JEE Main 20211 Sep, Evening shiftMathematicsHardIntegral Calculus369× since 2002Let Jn,m=∫012xnxm−1dx{J_{n,m}} = \int\limits_0^{{1 \over 2}} {{{{x^n}} \over {{x^m} - 1}}dx}Jn,m=0∫21xm−1xndx, ∀\forall∀ n > m and n, m ∈\in∈ N. Consider a matrix A=[aij]3×3A = {[{a_{ij}}]_{3 \times 3}}A=[aij]3×3 where aij={j6+i,3−ji+3,3,i≤j0,i>j{a_{ij}} = \left\{ {\matrix{ {{j_{6 + i,3}} - {j_{i + 3,3}},} & {i \le j} \cr {0,} & {i > j} \cr } } \right.aij={j6+i,3−ji+3,3,0,i≤ji>j. Then ∣adjA−1∣\left| {adj{A^{ - 1}}} \right|adjA−1 is :AOption A. (15)² ×\times× 2⁴²BOption B. (15)² ×\times× 2³⁴COption C. (105)² ×\times× 2³⁸DOption D. (105)² ×\times× 2³⁶CheckSkip · show solution
