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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-02-REL-01
Relations: Domain, Codomain & Range — Assignment
Chapter: Relations and Functions
Topic: Relations: Domain, Codomain and Range
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.
A relation $R$ from $A$ to $B$ is a subset of:
  • A.$A\cup B$
  • B.$A\times B$
  • C.$A\cap B$
  • D.$A-B$
2.
The domain of $\{(1,4),(2,5)\}$ is:
  • A.$\{4,5\}$
  • B.$\{1,2\}$
  • C.$\{1,2,4,5\}$
  • D.$\{1\}$
3.
The range of $\{(1,4),(2,5)\}$ is:
  • A.$\{1,2\}$
  • B.$\{4,5\}$
  • C.$\{1,4\}$
  • D.$\{5\}$
4.
The number of relations from a $2$-element to a $3$-element set is:
  • A.$6$
  • B.$64$
  • C.$8$
  • D.$9$
5.
If $R=\{(x,y):y=x+1\}$ on $\{1,2,3\}$, then $R=$
  • A.$\{(1,2),(2,3)\}$
  • B.$\{(1,2),(2,3),(3,4)\}$
  • C.$\{(2,1),(3,2)\}$
  • D.$\varnothing$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $R=\{(1,3),(2,6),(3,9)\}$, find the domain.
7.
For the same $R$, find the range.
8.
Write $R=\{(x,y):y=2x,\ x\in\{1,2,3\}\}$ in roster form.
9.
Find the number of relations from $A$ to $B$ if $n(A)=2,\ n(B)=2$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Write $R=\{(x,y):x+y=5,\ x,y\in\mathbb{N}\}$ in roster form.
11.
Find the domain and range of $R=\{(1,2),(1,3),(2,3)\}$.
12.
On $\{1,2,3,4\}$, write $R=\{(x,y):x
13.
If $n(A)=3,\ n(B)=2$, find the number of relations from $A$ to $B$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Let $A=\{1,2,3,4,5\}$ and $R=\{(x,y):y=x+2\}$. Write $R$ in roster form and find its domain and range.
15.
Let $R=\{(x,x^2):x\text{ is a prime number} <10\}$. Write $R$ and find its domain and range.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $A\times B$
  2. (B) $\{1,2\}$
  3. (B) $\{4,5\}$
  4. (B) $64$
  5. (A) $\{(1,2),(2,3)\}$
Section B — Short Answer (2 marks)
  1. $\{1,2,3\}$.
  2. $\{3,6,9\}$.
  3. $\{(1,2),(2,4),(3,6)\}$.
  4. $16$.
Section C — Short Answer (3 marks)
  1. $\{(1,4),(2,3),(3,2),(4,1)\}$.
  2. Domain $\{1,2\}$, range $\{2,3\}$.
  3. $\{(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)\}$.
  4. $64$.
Section D — Long Answer (5 marks)
  1. $R=\{(1,3),(2,4),(3,5)\}$; domain $\{1,2,3\}$, range $\{3,4,5\}$.
  2. $R=\{(2,4),(3,9),(5,25),(7,49)\}$; domain $\{2,3,5,7\}$, range $\{4,9,25,49\}$.
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