JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

Let

{J_{n,\,\,m}} = \int\limits_0^{\frac{1}{2}} {\frac{{{x^n}}}{{{x^m} - 1}}} dx,\,\forall n > m\mathrm{ }\,\,\mathrm{and}\,\,n,\,\,m \in N.

Consider a matrix

A = {[{a_{ij}}]_{3 \times 3}}

where

{a_{ij}} = \left\{ {\begin{array}{cccccccccccccccccccc} {{J_{6 + i,3}} - {J_{i + 3,3}}}&{i \le j}\\ {0,}&{i > j} \end{array}} \right.

Then,

|\mathrm{adj }\,\,{\mathrm{A}^{ - 1}}|

View answer and explanation

Correct option: C

{(105)^2} \times {2^{38}}

The correct answer is D (

{(105)^2} \times {2^{36}}

) after evaluating the determinant of the adjoint of the inverse of matrix A, which involves integral calculations and properties of determinants.

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