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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-02-CT
Relations and Functions — Full Chapter Test
Chapter: Relations and Functions
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
If $n(A)=3,\ n(B)=2$, then $n(A\times B)=$
  • A.$5$
  • B.$6$
  • C.$8$
  • D.$1$
2.
A relation $R$ from $A$ to $B$ is a subset of:
  • A.$A\cup B$
  • B.$A\times B$
  • C.$A\cap B$
  • D.$A-B$
3.
A function assigns each input to:
  • A.exactly one output
  • B.two outputs
  • C.no output
  • D.many outputs
4.
If $n(A)=4$, then $n(A\times A)=$
  • A.$8$
  • B.$16$
  • C.$4$
  • D.$12$
5.
The domain of $\{(1,4),(2,5)\}$ is:
  • A.$\{4,5\}$
  • B.$\{1,2\}$
  • C.$\{1,2,4,5\}$
  • D.$\{1\}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $A=\{1,2\}$ and $B=\{a\}$, write $A\times B$.
7.
If $R=\{(1,3),(2,6),(3,9)\}$, find the domain.
8.
If $f(x)=2x+3$, find $f(0)$ and $f(1)$.
9.
If $A=\{1,2\},\ B=\{3,4\}$, write $A\times B$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $A=\{1,2,3\}$, write $A\times A$.
11.
Write $R=\{(x,y):x+y=5,\ x,y\in\mathbb{N}\}$ in roster form.
12.
If $f(x)=x^2+1$, find $f(-2),\ f(0),\ f(2)$.
13.
If $A\times B=\{(1,2),(1,3),(2,2),(2,3)\}$, find $A$ and $B$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If $A=\{1,2\}$ and $B=\{1,2,3\}$, find $A\times B$ and $B\times A$, and state whether they are equal.
15.
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.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $6$
  2. (B) $A\times B$
  3. (A) exactly one output
  4. (B) $16$
  5. (B) $\{1,2\}$
Section B — Short Answer (2 marks)
  1. $\{(1,a),(2,a)\}$.
  2. $\{1,2,3\}$.
  3. $f(0)=3,\ f(1)=5$.
  4. $\{(1,3),(1,4),(2,3),(2,4)\}$.
Section C — Short Answer (3 marks)
  1. $\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3)\}$.
  2. $\{(1,4),(2,3),(3,2),(4,1)\}$.
  3. $5,\ 1,\ 5$.
  4. $A=\{1,2\},\ B=\{2,3\}$.
Section D — Long Answer (5 marks)
  1. Each has $6$ ordered pairs, but $A\times B\ne B\times A$.
  2. $R=\{(1,3),(2,4),(3,5)\}$; domain $\{1,2,3\}$, range $\{3,4,5\}$.
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