Here are 50 MCQs from Class 10 Maths – Chapter 1 (Real Numbers) 📘
🔢 Real Numbers MCQs (1–50)
Basic Concepts
Natural numbers include:
A) 0
B) 1
C) -1
D) Fractions
✅ Ans: B
Whole numbers include:
A) 0
B) -1
C) 1/2
D) √2
✅ Ans: A
Integers include:
A) Only positive
B) Only negative
C) Both positive & negative
D) Only fractions
✅ Ans: C
Rational number is of form:
A) p/q (q ≠ 0)
B) √2
C) π
D) ∞
✅ Ans: A
Irrational numbers include:
A) 1/2
B) 0.5
C) √3
D) 2
✅ Ans: C
Euclid’s Division Lemma
Euclid’s Division Lemma states:
A) a = bq + r
B) a = b + q
C) a = br
D) a = r
✅ Ans: A
In a = bq + r, r is:
A) Quotient
B) Remainder
C) Divisor
D) Dividend
✅ Ans: B
Condition for remainder r:
A) 0 ≤ r < b
B) r > b
C) r = b
D) r < 0
✅ Ans: A
If r = 0, numbers are:
A) Co-prime
B) Exactly divisible
C) Prime
D) Irrational
✅ Ans: B
Euclid’s algorithm is used to find:
A) LCM
B) HCF
C) Sum
D) Product
✅ Ans: B
HCF & LCM
HCF of 12 and 15 is:
A) 3
B) 5
C) 6
D) 15
✅ Ans: A
LCM of 4 and 6 is:
A) 10
B) 12
C) 24
D) 6
✅ Ans: B
Product of two numbers =
A) HCF + LCM
B) HCF × LCM
C) HCF – LCM
D) None
✅ Ans: B
If HCF = 1, numbers are:
A) Even
B) Prime
C) Co-prime
D) Odd
✅ Ans: C
HCF always divides:
A) Sum
B) Difference
C) Both numbers
D) None
✅ Ans: C
Prime Numbers
Prime numbers have:
A) 1 factor
B) 2 factors
C) 3 factors
D) Many
✅ Ans: B
Smallest prime number:
A) 1
B) 2
C) 3
D) 0
✅ Ans: B
1 is:
A) Prime
B) Composite
C) Neither
D) Even
✅ Ans: C
Even prime number is:
A) 2
B) 4
C) 6
D) 8
✅ Ans: A
Fundamental Theorem of Arithmetic deals with:
A) Factors
B) Prime factorization
C) Addition
D) Subtraction
✅ Ans: B
Prime Factorization
Every composite number can be expressed as:
A) Product of primes
B) Sum
C) Difference
D) Square
✅ Ans: A
Prime factorization of 24:
A) 2³ × 3
B) 2² × 6
C) 4 × 6
D) 12 × 2
✅ Ans: A
Unique factorization means:
A) Same factors always
B) One way only
C) Many ways
D) None
✅ Ans: B
LCM using primes is:
A) Lowest power
B) Highest power
C) Sum
D) Difference
✅ Ans: B
HCF using primes is:
A) Lowest power
B) Highest power
C) Sum
D) Difference
✅ Ans: A
Decimal Expansion
1/2 =
A) Terminating
B) Non-terminating
C) Irrational
D) Infinite
✅ Ans: A
1/3 =
A) Terminating
B) Non-terminating repeating
C) Irrational
D) Whole
✅ Ans: B
Denominator form for terminating decimal:
A) 2ⁿ5ᵐ
B) 3ⁿ
C) 7ⁿ
D) 11ⁿ
✅ Ans: A
7/8 is:
A) Terminating
B) Non-terminating
C) Irrational
D) None
✅ Ans: A
2/11 is:
A) Terminating
B) Repeating
C) Irrational
D) Whole
✅ Ans: B
Application & Mixed
HCF of co-prime numbers:
A) 0
B) 1
C) 2
D) Same
✅ Ans: B
LCM of co-prime numbers:
A) Sum
B) Product
C) Difference
D) 1
✅ Ans: B
If one number is 1, HCF is:
A) 1
B) 0
C) Same
D) None
✅ Ans: A
If numbers are equal, HCF =
A) Same number
B) 1
C) 0
D) Double
✅ Ans: A
If HCF = LCM, numbers are:
A) Equal
B) Prime
C) Even
D) Odd
✅ Ans: A
More Practice
LCM ≥ HCF always:
A) True
B) False
C) Sometimes
D) None
✅ Ans: A
Product = 180, HCF = 6 → LCM =
A) 30
B) 36
C) 60
D) 90
✅ Ans: A
HCF of 18 & 24:
A) 6
B) 12
C) 18
D) 3
✅ Ans: A
0 is:
A) Natural
B) Whole
C) Integer
D) All
✅ Ans: D
Negative numbers are:
A) Natural
B) Whole
C) Integers
D) Rational only
✅ Ans: C
Final Set
Rational numbers are:
A) Finite or repeating
B) Only finite
C) Only repeating
D) None
✅ Ans: A
√5 is:
A) Rational
B) Irrational
C) Whole
D) Integer
✅ Ans: B
π is:
A) Rational
B) Irrational
C) Whole
D) Natural
✅ Ans: B
Decimal of irrational is:
A) Terminating
B) Non-terminating non-repeating
C) Repeating
D) Whole
✅ Ans: B
0.125 is:
A) Irrational
B) Rational
C) Whole
D) Natural
✅ Ans: B
Prime factorization of 36:
A) 2² × 3²
B) 6 × 6
C) 4 × 9
D) All
✅ Ans: A
HCF of 8 & 9:
A) 1
B) 2
C) 3
D) 9
✅ Ans: A
LCM of 8 & 9:
A) 72
B) 18
C) 36
D) 9
✅ Ans: A
1/7 is:
A) Terminating
B) Repeating
C) Irrational
D) Whole
✅ Ans: B
Real numbers include:
A) Rational
B) Irrational
C) Both
D) None
✅ Ans:
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