 (c) exactly 25 (d) none of these
(a) A = { 6, 10, 14, 18} (b) B = {0, 3, 8, 15, 24, 35}
(c) C = { 1⁄4, 1/8, 1/16, 1/32, 1/64} (d) D = {2, 9, 28, 65, ........}
10. If X = {4n - 3n - 1 : n ε N} and Y = {9(n – 1) ; n ε N}, then X U Y is equal to
(e) E = {2, 10, 30, 68, ......} (f) F = {S, P, E, C, I, A, L, D,}
(a) X (b) Y (c) N (d) None of these
(g) G = { }

TYPE – D 19. Classify the following as Singleton Set, Null Set or Neither.
(a) A = {x: 3x – 1 = 0, x ε I} (b) B = {x: x3 – 1 = 0, x ε R}
(DIRECT CALCULATION BASED) (c) C = {x: x is a two digit even prime number} (d) D = {x: x < 1 & x > 3}
11. For all sets A and B , Using properties of sets prove the following statements (e) E = {x: x2 = 16 or 4x = 16}
(a) A ∪ (B – A) = A ∪ B (b) A – (A – B) = A ∩ B (c) A – (A ∩ B) = A – B (f) F = {x: 31.598< x <31.599, x ε R} (g) G = {Ф}
(d) (A ∪ B) – B = A – B
20. In a class of 25 students, it was found that 15 had taken Physics, 12 had taken
12. Write the set of all integers whose cube it an even integer.
Chemistry & 11 had taken Biology, 5 had taken Physics & Biology, 9 had taken Physics
13. If A = Set of letters of the word ‘DELHI’ and B= the set of letters the words ‘DOLL’ & Chemistry, 4 had taken Biology & Chemistry & 3 had taken all the three subjects.
Find A ∩ B and (A – B). Find the numbers of students that had
(a) Only Physics (b) Only Chemistry (c) Physics & Chemistry but not Biology
14. (a) If n (A U B) = 21, n (A) = 10, n (B) = 15, then find n (A ∩ B) and n (A – B).
(d) Biology & Physics but not Chemistry (e) Only one of the subjects
(f) At least one of the three subjects (g) None of the three subjects.
(b) Find A U B if A = {x : x = 2n + 1, n ≤ 5, n ε N} and B = {x : x = 3n – 2, n ≤ 4, n ε N}.

15. (a) Let A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}, Verify the following identity 21. Of the students in a certain class, 10 had taken a course in A, 11 had taken a course in
A U (B ∩ C) = (A U B) ∩ (A U C). B, and 14 had taken a course in C. If 3 students had taken a course in all of the A, B,

(PREPARED BY SHASHANK VOHRA (LECT. MATHEMATICS – DOE, DELHI) (PREPARED BY SHASHANK VOHRA (LECT. MATHEMATICS – DOE, DELHI)
 and C, and 20 students had taken a course in only one of A, B, and C, how many 3%, buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, find
students had taken a course in exactly two of A, B, and C? the no of families which buy(1) A only (2) B only (3) none of A, B and C (4) exactly two
newspapers (5) exactly one newspaper (6) A and C but not B (7) at least one of A,B, C.
22. (a) Two finite sets have a & b elements. The total number of subsets of the first
29. In a class, 18 students took Physics, 23 students took Chemistry and 24 students took
set is 56 more than thetotal number of subsets of the second set. Find the Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics
value of a & b. and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the
three subjects, find:
(b). A software company is developing a data encryption system. Each data block (1) The total number of students. (2) How many took Maths but not Chemistry.
is stored using unique subsets of two different categories of information : (3) How many took exactly one of the three subjects.
 Set A contains p types of user credentials
30. A media agency conducted a survey of TV viewership acrossa city.
 Set B contains q types of security tokens
The survey revealed:
To ensure flexibility and security, the system uses every possible subset of
 63% of respondents watch News Channel A
these two sets. The total number of subsets formed from both sets is 144.
 76% watch News Channel B
Given that sets A and B are disjoint and finite, and that all possible subsets
 Let x % represent thepeople who watch both channels A and B
of A and B together are used for encryption, find the value of  p  q  .
The marketing team wants to analyze the overlap in viewership to determine
23. State & prove De-morgan’s law.
potential audience saturation and advertising effectiveness on both channels.
24. Let U be the set of all boys and girls in a school, G be the set of all girls in the
Prove that the percentage of people whowatch both channels must satisfy the
school, B be the set of all boysin the school, and S be the set of all students in
inequality : 39  x  63
the school who take swimming. Some, butnot all, students in the school take
swimming. Draw a Venn diagram showing oneof the possible interrelationship 31. A school organized a Sports Day event where students could participate in Cricket,
among sets U, G, B and S. Football,and Hockey. Atotal of 60 students took part in at least one of these sports.
 45 students participated in Cricket
25. From 50 students taking examinations in Mathematics, Physics and Chemistry, each of
the student has passed in at least one of the subject, 37 passed Mathematics, 24
 30 students participated in Football
Physics and 43 Chemistry. At most 19 passed Mathematics and Physics, at most 29  40 students participated in Hockey
Mathematics and Chemistry and at most 20 Physics and Chemistry. What is the  At most 27 students played both Cricket and Football
largest possible number that could have passed all three examination?
 At most 32 students playedboth Football and Hockey
26. If A is the set of all divisors of the number 15. B is the set of prime numbers smaller  At most 25 students played both Cricket and Hockey
than 10 and C is the set of even number smaller than 9, then find the value of The school wants to reward the all-rounders — students who participated
(A U C) ∩ B and (C – A) – B.
27. In a group of 84 persons, each plays at least one game out of three viz. tennis, in all three sports — with a special medal.
badminton and cricket. 28 of them play cricket, 40 play tennis and 48 play badminton. Based on the data, determine the maximum number of students who could
If 6 play both cricket and badminton and 4 play tennis and badminton and no one receive the all  rounder medal.
plays all the three games, find the number of persons who play cricket but not tennis.

28. In a town of 10,000 families it was found that 40% families buy newspaper A, 20%
families buy newspaper B and 10% families by newspaper C. 5% families buy A and B,
(PREPARED BY SHASHANK VOHRA (LECT. MATHEMATICS – DOE, DELHI) (PREPARED BY SHASHANK VOHRA (LECT. MATHEMATICS – DOE, DELHI)