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Assertion : 113 x 114 = 1112Reason : If a > 0 be a real number and p and q be rational numbers.Then ap x aq = ap + q.10. Assertion : Rational number lying between 14 𝑎𝑛𝑑 12 𝑖𝑠 38.Reason : Rational number lying between two rational numbers x and y is 𝑥+𝑦2 .11. 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 qare integers and q ≠ 0.12. Assertion : 0.329 is a terminating decimal.Reason : A decimal in which a digit or a set of digits is repeated periodically, is called arepeating, or a recurring, decimal.13. 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 therationalising factor of the other.

Question

Assertion : 113 x 114 = 1112Reason : If a > 0 be a real number and p and q be rational numbers.Then ap x aq = ap + q.10. Assertion : Rational number lying between 14 𝑎𝑛𝑑 12 𝑖𝑠 38.Reason : Rational number lying between two rational numbers x and y is 𝑥+𝑦2 .11. 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 qare integers and q ≠ 0.12. Assertion : 0.329 is a terminating decimal.Reason : A decimal in which a digit or a set of digits is repeated periodically, is called arepeating, or a recurring, decimal.13. 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 therationalising factor of the other.

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Solution

Sure, I can do that. Here are the answers to your assertions and reasons:

  1. Assertion: False. Reason: True. The rational number lying between 1/4 and 1/2 is 3/8, not 38. The reason is correct, the number between two rational numbers x and y is indeed (x+y)/2.

  2. Assertion: True. Reason: True. √5 is indeed an irrational number because it cannot be expressed as a ratio of two integers, which is the definition of a rational number.

  3. Assertion: True. Reason: False. 0.329 is indeed a terminating decimal, but the reason given describes a repeating or recurring decimal, not a terminating one.

  4. Assertion: True. Reason: True. The rationalizing factor of 3 + 2√5 is indeed 3 - 2√5. The reason is correct, if the product of two irrational numbers is rational then each one is called the rationalising factor of the other.

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