, short answer questions, and concept-based problems from topics like real numbers, rational and irrational numbers, terminating and non-terminating decimals, and laws of exponents. Each mock test provides real-time scoring, detailed solutions, and performance analysis to help students identify their strengths and weaknesses. Take unlimited free tests, improve your accuracy, and gain confidence in the Number System chapter of Class 9 Mathematics. Perfect for exam revision, homework help, and self-assessment.

1. A rational number between  and  is

 
 
 
 

2. Value of  is

 
 
 
 

3. Simplified value of  is

 
 
 
 

4. An irrational number lying between the numbers 0.401001000100001… and 0.404004000400004… is

 
 
 
 

5. Value of is

 
 
 
 

6.

 
 
 
 

7. On simplifying (3 + ) (3 − ), we get

 
 
 
 

8.

The value of , where  = 3.162 is

 
 
 
 

9.

 
 
 
 

10. Let x and y be rational and irrational number, respectively. Then x + y is necessarily

 
 
 
 

11. Which of the following is equal to x?

 
 
 
 

12. On simplifying 83 ⋅ 24, we get

 
 
 
 

13.   is equal to

 
 
 
 

14.  can be written as

 
 
 
 

15. On simplifying , we get

 
 
 
 

16. On simplifying  we get

 
 
 
 

17. The value of x, if  = 5, is

 
 
 
 

18.   is equal to

 
 
 
 

19. The simplified form of  is

 
 
 
 

20. Value of (256)0.16 × (256)0.09 is

 
 
 
 

21.  is equal to

 
 
 
 

22. Simplified form of  is

 
 
 
 

23.

 On dividing  by , we get

 
 
 
 

24. Value of  is

 
 
 
 

25.

It is given that m and n are two natural numbers such that mn = 32. The value of nmn is equal to
 
 
 
 

26. Direction: In the following questions a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion (A): Sum of two irrational numbers  is rational number.
Reason (R): Sum of two irrational numbers can be rational/an irrational number.

 
 
 
 

27. The number 1.010010001 …… is

 
 
 
 

28. Direction: In the following questions a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

Assertion (A): 0.189 is a terminating decimal.
Reason (R): A decimal in which a digit or set of digits is repeated periodically, is called a repeating or recurring decimal.

 
 
 
 

29. To rationalise the denominator of , we multiply and divide by

 
 
 
 

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