Chapter Exam

Chapter-1 - Real Numbers — Online MCQ Test

Q: What is the name of the theorem that states every composite number can be uniquely expressed as a product of primes?

Answer: B. Fundamental Theorem of Arithmetic — The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of primes, apart from the order of factors.

Q: Numbers having non-terminating, non-repeating decimal expansion are known as:

Answer: C. Irrational numbers — Irrational numbers have non-terminating and non-repeating decimal expansions, which distinguishes them from rational numbers.

Q: Let x = 13/(2² × 5⁴). How many decimal places will x have when expanded as a terminating decimal?

Answer: C. 4 — The number of decimal places in a terminating decimal equals the highest power among 2 and 5 in the denominator. Here max(2, 4) = 4.

Q: If p and q are distinct primes, what is HCF(p², q²)?

Answer: C. 1 — Since p and q are distinct primes, p² = p×p and q² = q×q share no common prime factors. Therefore HCF(p², q²) = 1.

MATHS · Grade 10 · CBSE(NCERT)

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Chapter-1 - Real Numbers — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 10 MATHS — Chapter-1 - Real Numbers, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the name of the theorem that states every composite number can be uniquely expressed as a product of primes?

A. Euclid's Division Lemma
B. Fundamental Theorem of Arithmetic ✓
C. Fundamental Theorem of Algebra
D. Prime Factorization Theorem

Answer: B. Fundamental Theorem of Arithmetic
The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of primes, apart from the order of factors.

Numbers having non-terminating, non-repeating decimal expansion are known as:

A. Rational numbers
B. Natural numbers
C. Irrational numbers ✓
D. Integers

Answer: C. Irrational numbers
Irrational numbers have non-terminating and non-repeating decimal expansions, which distinguishes them from rational numbers.

Let x = 13/(2² × 5⁴). How many decimal places will x have when expanded as a terminating decimal?

A. 2
B. 3
C. 4 ✓
D. 5

Answer: C. 4
The number of decimal places in a terminating decimal equals the highest power among 2 and 5 in the denominator. Here max(2, 4) = 4.

In the proof of irrationality of √2, a contradiction is reached because:

A. 2 cannot be expressed as a fraction
B. Both a and b turn out to be divisible by 2, contradicting the assumption that they are coprime ✓
C. a² cannot equal 2b² for any integers
D. b must equal zero

Answer: B. Both a and b turn out to be divisible by 2, contradicting the assumption that they are coprime
The proof shows that both a and b must be divisible by 2, which contradicts the initial assumption that a/b is in lowest terms (coprime).

If p and q are distinct primes, what is HCF(p², q²)?