Roll No : Name of School : Witri R.

Learn Time : 00:00

Date : 2025-07-21 Name of Assessment : Class Test
Subject : Maths - Sets
Class : 11

1 Write all subsets of set A = {1, 2, 3}. 1

Ans : Subsets of set A are ϕ, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}

2 Represent in the set builder form. 1

Ans :

3 Insert the proper sign, for the following, from the signs ∈, ∉, ⊆, ⊂, ⊈. 1
1 ................. {1, 3, 5}
Ans : Is an element of (∈)

4 Insert the proper sign, for the following, from the signs ∈, ∉, ⊆, ⊂, ⊈. 1
7 .................{5, 6, 9, 7, 3}

Ans : Is an element of (∈)

5 Insert the proper sign, for the following, from the signs ∈, ∉, ⊆, ⊂, ⊈. 1
{7} ................. {5, 6, 9, 7, 3}
Ans : Is a proper subset of (⊂)

6 Insert the proper sign, for the following, from the signs ∈, ∉, ⊆, ⊂, ⊈. 1
{3, {4}} ............. {1, 2, 3, 4, 5, {4}, 6}
Ans : is a proper subset of (⊂)

7 From the adjoining Venn diagram, determine the following set A ∪ B. 1

Ans : A ∪ B = {2, 5, 3, 6, 0, 8}
8 Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 2
4, 5, 6}. find (i) A′ (ii) (A ∩ C)′ (iii) (A′)′ (iv) (B – C)′
We have
(i) A′ = U – A = {5, 6, 7, 8, 9}
(ii) A ∩ C = {3, 4} ⇒ (A ∩ C)′ = U – (A ∩ C) = {1, 2, 5, 6, 7, 8, 9}
(iii) (A′)′ = U – A′ = U – {5, 6, 7, 8, 9} = {1, 2, 3, 4} = A
Ans : (iv) (B – C) = {2, 8} ⇒ (B – C)′ = {1, 3, 4, 5, 6, 7, 9}

9 If A = {1, 3, 5, 7, 9, 11, 13, 15, 17}, B = {2, 4, 6, ....., 18} and N is the 2
universal set, then find A′ ∪ {(A ∪ B) ∩ B′}.
We have,
(A ∪ B) ∩ B′ = A [∵ A, B are disjoint sets]
Ans : ∴ A′ ∪ {(A ∪ B) ∩ B′} = A′ ∪ A = N.

10 2
Let T = . Is T an empty set ? Justify you answer.

Ans :

2
11Let U = {x ∈ N : x ≤ 8}, A = {x ∈ N : 5 < x < 50} and B = {x ∈ N : x is prime 4
number less than 10}. Draw a Venn diagram to show the relationship
between the given sets. Hence list the elements of the following sets (i) A′
(ii) B′ (iii) A – B (iv) A ∩ B′
 U = {1, 2, 3, 4, 5, 6, 7, 8}
A = {3, 4, 5, 6, 7} ; B = {2, 3, 5, 7}

(i) A′ = {1, 2, 8} (ii) B′ = {1, 4, 6, 8}

Ans : (iii) A – B = {4, 6} (iv) A ∩ B′ = {4, 6}

12 {2, 4, 6, 8, ....} is an example of 1

(a) finite set
(b) infinite set
(c) set of odd numbers
(d) set of whole numbers

Ans :
(b), in an infinite set the elements are not countable up to a certain
natural number.

13 In open interval (a, b) all the real numbers lying between a and b belong, 1
but a, b themselves ______ to this interval
(a) belong
(b) do not belong
(c) a including but b excluding
(d) a excluding but b including
Ans :
(b), in open interval (a, b), a and b do not belong to the interval.

14 Given the set A = {1, 3, 5}, B = {2, 4, 6}, C = {0, 2, 4, 6, 8}. Which of the 1
following can be considered as a universal set(s) for sets A, B, C?
(i) {0, 1, 2, 3, 4, 5, 6}
(ii) ϕ
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}
Ans : (iii) as A, B, C are subsets of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

15 The set (A ∩ B′)′ ∪ (B ∩ C) is equal to 1

(a) A′ ∪ B ∪ C (b) A′ ∪ B
(c) A′ ∪ C′ (d) A′ ∩ B
Ans :
(A ∩ B′)′ ∪ (B ∩ C) = {A′ ∪ (B′)′} ∪ (B ∩ C) = (A′ ∪ B) ∪ (B ∩ C) = A′ ∪ B
16 If X = {8n – 7n – 1|n ∈ N} and Y = {49n – 49| n ∈ N}. 1
Then
(a) X ⊂ Y (b) Y ⊂ X
(c) X = Y (d) X ∩ Y = ϕ

Ans : (a) for n = 1, x = {81 – 7 × 1 – 1} = 0,

y = 49 × 1 – 49 = 0
for n = 2, x = 82 – 7 × 2 – 1 = 49, y = 49 × 2 – 49 = 49
for n = 3, x = 83 – 7 × 3 – 1 = 490, y = 49 × 3 – 49 = 98
We see for n = 3, x = 490, y = 98

17 If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5}, B = {2, 4, 6, 7} and C = 1

{2, 3, 4, 8}, then
(i) (B ∪ C)′ is ______ (ii) (C – A)′ is ______

Ans : (i) B ∪ C = {2, 4, 6, 7} ∪ {2, 3, 4, 8} = {2, 3, 4, 6, 7, 8}

(B ∪ C)′ = U – (B ∪ C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {2, 3, 4, 6, 7, 8}
= {1, 5, 9, 10} (ii) C – A = {2, 3, 4, 8} – {1, 2, 3, 5} = {4, 8}
(C – A)′ = U – (C – A) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {4, 8}
= {1, 2, 3, 5, 6, 7, 9, 10}

18 Representation of set A = {x | x ∈ Z, x2 < 20} in the roster form is 1

(a) {1, 2, 3, ..., 20} (b) {1, 2, 3, 4}
(c) {0, 1, 2, 3, 4} (d) {–4, –3, –2, –1, 0, 1, 2, 3, 4}
Ans :
(d), We observe that the squares of integers 0, ± 1, ± 2, ± 3, ± 4 are less
than 20.
Therefore, the set A in roster form is
A = {– 4, – 3, – 2, – 1, 0, 1, 2, 3, 4}.

19 The given real number line represent various intervals as subsets of real number, find the correct 1
option to representation.

(a) (a, b], [a, b), [a, b], (a, b)

(b) [a, b], (a, b), (a, b], [a, b)

(c) (a, b), [a, b], [a, b), (a, b]

(d) (a, b), (a, b], [a, b), [a, b]

Ans : (c), represents open interval; a and b do not belong.

represents closed interval; a, b belong.

 represents open interval from a to b, including a but excluding b.

represents open interval from a to b, excluding a but including b.

20 Write the set of months of a year in the set builder form. 1

Ans : In the set builder form we write an element with a property.

∴ Set builder form is {x : x is month of a year}

21 Write the set A = {1, 2, 3, 4} as a Venn diagram. 1

Ans : We write elements in a circle/ellipse as

22 After explaning operation on sets, Mathematics teacher in class wrote 4

there sets as A = {2, 3, 4, 5}, B = {6, 7, 8},
C = {x : x is prime number less than 10}. She asked the students that the
following questions will judge how much you have understood. She asked
the students to write down the answers and later they can check from
the answers written by teacher and give marks.
(i) Find A ∪ B.
(ii) Find (A ∪ B) ∩ C.
(iii) Find (C – B).
Or
(iii) Find (A ∩ C) – B.

Ans : (i) A ∪ B = {2, 3, 4, 5} ∪ {6, 7, 8}

= {2, 3, 4, 5, 6, 7, 8}
(ii) (A ∪ B) ∩ C C = {x : x is prime number less than 10.}
= {2, 3, 5, 7} ∴ (A ∪ B) ∩ C = {2, 3, 4, 5, 6, 7, 8} ∩ {2, 3, 5, 7}
= {2, 3, 5, 7} (iii) C – B = {2, 3, 5, 7} – {6, 7, 8} = {2, 3, 5} Or
(iii) (A ∩ C) – B = [{2, 3, 4, 5} ∩ {2, 3, 5, 7} – {6, 7, 8}]
= [{2, 3, 5} – {6, 7, 8} = {2, 3, 5}

23To select the players for the sports tournament a school management 5
asked the students to assemble in ground and stand according to the
alloted area. In the ground three circular regions are marked as shown in
figure and there are total eight segments for the players to stand
according to their sports.
 Circle A is for those who can play hockey circle, B is for those who can
play cricket. Circle C is for those who can play volleyball.
On the basis of above information answer the following:
(i) If Rajesh can play all three games, then Rajesh should stand in the
segment
(a) I (b) II (c) VI (d) IV
(ii) Ravi can play only hockey and cricket, then he must stand in the
segement
(a) I (b) II (c) III (d) IV
(iii) If Suraj is standing in segment V, then he can play
(a) hockey and volleyball
(b) hockey and cricket
(c) hockey and volleyball only
(d) hockey or volleyball
(iv) Dev can play volleyball and cricket but not hockey, then he must
stand in the segment
(a) VI (b) VII (c) VIII (d) I
(v) Harish can not play any of the game he came to see the games,
then he must stand in the segment
(a) V (b) VI (c) VII (d) VIII
Ans : (i) (d) (ii) (b) (iii) (c) (iv) (a) (v) (d)

24 The set {2, 3, 5, 7, 11, 13} in set builder form can be written as 1
(a) {x : x is a prime number}
(b) {x : x is odd prime number < 15}
(c) {x : x is a prime number ≤ 13}
(d) {x : x is a number having exactly 2 factors}

Ans : (c), {x : x is a prime number ≤ 13}

25 A set which is subset of every set is 1

(a) null set
(b) universal set
(c) singleton set
 (d) power set

Ans : (a) null set

26 For all sets A and B, A – (A ∩ B) is equal to 1

(a) B – A
(b) A – B
(c) A′ ∩ B′
(d) A′ ∪ B′
[NCERT Exemplar]

Ans : (c) A – (A ∩ B) = A – B = A ∩ B′

27 The number of elements in the subset of null set are 1

(a) 0
(b) 1
(c) f
(d) {f}

Ans : (b) null set is f. So number of elements in the sub set = 20 = 1