Chapter-1 - Real Numbers — Online MCQ Test
MATHS · Grade 10 · CBSE(NCERT)
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This chapter covers: First Chapter.
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Chapter-1 - Real Numbers — Important Questions & Answers
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.
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.
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.
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).
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)?
- A. pq
- B. p²q²
- C. 1
- D. p²
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.
Since p and q are distinct primes, p² = p×p and q² = q×q share no common prime factors. Therefore HCF(p², q²) = 1.