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Mathematics

Assertion (A): If x = 9 and y = 2, then xy = yx.

Reason (R): a-n = (1a)n\Big(\dfrac{1}{a}\Big)^n when a is a real positive number and n is a rational number.

  1. Assertion (A) is true, Reason (R) is false.

  2. Assertion (A) is false, Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Indices

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Answer

According to Assertion: If x = 9 and y = 2, then xy = yx.

Taking L.H.S. = xy

= 92

= 81.

Taking R.H.S. = yx

= 29

= 512.

∴ L.H.S. ≠ R.H.S.

So, xy ≠ yx

∴ Assertion (A) is false.

a-n = (1a)n\Big(\dfrac{1}{a}\Big)^n when a is a real positive number and n is a rational number.

This statement is a fundamental property of exponents. It correctly defines how to handle negative exponents. For example, 2-3 = (12)3\Big(\dfrac{1}{2}\Big)^3

∴ Reason (R) is true.

∴ Assertion (A) is false, Reason (R) is true.

Hence, option 2 is the correct option.

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