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NCERT Class 10 Mathematics – Chapter 1: Real Numbers
Board Exam 2026 focused online test based strictly on NCERT textbook.
- Euclid’s Division Lemma: a = bq + r, 0 ≤ r < b
- HCF can be found using Euclid’s Division Algorithm
- Fundamental Theorem of Arithmetic ensures unique prime factorisation
- Rational numbers have terminating or non-terminating recurring decimals
- Irrational numbers have non-terminating, non-repeating decimals
Q1. Euclid’s Division Lemma states that for given integers a and b, there exist:
q and r such that a = bq + r, 0 ≤ r < b
q and r such that b = aq + r
only quotient q
only remainder r
As per NCERT, Euclid’s Division Lemma: a = bq + r, where 0 ≤ r < b.
Q2. Which method is used to find HCF of two positive integers?
Prime factorisation only
Euclid’s Division Algorithm
Estimation
LCM method
NCERT uses Euclid’s Division Algorithm for HCF.
Q3. The theorem that guarantees unique prime factorisation of every integer > 1 is:
Euclid’s Lemma
Division Algorithm
Fundamental Theorem of Arithmetic
Remainder Theorem
Fundamental Theorem of Arithmetic ensures uniqueness.
Q4. Which of the following is a composite number?
2
3
5
4
4 has more than two factors.
Q5. HCF of 12 and 18 is:
2
3
6
12
Using prime factors, HCF = 6.
Q6. If a and b are co-prime, then their HCF is:
2
1
b
a
Co-prime numbers have HCF 1.
Q7. The relation between HCF and LCM of two positive integers a and b is:
HCF × LCM = a × b
HCF + LCM = a + b
HCF = a × b
LCM = a + b
NCERT relation: HCF × LCM = product of numbers.
Q8. Which of the following has a terminating decimal expansion?
1/3
1/8
2/7
5/6
1/8 = 0.125 (terminating).
Q9. Which of the following is irrational?
0.25
1/7
√2
3/5
√2 is irrational.
Q10. The decimal expansion of a rational number is non-terminating recurring if the denominator has prime factors:
Other than 2 and 5
Only 2
Only 5
Only 2 and 5
Other primes cause recurring decimals.
Q11. Which is the smallest composite number?
1
2
3
4
4 is the smallest composite.
Q12. Which of the following is a rational number?
√5
0.375
π
√3
0.375 is rational.
Q13. Euclid’s Division Algorithm is based on:
Euclid’s Division Lemma
Prime factorisation
LCM method
Estimation
Algorithm uses the lemma repeatedly.
Q14. HCF of 16 and 24 is:
4
6
8
12
Common factors give HCF 8.
Q15. LCM of 4 and 6 is:
6
12
24
4
LCM = 12.
Q16. Which of the following statements is true?
Every integer greater than 1 is either prime or composite
1 is prime
0 is prime
All numbers are composite
NCERT definition holds.
Q17. The decimal expansion of 1/40 is:
0.025
0.0025
0.00025
0.025
1/40 = 0.025.
Q18. Which pair is co-prime?
8 and 12
9 and 28
10 and 20
14 and 21
9 and 28 share no common factor.
Q19. The prime factorisation of 36 is:
2×18
3×12
2²×3²
6×6
36 = 2²×3².
Q20. Which of the following numbers is irrational?
√5
0.2
7/8
1.75
√5 is irrational.
Q21. If HCF(a,b)=1, then a and b are:
Equal
Co-prime
Composite
Even
Definition of co-prime.
Q22. Which of the following is a terminating decimal?
2/7
5/12
7/9
3/8
3/8 terminates.
Q23. HCF of 15 and 20 is:
5
10
15
20
Common highest factor is 5.
Q24. LCM of 9 and 6 is:
9
12
18
36
LCM = 18.
Q25. Which of the following is not a rational number?
0
√7
-3/5
1.25
√7 is irrational.
Q26. The decimal expansion of 7/125 is:
0.056
0.56
0.0056
0.00056
7/125 = 0.056.
Q27. Which statement is correct?
All irrational numbers are integers
All integers are irrational
All rational numbers are integers
Every integer is a rational number
Integers can be written as p/q.
Q28. Which of the following is a non-terminating recurring decimal?
1/8
5/16
1/3
7/40
1/3 = 0.333…
Q29. HCF of two prime numbers is:
The product of primes
1
The larger prime
The smaller prime
Distinct primes are co-prime.
Q30. The LCM of two co-prime numbers is:
Their product
1
Their sum
Their difference
If HCF=1, LCM=product.
Q31. Which of the following is an irrational number?
0.125
5/9
√3
-2
√3 is irrational.
Q32. Prime factorisation of 72 is:
2×36
2³×3²
6×12
8×9
72 = 2³×3².
Q33. Which of the following numbers is rational?
-7/11
√11
π
√10
-7/11 is rational.
Q34. The decimal expansion of 5/2 is:
0.25
2.25
0.5
2.5
5/2 = 2.5.
Q35. A number with non-terminating non-repeating decimal expansion is:
Rational
Irrational
Integer
Whole
Definition of irrational.
Q36. HCF of 9 and 27 is:
9
3
27
1
Common highest factor is 9.
Q37. LCM of 5 and 7 is:
7
12
35
14
LCM = 35.
Q38. Which of the following is a whole number?
-1
0
-5
-2
Whole numbers include 0.
Q39. The number of prime factors of 30 is:
3
2
4
1
30 = 2×3×5.
Q40. Which of the following statements is false?
All integers are rational
All whole numbers are integers
All natural numbers are whole numbers
All rational numbers are integers
Rational numbers include fractions.
Q41. HCF of 14 and 21 is:
14
7
21
3
Common factor is 7.
Q42. LCM of 8 and 12 is:
24
12
48
96
LCM = 24.
Q43. Which of the following is an integer?
3/4
-1/2
-3
0.5
-3 is an integer.
Q44. The decimal expansion of 1/3 is:
0.3
0.333…
0.03
3.33
It is recurring.
Q45. Which of the following is a natural number?
1
0
-1
-5
Natural numbers start from 1.
Q46. The HCF of two consecutive natural numbers is:
2
The larger number
The smaller number
1
Consecutive numbers are co-prime.
Q47. The LCM of two consecutive natural numbers is:
1
Their product
Their sum
Their difference
Co-prime consecutive numbers.
Q48. Which of the following numbers is whole but not natural?
0
1
2
3
0 is whole but not natural.
Q49. The number √49 is:
Irrational
Prime
Rational
Negative
√49 = 7 (rational).
Q50. Which of the following best describes real numbers?
Only natural numbers
All rational and irrational numbers
Only integers
Only fractions
Real numbers include rational and irrational.
Your Score: 0 / 50
📘 NCERT Class 10 Maths – Chapter-wise Online Tests
- Chapter 1: Real Numbers – Online Test
- Chapter 2: Polynomials – Online Test
- Chapter 3: Pair of Linear Equations in Two Variables – Online Test
- Chapter 4: Quadratic Equations – Online Test
- Chapter 5: Arithmetic Progressions – Online Test
- Chapter 6: Triangles – Online Test
- Chapter 7: Coordinate Geometry – Online Test
- Chapter 8: Introduction to Trigonometry – Online Test
- Chapter 9: Applications of Trigonometry – Online Test
- Chapter 10: Circles – Online Test
- Chapter 11: Areas Related to Circles – Online Test
- Chapter 12: Surface Areas and Volumes – Online Test
- Chapter 13: Statistics – Online Test
- Chapter 14: Probability – Online Test
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