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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-02-CAR-01
Cartesian Product of Sets — Assignment
Chapter: Relations and Functions
Topic: Cartesian Product of Sets
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.
If $n(A)=3,\ n(B)=2$, then $n(A\times B)=$
  • A.$5$
  • B.$6$
  • C.$8$
  • D.$1$
2.
If $n(A)=4$, then $n(A\times A)=$
  • A.$8$
  • B.$16$
  • C.$4$
  • D.$12$
3.
If $(2,3)=(x,3)$, then $x=$
  • A.$3$
  • B.$2$
  • C.$0$
  • D.$5$
4.
If $n(A\times B)=6$ and $n(A)=2$, then $n(B)=$
  • A.$2$
  • B.$3$
  • C.$4$
  • D.$6$
5.
$A\times\varnothing$ equals:
  • A.$A$
  • B.$\varnothing$
  • C.$\{0\}$
  • D.$A\times A$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $A=\{1,2\}$ and $B=\{a\}$, write $A\times B$.
7.
If $A=\{1,2\},\ B=\{3,4\}$, write $A\times B$.
8.
Find $x,y$ if $(x+1,\ y-2)=(3,1)$.
9.
If $n(A)=n(B)=n(C)=2$, find $n(A\times B\times C)$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $A=\{1,2,3\}$, write $A\times A$.
11.
If $A\times B=\{(1,2),(1,3),(2,2),(2,3)\}$, find $A$ and $B$.
12.
If $n(A\times B)=15$ and $n(A)=5$, find $n(B)$.
13.
If $A=\{a,b\},\ B=\{1,2,3\}$, find $n(A\times B)$ and write two of its elements.
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.
If $A=\{1,2\},\ B=\{3,4\}$, verify $n(A\times B)=n(A)\cdot n(B)$ and list $A\times B$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $6$
  2. (B) $16$
  3. (B) $2$
  4. (B) $3$
  5. (B) $\varnothing$
Section B — Short Answer (2 marks)
  1. $\{(1,a),(2,a)\}$.
  2. $\{(1,3),(1,4),(2,3),(2,4)\}$.
  3. $x=2,\ y=3$.
  4. $8$.
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. $A=\{1,2\},\ B=\{2,3\}$.
  3. $3$.
  4. $n(A\times B)=6$; e.g. $(a,1),(b,3)$.
Section D — Long Answer (5 marks)
  1. Each has $6$ ordered pairs, but $A\times B\ne B\times A$.
  2. $n(A\times B)=4$; $\{(1,3),(1,4),(2,3),(2,4)\}$.
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