JEE Main 2021 — Probability Question with Solution
From: JEE Main 2021 (Online) 22th July Evening Shift
Question
Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 2 matrices. The probability that such formed matrix have all different entries and are non-singular, is :
Choose an option
Show full solutionCorrect option: D
Correct answer
D
Step-by-step explanation
A = \left| {\matrix{
a & b \cr
c & d \cr
} } \right|
| A | = ad bc
Total case = 64
For non-singular matrix | A | 0 ad bc 0
ad bc
And a, b, c, d are all different numbers in the set {1, 2, 3, 4, 5, 6}
Now for ad = bc
(i) 6 1 = 2 3
8 each cases
(ii) 6 2 = 3 4
8 such cases
favourable cases
=
required probability
| A | = ad bc
Total case = 64
For non-singular matrix | A | 0 ad bc 0
ad bc
And a, b, c, d are all different numbers in the set {1, 2, 3, 4, 5, 6}
Now for ad = bc
(i) 6 1 = 2 3
8 each cases
(ii) 6 2 = 3 4
8 such cases
favourable cases
=
required probability
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This is a previous-year question from JEE Main 2021, covering the Probability 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.