ℕ ℤ ℚ √2 ℝ ℝ ℚ ℤ ℕ 1/(√a+√b) · (√a−√b)/(√a−√b) aᵐ·aⁿ = aᵐ⁺ⁿ √4=2 (rational!) ℕ⊂ℤ⊂ℚ⊂ℝ
√2
Chapter 1  ·  Class IX Mathematics  ·  MCQ Practice

MCQ Practice Arena

Number Systems

From Natural Numbers to Irrationals — Command Every Number on the Line

📋 50 MCQs ⭐ 28 PYQs ⏱ 55 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
22Easy
20Medium
8Hard
28PYQs
55 secAvg Time/Q
8Topics
Easy 44% Medium 40% Hard 16%

Why Practise These MCQs?

CBSE Class IXNTSEState BoardsOlympiad

Number Systems is the foundational chapter of Class IX — MCQs test classification of numbers, irrational number operations, rationalisation, and laws of exponents. CBSE Term tests and Boards include 1–2 direct MCQs from this chapter every year. NTSE Maths Stage I includes number line representation and surds simplification. Rationalisation and exponent law questions are solvable in under 60 seconds with practice.

Topic-wise MCQ Breakdown

Natural, Whole, Integer, Rational Numbers6 Q
Irrational Numbers & Identification8 Q
Real Numbers & Number Line6 Q
Decimal Expansions (Terminating/NT)7 Q
Operations on Irrational Numbers8 Q
Rationalisation of Surds8 Q
Laws of Exponents (Real Exponents)5 Q
Representation on Number Line2 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) = a-b$
$\frac{1}{\sqrt{a}+\sqrt{b}} = \frac{\sqrt{a}-\sqrt{b}}{a-b}$
$a^m \cdot a^n = a^{m+n}$
$(a^m)^n = a^{mn}$
$a^{1/n} = \sqrt[n]{a}$
$a^0 = 1\ (a \ne 0)$

MCQ Solving Strategy

For classification MCQs, use the hierarchy: ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ — every natural number is an integer, every integer is rational, but not vice versa. For irrational identification, check if the decimal is non-terminating non-repeating. Rationalisation MCQs: multiply numerator and denominator by the conjugate of the denominator. For exponent laws, identify the base first — all terms must share the same base before applying laws.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Classify numbers (rational/irrational), apply basic exponent laws, identify terminating decimals

② Medium

Rationalise denominators, simplify surds, operations on irrational numbers

③ Hard

Multi-step surd simplification, exponent equations, represent surds on number line

★ PYQ

CBSE — rationalise + simplify; NTSE — classification and number line reasoning

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Polynomials
🎯 Knowledge Check

Maths — Number Systems

50 Questions Class 9 MCQs
1
Which of the following is a natural number?
2
Which of the following is a whole number?
3
Which of the following is an integer?
4
Which of the following is a rational number?
5
Which of the following is irrational?
6
Decimal expansion of 1/2 is:
7
Decimal expansion of 1/3 is:
8
Which is not a rational number?
9
Value of \(\sqrt{4}\) is:
10
Which is irrational?
11
If p/q is rational, then q ?:
12
Which is a terminating decimal?
13
\(\sqrt{9}\) is:
14
Which is irrational?
15
p is:
16
Which of the following is rational?
17
Decimal expansion of 7/8:
18
Which is irrational?
19
Rational numbers include:
20
Which is whole number?
21
Which is irrational?
22
The decimal expansion of rational numbers is:
23
\(\sqrt{25}\) is:
24
Which is irrational?
25
Which number is neither rational nor irrational?
26
Express 0.125 as fraction:
27
\(\sqrt{49}\) is:
28
Which is irrational?
29
Which is terminating?
30
Which is non-terminating repeating?
31
\(\sqrt{50}\) can be written as:
32
Which is irrational?
33
Simplify \(\sqrt{18}\)
34
Which is irrational?
35
Product of rational and irrational is:
36
Sum of rational and irrational:
37
\(\sqrt{2} × \sqrt{2} =\)
38
\(\sqrt{(3)}^2\) =
39
Rationalising denominator of \(1/\sqrt{2}\):
40
Rationalise \(1/(\sqrt{3})\):
41
\((\sqrt{2} + \sqrt{3})^2 =\)
42
\((\sqrt{5} - \sqrt{2})^2\) =
43
Rationalise denominator: \(1/(\sqrt{5} - \sqrt{2})\)
44
Which is irrational?
45
Which is rational?
46
\(\sqrt{7}\) is:
47
Which is irrational?
48
Simplify \(\sqrt{72}\):
49
Which is rational?
50
Which is irrational?
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NCERT Class 9 Maths Chapter 1 Number Systems MCQs
NCERT Class 9 Maths Chapter 1 Number Systems MCQs — Complete Notes & Solutions · academia-aeternum.com
🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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Frequently Asked Questions

A number system is a way of expressing numbers using symbols and rules. It includes natural numbers, whole numbers, integers, rational, and irrational numbers.

Real numbers include both rational and irrational numbers that can be represented on the number line.

Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and \(q \neq 0.\)

Irrational numbers cannot be written as a simple fraction and have non-terminating, non-repeating decimals, like v2 or p.

Rational numbers can be expressed as p/q, while irrational numbers cannot. Rational decimals terminate or repeat; irrational decimals do not.

Natural numbers are counting numbers starting from 1, 2, 3, and so on.

Whole numbers include all natural numbers and 0, i.e., 0, 1, 2, 3, 4, ...

Integers include all whole numbers and their negatives, such as … -3, -2, -1, 0, 1, 2, 3 …

The decimal expansion of rational numbers is either terminating or non-terminating repeating.

The decimal expansion of irrational numbers is non-terminating and non-repeating.

Yes, every real number, whether rational or irrational, can be represented on the number line.

All rational numbers are real, but not all real numbers are rational. Real numbers include both rational and irrational types.

Construct a right-angled triangle with both legs of 1 unit each; the hypotenuse represents v2 when plotted on the number line.

A non-terminating decimal continues infinitely without ending, like 0.333... or 0.142857142857...

A repeating decimal has digits that repeat in a pattern, for example, 0.666… or 0.142857142857…

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    Number Systems — Learning Resources

    📄 Detailed Notes
    ✔️ True / False
    📌 Exercise
    📝 Exercises
    Exercise 1.1 Exercise 1.2 Exercise 1.3 Exercise 1.4 Exercise 1.5
    📚
    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    NCERT Class 9 Maths Chapter 1 Number Systems MCQs
    NCERT Class 9 Maths Chapter 1 Number Systems MCQs — Complete Notes & Solutions · academia-aeternum.com
    🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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