Weekly chapter test: CBSE Class 9

1. If we change the condition in the definition of rational numbers from 'q ≠ 0' to 'q can be any integer', what problem would arise?

• A. All numbers would become irrational
• B. Division by zero would be allowed, which is undefined
• C. Negative fractions would not exist
• D. Only whole numbers would be rational

2. Which of the following is an irrational number?

• A. √49
• B. 0.125
• C. √11
• D. 22/7

3. If √3 is irrational, what can be said about 5 + √3?

• A. It is rational because 5 is a whole number
• B. It is irrational because the sum of a rational and irrational is irrational
• C. It is an integer
• D. It cannot be determined

4. Prove by contradiction: √2 is irrational. In this proof, if we assume √2 = p/q in lowest terms and reach p² = 2q², what do we conclude first?

• A. q is divisible by 2
• B. p is divisible by 2
• C. p and q are both odd
• D. p/q is already in lowest terms

5. Ravi claims that the number -12 is a rational number. Which reasoning correctly supports his claim?

• A. -12 can be written as -12/1, which is of the form p/q
• B. -12 has a non-terminating decimal expansion
• C. -12 is a counting number
• D. -12 cannot be placed on a number line

6. A student says √36 is irrational because square roots are irrational. Why is this reasoning flawed?

• A. Square roots are always rational
• B. 36 is a perfect square, so √36 = 6, which is rational
• C. Only square roots of odd numbers are irrational
• D. √36 equals 18, which is rational

7. What is the sum of the rational number 2/3 and the irrational number √5?

• A. A rational number
• B. An irrational number
• C. An integer
• D. Cannot be determined

8. Rahul claims that 0.5 is irrational because it has a decimal point. What is wrong with his reasoning?

• A. Numbers with decimal points are always irrational
• B. 0.5 terminates, so it can be written as 1/2, making it rational
• C. 0.5 is neither rational nor irrational
• D. Only repeating decimals are rational

9. Which statement correctly describes the relationship between number sets?

• A. Every rational number is an integer
• B. Every integer is a natural number
• C. Every whole number is a rational number
• D. Every real number is a rational number

10. Meera converts 0.777... to a fraction and gets 7/9. If she instead had 0.0777..., what would change in her method?

• A. She would multiply by 100 instead of 10
• B. She would still multiply by 10, but the result would be 7/90
• C. The decimal cannot be converted to a fraction
• D. The answer would remain 7/9