TS EAMCET · Maths · Statistics
If \(S_1\) and \(S_2\) are the variances of the first \(2 k\) and \(k(k>1)\) natural numbers respectively, then \(\left(S_1 / S_2\right)\) lies in the interval
- A \([4, \infty)\)
- B \((1,4]\)
- C \((4,5]\)
- D \([7, \infty)\)
Answer & Solution
Correct Answer
(B) \((1,4]\)
Step-by-step Solution
Detailed explanation
The variance of first \(2 k\) natural numbers \(S_1=\frac{2 k(2 k+1)(4 k+1)}{6 \times 2 k}-\left(\frac{2 k(2 k+1)}{2 \times 2 k}\right)^2\) \(=(2 k+1)\left[\frac{4 k+1}{6}-\frac{2 k+1}{4}\right]\) \(=\frac{2 k+1}{12}[8 k+2-6 k-3]=\frac{4 k^2-1}{12}\) and variance of first \(k\)…
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