**Assertion and Reason Questions for Class 9 Maths Chapter 1 Number System**

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

(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.

**Q.1. Assertion:** Rational number lying between 1/4 and 1/2 is 3/8. **Reason:** Rational number lying between two rational numbers x and y is (x+y)/2

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Answer: (c)**Q.2. Assertion:** 0.329 is a terminating decimal. **Reason: **A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring decimal.

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Answer: (b)**Q.3. Assertion: **Rational number lying between two rational numbers x and y is (x+y)/2. **Reason: **There is one rational number lying between any two rational numbers.

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Answer: (c)**Q.4. Assertion: **5 is a rational number. **Reason: **The square roots of all positive integers are irrationals.

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Answer: (c)**Q.5. Assertion: **Sum of two irrational numbers 2 + √3 and 4 + √3 is irrational number. **Reason: **Sum of two irrational numbers is always an irrational number.

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Answer: (c)**Q.6. Assertion: **7^{8} ÷ 7^{4} = 7^{4} **Reason:** If a > 0 be a real number and p and q be rational numbers. Then a^{p} x a^{q} = a^{p+q}

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Answer: (b)**Q.7. Assertion: **√5 is an irrational number. **Reason: **A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q≠0

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Answer: (a)**Q.8. Assertion: **the rationalizing factor of 3+2√5 is 3-2√5. **Reason:** If the product of two irrational numbers is rational then each one is called the rationalizing factor of the other

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Answer: (a)**Q.9. Assertion: **11^{3} x 11^{4} = 11^{12} **Reason:** If a > 0 be a real number and p and q be rational numbers. Then a^{p} x a^{q} = a^{p+q}