class 9 maths chapter 3 world of numbers revision test based on NCERT book Ganita Prakash

Class IX Mathematics Test (30 Marks)

Chapter 3 The World of Numbers (Number Systems)
 Time: 1 Hour
 Maximum Marks: 30

Section A: MCQs (8 × 1 = 8 Marks)

1. Which of the following is an irrational number?
 (a) √25  (b) √36  (c) √7  (d) √49

2. The decimal expansion of a rational number can be:
 (a) Only terminating  (b) Only non-terminating recurring
 (c) Either terminating or non-terminating recurring
 (d) Non-terminating non-recurring

3. Between two distinct rational numbers, there are:
 (a) No rational numbers  (b) One rational number
 (c) Finite rational numbers  (d) Infinitely many rational numbers

4. Which of the following has a terminating decimal expansion?
 (a) 7/15  (b) 3/5  (c) 1/3  (d) 5/11

5. The decimal expansion of √2 is:
 (a) Terminating  (b) Non-terminating recurring
 (c) Non-terminating non-recurring  (d) Integer

6. Which of the following is a rational number?
 (a) π  (b) √10  (c) 0.272727...  (d) √5

7. A rational number between 1/2 and 3/4 is:
 (a) 2/5  (b) 5/8  (c) 4/5  (d) 7/8

8. Which statement is correct?
 (a) Every irrational number is rational.
 (b) Every rational number is an integer.
 (c) Every irrational number is a real number.
 (d) Every real number is irrational.

Section B: Assertion–Reason Questions (2 × 1 = 2 Marks)

For Questions 9–10, choose the correct option:
 (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
 (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
 (c) Assertion (A) is true but Reason (R) is false.
 (d) Assertion (A) is false but Reason (R) is true.

9. Assertion (A): The number 0.6666... is a rational number.
 Reason (R): Every non-terminating recurring decimal is a rational number.

10. Assertion (A): √5 is an irrational number.
 Reason (R): √5 cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.

Section C: Case Study (4 Marks)

11. Riya is playing a number classification game. She is given the numbers:
 √2, 0.75, π, 0.1010010001..., 7/8
 
 (a) Write any two rational numbers from the list. (1)
 (b) Write any one irrational number from the list. (1)
 (c) State whether 0.1010010001... is rational or irrational. Give reason. (1)
 (d) Express 0.75 in the form p/q. (1)

Section D: Competency-Based Questions (16 Marks)

12. Without performing long division, determine whether the decimal expansion of the following numbers is terminating or non-terminating recurring: (2)
 (a) 13/40
 (b) 7/18

13. Find:
 (a) A rational number between 2/5 and 3/5. (1)
 (b) An irrational number between √2 and √3. (1)

14. Prove that √5 is an irrational number. (3)
 
 15. A student claims that all non-terminating decimals are irrational.
 (a) Is the statement correct? (1)
 (b) Justify your answer with one example. (2)

16. Express the following as rational numbers in p/q form: (4)
 (a) 0.12
 (b) 0.

17. Consider the numbers: √3, 1.414, 22/7, √16
 Classify them into rational and irrational numbers. (2)

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Answer Key

MCQs: 1(c), 2(c), 3(d), 4(b), 5(c), 6(c), 7(b), 8(c)

Assertion–Reason: 9(a), 10(a)