JEE Mains · Maths · STD 11 - 13. statistics
If the variance of the first \(n\) natural numbers is \(10\) and the variance of the first m even natural numbers is \(16\), then \(m + n\) is equal to
- A \(16\)
- B \(18\)
- C \(24\)
- D \(22\)
Answer & Solution
Correct Answer
(B) \(18\)
Step-by-step Solution
Detailed explanation
Variance of first 'n' natural numbers \(=\frac{\mathrm{n}^{2}-1}{12}=10\) \(\Rightarrow n=11\) and variance of first 'm' even natural numbers \(=4\left(\frac{\mathrm{m}^{2}-1}{12}\right) \Rightarrow \frac{\mathrm{m}^{2}-1}{3}=16 \Rightarrow \mathrm{m}=7\) \(m+n=18\)
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