We have included 30 MCQ questions for class 9 chapter 1 Chapter 1 Number System. Rational numbers, like 3/4, behave predictably with neat decimal endings. But irrational numbers, such as √2, dance to their own tune, with endless, unpredictable decimals. It might feel tricky at first, but think of it as learning the unique language that numbers speak. Understanding the concepts is crucial for solving tricky questions and I am sure with practice you can excel the Chapter 1.
CBSE Class 9th Maths Important MCQs with Answers from Chapter 1 – Number System
Question 1. Which of the following numbers has a terminating decimal expansion?
a) 7/8
b) 1/3
c) 2/7
d) 5/6
Answer:
a) 7/8 — A number has a terminating decimal expansion if the denominator in its simplest form contains only the prime factors 2 and/or 5. Here, 7/8 = 0.875, which terminates.
Question 2. Which of the following is the sum of a rational and an irrational number?
a) 3 + √2
b) 4 – 3
c) 2 + 5/2
d) 6 + 0.5
Answer:
a) 3 + √2 — The sum of a rational number (3) and an irrational number (√2) is always irrational.
Question 3. What is the square root of 8 simplified in the form of a surd?
a) 4√2
b) 2√2
c) √16
d) √32
Answer:
b) 2√2 — √8 can be simplified as √(4×2) = √4 × √2 = 2√2.
Question 4. How many digits can there be in the repeating block of the decimal expansion of 1/17?
a) 16
b) 17
c) 15
d) 14
Answer:
a) 16 — The maximum number of repeating digits in the decimal expansion of 1/p is p-1, where p is a prime number.
Question 5. What type of number is π?
a) Rational
b) Terminating
c) Non-terminating and repeating
d) Non-terminating and non-repeating
Answer:
d) Non-terminating and non-repeating — π is an irrational number because its decimal expansion is non-terminating and non-repeating.
Question 6. Which of the following operations always results in a rational number?
a) Addition of √3 and √3
b) Multiplication of 2 and √5
c) Subtraction of √2 from √5
d) Division of √2 by √2
Answer:
d) Division of √2 by √2 — Dividing any non-zero irrational number by itself results in 1, which is rational.
Question 7. What is the value of (√2 + √3)(√2 – √3)?
a) 1
b) -1
c) 2
d) -2
Answer:
b) -1 — Using the identity (a + b)(a – b) = a² – b², we get (√2)² – (√3)² = 2 – 3 = -1.
Question 8. Which of the following numbers cannot be represented as a rational number?
a) 0.121212…
b) 1.414213…
c) 0.5
d) -7/2
Answer:
b) 1.414213… — This is √2, which is an irrational number as its decimal expansion is non-terminating and non-repeating.
Question 9. What is the simplified form of √50?
a) 25
b) 5√2
c) 10√2
d) 50
Answer:
b) 5√2 — √50 = √(25×2) = √25 × √2 = 5√2.
Question 10. If x = 2 + √3, what is the value of 1/x?
a) 2 – √3
b) 2 + √3
c) 4 – √3
d) 4 + √3
Answer:
a) 2 – √3 — Rationalize 1/(2+√3) by multiplying numerator and denominator by (2-√3), yielding (2-√3)/(4-3) = 2-√3.
Question 11. Which of the following is an example of a non-terminating repeating decimal?
a) 0.101101110111…
b) 0.666…
c) 3.14159…
d) √7
Answer:
b) 0.666… — A non-terminating repeating decimal repeats a pattern, and 0.666… is equal to 2/3, a rational number.
Question 12. If p is a prime number, which of the following expressions is irrational?
a) √p
b) p/2
c) p²
d) p/p
Answer:
a) √p — The square root of a prime number is irrational because it cannot be expressed as a ratio of two integers.
Question 13. Which of the following expressions simplifies to a rational number?
a) (√3 + 2)(√3 – 2)
b) √5 × √3
c) √7/√2
d) 1/√2
Answer:
a) (√3 + 2)(√3 – 2) — Using the identity (a + b)(a – b) = a² – b², we get (√3)² – 2² = 3 – 4 = -1, which is rational.
Question 14. Which of the following numbers lies between √2 and √3?
a) 1.7
b) 1.6
c) 1.5
d) 1.4
Answer:
a) 1.7 — √2 ≈ 1.414 and √3 ≈ 1.732, so 1.7 lies between these two values.
Question 15. Which of the following is true about the sum of √2 and √8?
a) It is rational.
b) It is irrational.
c) It equals 2√2.
d) It equals √10.
Answer:
c) It equals 2√2 — √8 can be simplified as 2√2, so √2 + √8 = √2 + 2√2 = 2√2.
Question 16. How many distinct irrational numbers exist between 1 and 2?
a) None
b) One
c) Infinite
d) Five
Answer:
c) Infinite — Between any two real numbers, there are infinitely many irrational numbers.
Question 17. Which of the following operations always produces an irrational result?
a) √5 × √5
b) √5 × 2
c) √5 + √5
d) √5 + √7
Answer:
d) √5 + √7 — Adding two different square roots typically results in an irrational number.
Question 18. Which of the following represents the decimal expansion of a rational number?
a) 0.101101110111…
b) 0.123123123…
c) 3.141592653…
d) √3
Answer:
b) 0.123123123… — This is a non-terminating repeating decimal, which represents a rational number.
Question 19. What is the simplified value of (2 + √3)(2 – √3)?
a) 1
b) 4 – √3
c) √3
d) 1/2
Answer:
a) 1 — Using the identity (a + b)(a – b) = a² – b², we get (2)² – (√3)² = 4 – 3 = 1.
Question 20. Which of the following is irrational?
a) 22/7
b) 3.75
c) 1.414213…
d) 0.25
Answer:
c) 1.414213… — This is √2, an irrational number with a non-terminating, non-repeating decimal expansion.
Question 21. What is the value of (√7 + 2)(√7 – 2)?
a) 3
b) 5
c) 7
d) -5
Answer:
d) -5 — Using the identity (a + b)(a – b) = a² – b², we get (√7)² – (2)² = 7 – 4 = -5.
Question 22. Which of the following cannot be expressed as a fraction p/q?
a) 1.75
b) √10
c) 0.333…
d) 3.5
Answer:
b) √10 — √10 is irrational because it cannot be expressed as a fraction.
Question 23. What is the value of (√3 + √5)²?
a) 8 + 2√15
b) 8 – 2√15
c) 15 + 2√3
d) 15 – 2√3
Answer:
a) 8 + 2√15 — Using (a + b)² = a² + 2ab + b², we get (√3)² + 2(√3)(√5) + (√5)² = 3 + 10 + 2√15 = 8 + 2√15.
Question 24. If a rational number is divided by an irrational number, the result is:
a) Always rational
b) Always irrational
c) Rational or irrational
d) Undefined
Answer:
c) Rational or irrational — It depends on the specific numbers. For example, (2/√2) = √2 (irrational), but 0/√2 = 0 (rational).
Question 25. What is the decimal representation of 2/7?
a) 0.285714285714…
b) 0.142857142857…
c) 0.333…
d) 0.5
Answer:
a) 0.285714285714… — This is a non-terminating repeating decimal expansion, which is rational.
Question 26. What is the result of rationalizing the denominator of 1/(√3 – 1)?
a) (√3 + 1)/2
b) (√3 – 1)/2
c) 2/(√3 – 1)
d) 2/(√3 + 1)
Answer:
a) (√3 + 1)/2 — Multiply numerator and denominator by (√3 + 1), using (a – b)(a + b) = a² – b².
Question 27. Which of the following identities is valid for square roots?
a) √(a + b) = √a + √b
b) √(a – b) = √a – √b
c) √(ab) = √a × √b
d) √(a/b) = √a – √b
Answer:
c) √(ab) = √a × √b — This property holds for all positive real numbers a and b.
Question 28. What is the simplified value of 1/(√2 + √3)?
a) √2 – √3
b) (√2 – √3)/1
c) (√2 – √3)/2
d) (√2 – √3)/5
Answer:
c) (√2 – √3)/2 — Multiply numerator and denominator by (√2 – √3) to rationalize the denominator.
Question 29. Which of the following is an irrational number?
a) (√5 + 1)²
b) (√2 + √3) × (√2 – √3)
c) (√7 + √2)
d) (√3)²
Answer:
c) (√7 + √2) — The sum of two different irrational numbers is typically irrational unless they simplify to a rational number.
Question 30. How many irrational numbers are there between 0 and 1?
a) None
b) Finite
c) Infinite
d) Two
Answer:
c) Infinite — There are infinitely many irrational numbers between any two real numbers, including 0 and 1.
