JEE Main 2023 — Statistics Question with Solution
From: JEE Main 2023 (Online) 12th April Morning Shift
Question
Let the positive numbers and be in a G.P. Let their mean and variance be and respectively, where and are co-prime. If the mean of their reciprocals is and , then is equal to ___________.
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Show full solutionCorrect answer: 186
Correct answer
186
Step-by-step explanation
Since are in geometric progression, we can write :
,
,
,
.
where is the common ratio and = is the first term.
Given that the mean of the series is , we get
Substituting the terms with the values of and gives
Simplifying this gives
From (1) and (2)
From (1)
,
,
,
.
where is the common ratio and = is the first term.
Given that the mean of the series is , we get
Substituting the terms with the values of and gives
Simplifying this gives
From (1) and (2)
From (1)
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