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DIRECTIONS: This question contains two statements: statement-1 (Assertion) and statement-2 (Reason). This question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice. Statement-1: The variance of first n even natural numbers is n^2 - 1 / 4. Statement-2: The sum of first n natural numbers is n(n+1)/2 and the sum of squares of first n natural numbers is n(n+1)(2n+1)/6.
- Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
- Statement-1 is true, Statement-2 is false.
- Statement-1 is false, Statement-2 is true.
- Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
Correct answer: Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1.
Solution
Statement-1 accurately describes the variance of the first n even natural numbers, while Statement-2 correctly provides formulas for the sum and sum of squares of the first n natural numbers. However, the reasoning in Statement-2 does not directly explain the calculation of variance in Statement-1, making it a separate mathematical fact.
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