Class X Math - Real Numbers (Set 1)

 

Class X Math - Real Numbers (Set 1)

Class X Mathematics – Chapter 1: Real Numbers (Set 1)

1. The HCF of 60 and 72 is:
A. 6
B. 12
C. 18
D. 24
Answer: B. 12
Explanation: 12 is the highest number that divides both 60 and 72.
2. Euclid’s Division Lemma is used to find:
A. Prime numbers
B. LCM
C. HCF
D. Composite numbers
Answer: C. HCF
Explanation: Euclid’s Division Lemma is used repeatedly to compute HCF.
3. The decimal expansion of 1/3 is:
A. Terminating
B. Repeating
C. Non-repeating
D. Finite
Answer: B. Repeating
Explanation: 1/3 = 0.333... which repeats forever.
4. Which of the following is an irrational number?
A. 22/7
B. 3.1416
C. √2
D. 0.25
Answer: C. √2
Explanation: √2 cannot be expressed as a ratio of two integers.
5. If p and q are two integers with q ≠ 0, then p/q is:
A. Rational
B. Irrational
C. Integer
D. Real
Answer: A. Rational
Explanation: A rational number is defined as p/q where p and q are integers and q ≠ 0.
6. Which number has a terminating decimal expansion?
A. 1/7
B. 1/3
C. 3/8
D. 2/11
Answer: C. 3/8
Explanation: Denominator has factors of only 2 and/or 5 → terminating.
7. Every composite number has:
A. No factor
B. Only 2 factors
C. More than 2 factors
D. Only 1 factor
Answer: C. More than 2 factors
Explanation: Composite numbers have more than 2 distinct positive factors.
8. The Fundamental Theorem of Arithmetic states:
A. Every number has infinite factors
B. Every composite number has a unique prime factorization
C. Every prime number is even
D. None of these
Answer: B. Every composite number has a unique prime factorization
Explanation: This is the core of the Fundamental Theorem of Arithmetic.
9. LCM of two co-prime numbers is:
A. Their product
B. Their sum
C. Their difference
D. Always 1
Answer: A. Their product
Explanation: If two numbers are co-prime, LCM × HCF = Product; HCF = 1.
10. Which of these numbers is not a rational number?
A. 5
B. 0
C. √5
D. –3/4
Answer: C. √5
Explanation: √5 is irrational since it cannot be expressed as a fraction.

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