JEE Math Practice Question

Let $${J_{n,m}} = \int\limits_0^{{1 \over 2}} {{{{x^n}} \over {{x^m} - 1}}dx} $$, $$\forall$$ n > m and n, m $$\in$$ N. Consider a matrix $$A = {[{a_{ij}}]_{3 \times 3}}$$ where $${a_{ij}} = \left\{ {\begin{matrix} {{j_{6 + i,3}} - {j_{i + 3,3}},} & {i \le j} \\ {0,} & {i > j} \\ \end{matrix} } \right.$$. Then $$\left| {adj{A^{ - 1}}} \right|$$ is :

1. A.(15)2 $$\times$$ 242
2. B.(15)2 $$\times$$ 234
3. C.(105)2 $$\times$$ 238
4. D.(105)2 $$\times$$ 236