Q74.If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then the value of m + n is equal to
What This Question Tests
The problem requires applying the standard formulas for the variance of the first n natural numbers and the first m even natural numbers, then solving the resulting equations to find m and n, and finally their sum.
Concepts Tested
Formulas Used
Variance of first n natural numbers = (n^2 - 1) / 12
Variance of first m even natural numbers = m^2 - 1 / 3
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📋 Question Details
- Chapter
- Statistics
- Topic
- Variance
- Year
- 2020
- Shift
- 07 Jan Shift 1
- Q Number
- Q74
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 15: Statistics
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Q72.Statement-1 : The variance of first n even natural numbers is n2−14 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 (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true