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Matrices and Determinants question

2022 · 29 Jul · Shift 1 · Q45

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JEE Main
Mathematics
Matrices and Determinants
2022 · 29 Jul · Shift 1 · Q45

Matrices and Determinants question

2022 · 29 Jul · Shift 1 · Q45

JEE MainMathematicsMatrices and DeterminantsNumerical+4 / −1

Let p and p + 2 be prime numbers and let

\Delta=\left|\begin{array}{ccc} \mathrm{p} ! & (\mathrm{p}+1) ! & (\mathrm{p}+2) ! \\ (\mathrm{p}+1) ! & (\mathrm{p}+2) ! & (\mathrm{p}+3) ! \\ (\mathrm{p}+2) ! & (\mathrm{p}+3) ! & (\mathrm{p}+4) ! \end{array}\right|

Then the sum of the maximum values of

\alpha

and

\beta

, such that

\mathrm{p}^{\alpha}

and

(\mathrm{p}+2)^{\beta}

divide

\Delta

, is

\underline{\hspace{2cm}}

.

Numerical answer

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