Public question bank · Class 10 · Mathematics

Class 10 Mathematics - Chapters 1-4

110 original MCQs with answers and worked explanations, aligned with NCERT Class 10 Mathematics: Real Numbers (20), Polynomials (30), Pair of Linear Equations in Two Variables (30), Quadratic Equations (30).

Chapters / topics

Chapter 1: Real Numbers · 20 Chapter 2: Polynomials · 30 Chapter 3: Pair of Linear Equations in Two Variables · 30 Chapter 4: Quadratic Equations · 30

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110 ready questions · 10 per page

1. Chapter 1: Real Numbers · mcq

What is the HCF of 96 and 144?

Show answer and explanation

$96=2^5\times3$ and $144=2^4\times3^2$ . Taking the smaller exponent of each common prime gives $2^4\times3=48$ .

2. Chapter 1: Real Numbers · mcq

What is the LCM of 18 and 24?

144

Show answer and explanation

$18=2\times3^2$ and $24=2^3\times3$ . Taking the larger exponents gives $2^3\times3^2=72$ .

3. Chapter 1: Real Numbers · mcq

Two positive integers have HCF 8 and LCM 240. If one integer is 48, what is the other?

Show answer and explanation

For two positive integers, their product equals HCF $\times$ LCM. The other integer is $(8\times240)/48=40$ . Its HCF with 48 is 8.

4. Chapter 1: Real Numbers · mcq

Which is the prime factorisation of 540?

$2^3\times3^2\times5$

$2^2\times3^2\times5$

$2\times3^3\times5^2$

$2^2\times3^3\times5$

Show answer and explanation

$2^2\times3^3\times5$

Dividing 540 by prime factors gives $540=4\times135=2^2\times3^3\times5$ .

5. Chapter 1: Real Numbers · mcq

How many distinct prime factors does 156 have?

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$156=2^2\times3\times13$ . The distinct prime factors are 2, 3 and 13, so there are three.

6. Chapter 1: Real Numbers · mcq

What is the smallest positive integer by which 180 must be multiplied to obtain a perfect square?

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$180=2^2\times3^2\times5$ . A square has even prime exponents. Multiplication by 5 gives $900=30^2$ .

7. Chapter 1: Real Numbers · mcq

What is the smallest positive integer by which 432 must be divided to obtain a perfect cube?

Show answer and explanation

$432=2^4\times3^3$ . Dividing by 2 gives $2^3\times3^3=216=6^3$ . The original number is not a cube.

8. Chapter 1: Real Numbers · mcq

What is the HCF of any two coprime positive integers?

Their sum

Their product

Show answer and explanation

Coprime integers have no common positive factor except 1. Therefore their highest common factor is 1.

9. Chapter 1: Real Numbers · mcq

What is the LCM of the coprime integers 14 and 25?

350

175

700

Show answer and explanation

350

For coprime positive integers, HCF is 1, so their LCM is their product: 14 × 25 = 350.

10. Chapter 1: Real Numbers · mcq

$7\times11\times13+13$ is which kind of number?

Neither prime nor composite

Composite

Prime

Irrational

Show answer and explanation

Composite

$7\times11\times13+13=13(77+1)=13\times78$ . It has factors other than 1 and itself, so it is composite.