JEE Mains · Maths · STD 12 - 13. probability
Four dice are thrown simultaneously and the numbers shown on these dice are recorded in \(2 \times 2\) matrices. The probability that such formed matrices have all different entries and are nonsingular, is :
- A \(\frac{23}{81}\)
- B \(\frac{22}{81}\)
- C \(\frac{45}{162}\)
- D \(\frac{43}{162}\)
Answer & Solution
Correct Answer
(D) \(\frac{43}{162}\)
Step-by-step Solution
Detailed explanation
\(A=\left|\begin{array}{ll} a & b \\ c & d \end{array}\right| \quad|A|=a d-b c\) \(\text { Total case }=6^{4}\) For non-singular matrix \(|\mathrm{A}| \neq 0 \Rightarrow \mathrm{ad}-\mathrm{bc} \neq 0\) \(\Rightarrow \mathrm{ad} \neq \mathrm{bc}\) And…
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