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Mathematics

Assertion (A): -10 + π is an irrational number.

Reason (R): Sum of a non-zero rational number and an irrational number is an irrational 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).

Rational Numbers

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Answer

Sum of a non-zero rational number and an irrational number is always an irrational number.

This is a fundamental property of irrational and rational numbers.

∴ Reason (R) is true.

π is an irrational number, -10 is a rational number.

So, their sum -10 + π, will be an irrational number.

∴ Assertion (A) is true.

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

Hence, option 3 is the correct option.

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