MathsJEE Main 24 Jan 2026, Shift 2·Q1·MCQ·Moderate

Matrices & Determinants · Adjoint and determinant properties

Let

f(x) = \displaystyle\int\dfrac{7x^{10} + 9x^8}{(1 + x^2 + 2x^9)^2}\,dx

,

x > 0

,

\displaystyle\lim_{x\to0} f(x) = 0

and

f(1) = \dfrac14

. If

A = \begin{bmatrix} 0 & 0 & 1\\[2pt] \dfrac14 & f'(1) & 1\\[2pt] \alpha^2 & 4 & 1\end{bmatrix}

and

B = \operatorname{adj}(\operatorname{adj} A)

be such that

\lvert B\rvert = 81

, then

\alpha^2

is equal to

(1)2
(2)3
(3)1
(4)4

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