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.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
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.
Related Questions
Consider the following two statements:
Statement 1: 2m x 3n = (2 + 3)m + n, where m, n are positive integers.
Statement 2: If a is a rational number, and m, n are integers, then am.an = am + n
Which of the following is valid?
Both the Statements are true.
Both the Statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Assertion (A): All surds are irrational numbers.
Reason (R): All irrational numbers are surds.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).