JEE Main 2026 — Statistics Question with Solution
JEE Main 2026 (21 January Shift 1)
Question
Let the mean and variance of 7 observations , be 8 and 16 respectively. Two numbers are chosen from one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :
Choose an option
Show full solutionCorrect option: D
Correct answer
D
Step-by-step explanation
Mean = 8 gives .
Variance = 16 gives .
Solving: , (since ).
Set becomes .
Total ways to choose 2 numbers = .
Favorable cases (smaller ): smaller = 1 gives 5 pairs, smaller = 2 gives 4 pairs, smaller = 3 gives 3 pairs.
Total favorable = 12.
Probability .
Variance = 16 gives .
Solving: , (since ).
Set becomes .
Total ways to choose 2 numbers = .
Favorable cases (smaller ): smaller = 1 gives 5 pairs, smaller = 2 gives 4 pairs, smaller = 3 gives 3 pairs.
Total favorable = 12.
Probability .
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This is a previous-year question from JEE Main 2026, covering the Statistics chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.