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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-01-CT
Sets — Full Chapter Test
Chapter: Sets
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.
The empty set is denoted by:
  • A.$\{0\}$
  • B.$\varnothing$
  • C.$U$
  • D.$\{\varnothing\}$
2.
The number of subsets of $\{1,2,3,4\}$ is:
  • A.$8$
  • B.$16$
  • C.$4$
  • D.$32$
3.
$A\cap A'$ equals:
  • A.$A$
  • B.$U$
  • C.$\varnothing$
  • D.$A'$
4.
$\{1,2,3\}$ in set-builder form is:
  • A.$\{x:x\in\mathbb{N},\ x<4\}$
  • B.$\{x:x\in\mathbb{Z}\}$
  • C.$\{x:x<3\}$
  • D.$\{x:x\le4\}$
5.
The number of proper subsets of a $3$-element set is:
  • A.$8$
  • B.$7$
  • C.$6$
  • D.$3$
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 all subsets of $\{1,2\}$.
8.
If $A=\{1,2,3\}$ and $B=\{3,4\}$, find $A\cup B$.
9.
Write the set of even natural numbers up to $10$ in roster 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.
Write the power set of $\{a,b,c\}$.
12.
If $A=\{1,2,3,4\}$ and $B=\{3,4,5,6\}$, find $A-B$ and $B-A$.
13.
Describe $\left\{1,\tfrac12,\tfrac13,\tfrac14,\dots\right\}$ 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.
If $A=\{1,2,3,4\}$, write the power set $P(A)$ and state $n(P(A))$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $\varnothing$
  2. (B) $16$
  3. (C) $\varnothing$
  4. (A) $\{x:x\in\mathbb{N},\ x<4\}$
  5. (B) $7$
Section B — Short Answer (2 marks)
  1. $\{S,C,H,O,L\}$.
  2. $\varnothing,\{1\},\{2\},\{1,2\}$.
  3. $\{1,2,3,4\}$.
  4. $\{2,4,6,8,10\}$.
Section C — Short Answer (3 marks)
  1. $\{2,3,5,7,11,13,17,19\}$.
  2. $\{\varnothing,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\}$.
  3. $A-B=\{1,2\}$, $B-A=\{5,6\}$.
  4. $\left\{x:x=\tfrac1n,\ n\in\mathbb{N}\right\}$.
Section D — Long Answer (5 marks)
  1. $A=\{-4,-3,-2,-1,0,1,2,3,4\}$; $n(A)=9$.
  2. $P(A)$ has all $16$ subsets; $n(P(A))=16$.
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