Class 10 • Maths • Chapter 1
Real Numbers
True & False Quiz
Irrational. Prime. Infinite.
✓True
✗False
25
Questions
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Ch.1
Chapter
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X
Class
Why True & False for Real Numbers?
How this format sharpens your conceptual clarity
🔵 Real Numbers form the complete number line — every decimal, fraction, and irrational lives here, foundational to all of Class X.
✅ T/F questions target the Fundamental Theorem of Arithmetic, Euclid's Lemma, and rationality of √p — all Board exam favourites.
🎯 Classic trap: the decimal expansion of a rational number is always terminating OR recurring — never random.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
Every natural number is a real number.
Q 2
Every irrational number is a real number.
Q 3
Every integer is a rational number.
Q 4
Every real number is an irrational number.
Q 5
The decimal expansion of every rational number is either terminating or non-terminating repeating.
Q 6
All prime numbers are odd numbers.
Q 7
0 is a natural number.
Q 8
The square of every prime number has exactly 3 factors.
Q 9
Every rational number can be expressed as a terminating decimal.
Q 10
The sum of two irrational numbers is always irrational.
Q 11
The product of two irrational numbers is always irrational.
Q 12
All integers are real numbers.
Q 13
The HCF of two consecutive numbers is always 1.
Q 14
0 is a rational number.
Q 15
The Fundamental Theorem of Arithmetic is about expressing numbers as products of prime numbers.
Q 16
The product of two rational numbers is always rational.
Q 17
Every point on the number line corresponds to a real number.
Q 18
There are infinitely many prime numbers.
Q 19
The LCM of two co-prime numbers is equal to their product.
Q 20
If a number is divisible by 2 and 3, it must be divisible by 6.
Q 21
The decimal expansion of an irrational number is non-terminating and non-repeating.
Q 22
Every real number can be written as a fraction.
Q 23
The HCF of two numbers is always one of the numbers.
Q 24
Every terminating decimal is a rational number.
Q 25
The set of rational numbers is closed under subtraction.
Key Takeaways — Real Numbers
Core facts for CBSE Boards & exams
1
Every composite number can be expressed as a unique product of primes (FTA).
2
HCF(a,b) × LCM(a,b) = a × b — only valid for EXACTLY TWO numbers.
3
√2, √3, √5 are irrational — provable by contradiction.
4
A rational number p/q (q≠0, lowest terms) has a terminating decimal iff q = 2ᵛ5ᵐ.
5
Non-terminating, non-recurring decimals are irrational.
6
Euclid's Division Lemma: a = bq + r, 0 ≤ r < b.