Question

Assertion (A): The mean of x₁, x₂ and x₃ is m. Then the value of (x₁ − m) + (x₂ − m) + (x₃ − m) = 0.

Reason (R): x₁ + x₂ + x₃ = 3m ⇒ (x₁ − m) + (x₂ − m) + (x₃ − m) = (x₁ + x₂ + x₃) − 3m.

पर्याय

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

The mean of x₁, x₂ and x₃ being m indicates that their sum equals 3m by definition. Expanding the expression in the assertion results in (x₁ + x₂ + x₃) − 3m, and substituting 3m into this expression yields 3m − 3m = 0, proving that Assertion (A) is true. Reason (R) accurately outlines this exact algebraic expansion and substitution, making it the correct explanation for Assertion (A).