CHAPTER 1 SETS
MCQ TYPES QUESTIONS
Que1.
If A ={ 0 1 2 3 4 5 6 7 8 9 10}, then insert appropriate symbol ∈ or ∉in
each of the following blank spaces. (i) 4 ... A (ii) − 4 ... A (iii) 12 ... A
are
(a)
∈, ∈, ∈
(b)
∈, ∉, ∈
(c)
∈, ∉, ∉
(d)
∉, ∉, ∉
Answer
» c
Solution » ( View the Solution )
Que2.
The following set in Roster form is {x : x is positive integer and a divisor of
9}
(a)
{1, 3, 9}
(b)
{1, 3, 8}
(c)
{9, 8, 27}
(d)
None of these
Answer
» a
Solution » ( View the Solution )
Que3.
The set of all natural numbers x such that 4x + 9 < 50 in roster form is
(a)
{1, 2, 4, 6, 8, 10}
(b)
{1, 3, 5, 7, 9}
(c)
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(d)
None of the above
Answer
» c
Solution » ( View the Solution )
Que5.
The set A = {14, 21, 28, 35, 42, ..., 98} in set-builder form is
(a)
A x x n n N = = ∈ { :
,7 and1 15 ≤ ≤ n }
(b)
A x x n n N = = ∈ { :
,7 and2 14 ≤ ≤ n }
(c)
A x x n n N = = ∈ { :
,7 and 3 13 ≤ ≤ n }
(d)
A x x n n N = = ∈ { :
,7 and4 12 ≤ ≤ n }
Answer
» b
Solution » ( View the Solution )
Que6.
If a set is denoted as A = φ, then number of elements in A is
(a)
0
(b)
1
(c)
2
(d)
3
Answer
» a
Solution » ( View the Solution )
Que7.
A set B = { 5} is called
(a)
singleton set
(b)
empty set
(c)
infinite set
(d)
None of these
Answer
» a
Solution » ( View the Solution )
Que8.
The set of months of a year is …X… set. Here, X refers to
(a)
empty
(b)
finite
(c)
infinite
(d)
singleton
Answer
» b
Solution » ( View the Solution )
Que9.
Let A = {x : x is a square of a natural number and x is less than 100} and B ={
x:x is a set of even natural numbers}. The cardinality of A ∩B is
(a)
4
(b)
5
(c)
9
(d)
None of these
Answer
» a
Solution » ( View the Solution )
Que10.
The set {1, 2, 3,...} is …Y… set. Here, Y refers to
(a)
null
(b)
finite
(c)
infinite
(d)
singleton
Answer
» c
Solution » ( View the Solution )
Que11.
From the following sets given below, pair the equivalent sets. A = { 1 2 3} , B=
{ t p q r s},C = { α β γ} and D = {a, e, i, o, u}
(a)
Sets A ,C, and A, D
(b)
Sets A, B, andB, D
(c)
Sets A ,C, andB, D
(d)
Sets A, C, andB, C
Answer
» c
Solution » ( View the Solution )
Que12.
If A = the set of letters in ‘ALLOY’ and B = the set of letters in ‘LOYAL’,
then A and B are …X… . Here, X refers to
(a)
equal
(b)
unequal
(c)
disjoint
(d)
None of these
Answer
» a
Solution » ( View the Solution )
Que13.
If X ={8n–7n–1} n∈N and
Y = {49n –49 | n∈N } .
Then,
(a)
X ⊂ Y
(b)
Y ⊂ X
(c)
X = Y
(d)
X ∩Y = φ
Answer
» a
Solution » ( View the Solution )
Que14.
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 values of m and n are,
respectively
(a)
4, 7
(b)
7, 4
(c)
4, 4
(d)
7, 7
Answer
» b
Solution » ( View the Solution )
Que15.
Write the { x : x ∈ R, − 5 < x ≤ 6 } as interval, then the length
of the interval is
(a)
9
(b)
10
(c)
11
(d)
12
Answer
» c
Solution » ( View the Solution )
Que16.
If A = {2, 4, 6}, B = {1, 3, 5} and C = {0, 7},then the universal set will be
(a)
{0, 7}
(b)
{1, 2, 3, 4, 5, 6}
(c)
{0,1, 3, 5, 7}
(d)
{0, 1, 2, 3, 4, 5, 6, 7}
Answer
» d
Solution » ( View the Solution )
Que17.
Total number of elements in the power set of A containing 15 elements is
(a)
2 15
(b)
152
(c)
2 15–1
(d)
215–1
Answer
» a
Solution » ( View the Solution )
Que18.
If A = P ({ 1,2 }), where P denotes the power set, then which one of the
following is correct?
(a)
{1,2 } ⊂ A
(b)
1 ∈ A
(c)
φ ∉A
(d)
{ 1,2 } ∈A
Answer
» d
Solution » ( View the Solution )
Que19.
If A = {1,3, 5, 7 }, then what is the cardinality of the power set P (A)?
(a)
8
(b)
15
(c)
16
(d)
17
Answer
» c
Solution » ( View the Solution )
Que20.
. If A and B are two sets, then A∩(A∪B)
equals to (a) A (b) B (c) φ (d) A∩B
Q21.
If A = { , , , 2 4 6 8} and B = { , , , 6 8 10 12 }, then A ∪B is
(a)
{2, 4, 6, 8}
(b)
{6, 8, 10, 12}
(c)
{6, 8}
(d)
{2, 4, 6, 8, 10, 12}
Answer
» a
Solution » ( View the Solution )
Que22.
If A ={1 3 9 } and B ={ 2 4 5 6, } , then A ∪B is
(a)
{1, 3, 2, 4, 9}
(b)
{1, 2, 3, 4, 5, 6}
(c)
{1, 2, 3, 4, 5, 9}
(d)
{1, 2, 3, 4, 5, 6, 9}
Answer
» d
Solution » ( View the Solution )
Que23.
Let A = { a e i o u} and B = { a i u }. Then, A∪ B is …X… .
Here, X refers to
(a)
A
(b)
B
(c)
A and B
(d)
None of these
Answer
» a
Solution » ( View the Solution )
Que25.
Let X = {Ram, Geeta, Akbar} be the set of students of class XI, who are in
school hockey team and Y = {Geeta, David, Ashok} be the set of students from
class XI, who are in the school football team. Then, X ∩ Y is
(a)
{Ram, Geeta}
(b)
{Ram}
(c)
{Geeta}
(d)
None of these
Answer
» c
Solution » ( View the Solution )
Que26.
Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = {2, 3, 5, 7}. Then, which of
following is true?
(a)
A ∩B=A
(b)
A∩B =B
(c)
A∩B⊄B
(d)
None of these
Answer
» b
Solution » ( View the Solution )
Que28.
Are the given sets disjoint? A = { x:x is the boys of your school} B = {x :x is the girls of your school}
(a)
Yes
(b)
No
(c)
Can’t say
(d)
Insufficient data
Answer
» a
Solution » ( View the Solution )
Que30.
If X and Y are two sets such that X has 40 elements, X ∪Y has 60
elements and X∩ Y has 10 elements, then
the number of elements does Y have
(a)
10
(b)
20
(c)
30
(d)
40
Answer
» c
Solution » ( View the Solution )
Que31.
In a committee, 50 people speak French, 20 speak Spanish and 10 speak both
Spanish and French. The number of people who speak atleast one of these two
languages, is
(a)
40
(b)
60
(c)
20
(d)
80
Answer
» b
Solution » ( View the Solution )
Que32.
In a town with a population of 5000, 3200 people are egg-eaters, 2500
meat-eaters and 1500 eat both egg and meat. Then, the number of pure
vegetarians is
(a)
800
(b)
1000
(c)
1600
(d)
2000
Answer
» a
Solution » ( View the Solution )
Que33.
In a group of students, 100 students know Hindi, 50 know English and 25 know
both. Each of the students knows either Hindi or English. The number of
students in the group is
(a)
50
(b)
125
(c)
75
(d)
175
Answer
» b
Solution » ( View the Solution )
Que34.
In a school sports event, 50 students participate for football, 30 students
participate for cricket and 15 students participate for both. Then, the number
of students who participated for either football or for cricket, is
(a)
60
(b)
55
(c)
65
(d)
75
Answer
» c
Solution » ( View the Solution )
35.
Assertion (A) ‘The collection of all natural numbers less than 100’ is a set.
Reason
(R) A set is a well-defined collection of the distinct objects.
36.
Assertion (A) The set D x x = { : is a prime number which is a divisor of 60}
in roster form is {1, 2, 3, 4, 5}.
Reason
(R) 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}
37.
Assertion (A) The set {1, 4, 9, ... 100} in the set-builder form is { : x x n =
2 , where n N ∈ and 1 10 ≤ ≤ n
}.
Reason
(R) In roster form, the order in which the elements are listed is, immaterial.
38.
Assertion (A) The set { x: x is a month of a year not having 31 days} in roster
form is {February, April, June, September, November}.
Reason
(R) The set F= {x :x is a consonant in the English alphabet which precedes k }
in roster form is F = { b c d f g h j }.
39.
Assertion (A) The set A = { x:x is an
even prime number greater than 2} is the empty set. Reason (R) The set B = {x :x2= 4 is odd} is not an
empty set.
40.
Assertion (A) The set A = { a b c d e g} is finite set.
Reason
(R) The set B = { men living presently in different parts of the world} is
finite set.
41.
Assertion (A) The set of positive integers greater than 100 is infinite.
Reason
(R) The set of prime numbers less than 99 is finite.
Assertion
(A) If A = set of prime numbers less than 6 and B = set of prime factors of 30,
then A =B.
Reason
(R) If P = { 1 2 3}andQ = { 2 2 1 3 3}, then P and Q are not equal.
43.
Assertion (A) Let A = { , , }1 2 3 and B = { , , , }1 2 3 4 . Then, A B ⊂ .
Reason
(R) If every element of X is also an element of Y, then X is a subset of Y
