JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(p\) and \(p+2\) be prime numbers and let \(\Delta=\left|\begin{array}{ccc}p ! & (p+1) ! & (p+2) ! \\ (p+1) ! & (p+2) ! & (p+3) ! \\ (p+2) ! & (p+3) ! & (p+4) !\end{array}\right|\) Then the sum of the maximum values of \(\alpha\) and \(\beta\), such that \(p ^{\alpha}\) and \(( p +2)^{\beta}\) divide \(\Delta\), is \(........\)
- A \(4\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc} P ! & ( P +1) ! & ( P +2) ! \\( P +1) ! & ( P +2) ! & ( P +3) ! \\( P +2) ! & ( P+3) ! & ( P +4) !\end{array}\right|\) \(\Delta= P !( P +1) !( P +2) !\left|\begin{array}{ccc}1 & 1 & 1 \\P +1 & P +2 & P +3 \…
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