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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-01-CT
Number Systems — Full Chapter Test
Chapter: Number Systems
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.
Euclid's lemma: $a=bq+r$ with:
  • A.$0\le r
  • B.$0
  • C.$r=0$
  • D.$r>b$
2.
Every composite number is a product of primes:
  • A.in many ways
  • B.uniquely
  • C.never
  • D.only if even
3.
$\sqrt2$ is:
  • A.rational
  • B.irrational
  • C.an integer
  • D.zero
4.
$\tfrac{p}{q}$ (lowest terms) terminates iff $q$ has the form:
  • A.$2^m5^n$
  • B.$2^m3^n$
  • C.$3^m5^n$
  • D.any
5.
The HCF of $6$ and $8$ is:
  • A.$1$
  • B.$2$
  • C.$4$
  • D.$24$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the HCF of $12$ and $18$.
7.
Write the prime factorisation of $84$.
8.
Is $3+\sqrt2$ rational or irrational?
9.
Without dividing, state whether $\tfrac{13}{8}$ terminates.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find HCF$(135,225)$ using Euclid's algorithm.
11.
Find the HCF and LCM of $96$ and $404$.
12.
Prove that $\sqrt2$ is irrational (state the method).
13.
State (with reason) whether $\tfrac{6}{15}$ has a terminating decimal.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Find the HCF of $867$ and $255$ using Euclid's division algorithm.
15.
Find the HCF and LCM of $510$ and $92$ and verify HCF$\times$LCM $=$ product.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $0\le r
  2. (B) uniquely
  3. (B) irrational
  4. (A) $2^m5^n$
  5. (B) $2$
Section B — Short Answer (2 marks)
  1. $6$.
  2. $2^2\cdot3\cdot7$.
  3. Irrational.
  4. Terminating ($8=2^3$).
Section C — Short Answer (3 marks)
  1. $45$.
  2. HCF $4$, LCM $9696$.
  3. By contradiction; $\sqrt2$ is irrational.
  4. $\tfrac{6}{15}=\tfrac25$ — terminating.
Section D — Long Answer (5 marks)
  1. $51$.
  2. HCF $2$, LCM $23460$ (verified).
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