Real Numbers (10 Mathematics)
Real numbers include all rational and irrational numbers. Understanding properties like divisibility, prime factorization, and the Euclidean algorithm is f
TL;DR: Real numbers include all rational and irrational numbers. Understanding properties like divisibility, prime factorization, and the Euclidean algorithm…
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Real numbers include all rational and irrational numbers. Understanding properties like divisibility, prime factorization, and the Euclidean algorithm is f
Real Numbers MCQs with Answers & Explanations
Q1. Which of the following is an irrational number?
- 0.5
- 0.333...
- √2 ✓ (correct)
- 22/7
Q2. The Euclidean algorithm is used to find:
- Prime factors
- Greatest Common Divisor (GCD) ✓ (correct)
- Least Common Multiple (LCM)
- Square roots
Q3. If HCF(a, b) = 12 and LCM(a, b) = 72, then a × b equals:
- 60
- 144
- 864 ✓ (correct)
- 720
Q4. Which of the following is a prime number?
- 91
- 87
- 97 ✓ (correct)
- 93
Q5. The decimal expansion of a rational number is always:
- Non-terminating
- Terminating or non-terminating repeating ✓ (correct)
- Non-terminating and non-repeating
- Terminating
Q6. By the Fundamental Theorem of Arithmetic, every composite number can be uniquely expressed as:
- Sum of primes
- Product of primes ✓ (correct)
- Difference of squares
- Sum of two squares
Q7. The HCF of 15 and 25 is:
- 5 ✓ (correct)
- 75
- 15
- 25
Q8. If p/q is a rational number in lowest terms, then q must be:
- A multiple of p
- Not equal to 1
- Coprime to p ✓ (correct)
- A perfect square
Q9. The LCM of 12 and 18 is:
- 36 ✓ (correct)
- 6
- 216
- 72
Q10. Which statement is true about irrational numbers?
- They can be expressed as p/q
- Their decimal expansion never terminates or repeats ✓ (correct)
- They are less common than rational numbers
- They cannot be negative
Frequently Asked Questions
What is the relationship between HCF and LCM?
For any two positive integers a and b, their product equals the product of their HCF and LCM: a × b = HCF(a, b) × LCM(a, b). This relationship helps solve many problems involving divisibility.
How do you prove that √2 is irrational?
Assume √2 = p/q in lowest terms. Then 2q² = p², meaning p is even (say p = 2k). Substituting: 2q² = 4k², so q² = 2k², meaning q is also even. This contradicts our assumption that p/q is in lowest terms, so √2 is irrational.
More 10 Mathematics MCQs
- Coordinate Geometry
- Arithmetic Progressions
- Circles
- Surface Areas and Volumes
- Trigonometry (Applications Case Study)
- Probability (Case Study)
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