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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-01-SET-01
Sets & Their Representation — Assignment
Chapter: Sets
Topic: Sets and Their Representation
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
The empty set is denoted by:
  • A.$\{0\}$
  • B.$\varnothing$
  • C.$U$
  • D.$\{\varnothing\}$
2.
$\{1,2,3\}$ in set-builder form is:
  • A.$\{x:x\in\mathbb{N},\ x<4\}$
  • B.$\{x:x\in\mathbb{Z}\}$
  • C.$\{x:x<3\}$
  • D.$\{x:x\le4\}$
3.
Which is a finite set?
  • A.$\{x:x\in\mathbb{N}\}$
  • B.$\{x:x\in\mathbb{N},\ x<10\}$
  • C.set of points on a line
  • D.$\{x:x\in\mathbb{Z}\}$
4.
The number of vowels in the word "EQUATION" forms a set with how many elements?
  • A.$4$
  • B.$5$
  • C.$6$
  • D.$3$
5.
The roster form of $\{x:x\in\mathbb{Z},\ x^2=9\}$ is:
  • A.$\{3\}$
  • B.$\{-3,3\}$
  • C.$\{9\}$
  • D.$\{-9,9\}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write $\{x:x\text{ is a letter in the word SCHOOL}\}$ in roster form.
7.
Write the set of even natural numbers up to $10$ in roster form.
8.
State whether $\{x:x\in\mathbb{N},\ x<1\}$ is finite or infinite, and name it.
9.
Write $\{1,4,9,16,25\}$ in set-builder form.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Write $\{x:x\text{ is a prime number} <20\}$ in roster form.
11.
Describe $\left\{1,\tfrac12,\tfrac13,\tfrac14,\dots\right\}$ in set-builder form.
12.
State whether the set of points on a line is finite or infinite.
13.
Write $\{-5,-4,\dots,5\}$ in set-builder form.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
List all elements of $A=\{x:x\in\mathbb{Z},\ x^2\le16\}$ and state $n(A)$.
15.
Express the set of two-digit numbers divisible by $11$ in both roster and set-builder form.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\varnothing$
  2. (A) $\{x:x\in\mathbb{N},\ x<4\}$
  3. (B) $\{x:x\in\mathbb{N},\ x<10\}$
  4. (B) $5$
  5. (B) $\{-3,3\}$
Section B — Short Answer (2 marks)
  1. $\{S,C,H,O,L\}$.
  2. $\{2,4,6,8,10\}$.
  3. The empty set (finite).
  4. $\{x:x=n^2,\ n\in\mathbb{N},\ 1\le n\le5\}$.
Section C — Short Answer (3 marks)
  1. $\{2,3,5,7,11,13,17,19\}$.
  2. $\left\{x:x=\tfrac1n,\ n\in\mathbb{N}\right\}$.
  3. Infinite.
  4. $\{x:x\in\mathbb{Z},\ -5\le x\le5\}$.
Section D — Long Answer (5 marks)
  1. $A=\{-4,-3,-2,-1,0,1,2,3,4\}$; $n(A)=9$.
  2. Roster $\{11,22,33,44,55,66,77,88,99\}$; set-builder $\{x:x=11k,\ k\in\mathbb{N},\ 1\le k\le9\}$.
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