Let f(x)=∫(7x¹⁰+9x⁸)/((1+x²+2x⁹)²)dx, x>0, lim x→0 f(x)=0 and f(1)=1/4. If A= 0 0 1 1/4 f'(1) 1 α² 4 1 and B=adj(adj A) be such that |B|=81, then α² is equal to

Matrices and Determinants: JEE Main 2026 Mathematics question

JEE Main 2026 · 24 Jan, Evening shift · Q17

JEE Main 202624 Jan, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

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

x>0

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

and

f(1)=\frac14

. If

A=\begin{bmatrix}0&0&1\\ \frac14&f'(1)&1\\ \alpha^2&4&1\end{bmatrix}

and

B=adj(adj\,A)

be such that

|B|=81

, then

\alpha^2

is equal to

JEE Main 2026 · 24 Jan, Evening shift · Q17

JEE Main 202624 Jan, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

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

x>0

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

and

f(1)=\frac14

. If

A=\begin{bmatrix}0&0&1\\ \frac14&f'(1)&1\\ \alpha^2&4&1\end{bmatrix}

and

B=adj(adj\,A)

be such that

|B|=81

, then

\alpha^2

is equal to