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Class 11 | CBSE | MATHEMATICS
EXTRA QUESTIONS SOLUTIONS
Solutions — Extra Practice Worksheet (Sets)
SECTION A: OBJECTIVE TYPE
1. Fill in the blanks
- The symbol used to denote “belongs to” is ∈
- The set of all positive integers is denoted by Z⁺
- A collection which is not well-defined is called a not well-defined collection
- In roster form, repetition of elements is not allowed
- The set of all real numbers is denoted by R
2. Choose the correct option
-
Correct answer: (c)
Collection of most intelligent students in a class -
Correct answer: (c)
\[ 5 ∈ A \]
SECTION B: VERY SHORT ANSWER
3. Answers
(i) A set is a well-defined collection of objects.
(ii) Examples of well-defined collections:
- Set of natural numbers less than 10
- Set of vowels in the English alphabet
(iii) Roster form of first five natural numbers:
\[ \{1, 2, 3, 4, 5\} \](iv) If
\[ A = \{2, 4, 6, 8\} \]Two elements not belonging to A are:
\[ 1,\; 3 \]SECTION C: SHORT ANSWER
4. Identify whether the following are sets
(i) Collection of all rivers in India — Set
Reason: Rivers are clearly defined.
(ii) Collection of best movies of the year — Not a set
Reason: “Best” is subjective.
(iii) Collection of all multiples of 5 — Set
Reason: Multiples of 5 are well-defined.
5. Insert ∈ or ∉
Given:
\[ A = \{x : x ∈ N,\; x ≤ 10\} \]- \(7 ∈ A\)
- \(12 ∉ A\)
- \(0 ∉ A\)
- \(10 ∈ A\)
SECTION D: CONVERSION TYPE
6. Write in roster form
(i)
\[ A = \{x : x ∈ Z,\; −2 ≤ x ≤ 4\} \] \[ \{−2, −1, 0, 1, 2, 3, 4\} \](ii)
\[ B = \{x : x ∈ N,\; x² < 30\} \] \[ \{1, 2, 3, 4, 5\} \](iii)
\[ \{2, 3, 5, 7, 11, 13, 17, 19\} \]7. Write in set-builder form
(i)
\[ \{x : x = 4n,\; n ∈ N,\; 1 ≤ n ≤ 4\} \](ii)
\[ \{x : x = n²,\; n ∈ N,\; 1 ≤ n ≤ 5\} \](iii)
\[ \{x : x = 3n,\; n ∈ N\} \]SECTION E: LISTING ELEMENTS
(i)
\[ A = \{x : x ∈ Z,\; x² ≤ 9\} \] \[ \{−3, −2, −1, 0, 1, 2, 3\} \](ii)
\[ \{\text{April, June, September, November}\} \](iii)
\[ \{b, c, d, f, g, h, j, k, l\} \]SECTION F: MATCH THE FOLLOWING
- (i) {2, 3, 5} → (b)
- (ii) {1, 2, 3, 6} → (a)
- (iii) {a, e, i, o, u} → (c)
- (iv) {1, 3, 5, 7} → (d)