KVPY Sample Paper KVPY Stream-SX Model Paper-8

If \[A={{[aij]}_{4\times 4}}\] such that \[aij=\left\{ \begin{matrix}    2, & when\,\,i=j \\    0, & when\,\,i\ne j \\ \end{matrix} \right.,\] the\[\left\{ \frac{\det \,\,(adj\,\,(adj\,A))}{7} \right\}\] is (where {.} represents fractional pan function)-

A) 1/7

B) 2/7

C) 3/7

D) None of these

Correct Answer: A

Solution :

\[|\,A\,|={{2}^{4}},|adj.\,\,(adj\,\,A)|\,={{({{2}^{4}})}^{9}}={{2}^{36}}\]

=\[\left\{ \frac{\det (adj.(adjA))}{7} \right\}=\left\{ \frac{{{2}^{36}}}{7} \right\}\]

\[=\left\{ \frac{{{8}^{12}}}{7} \right\}=\left\{ \frac{{{(7+1)}^{12}}}{7} \right\}=\frac{1}{7}\]