Let f ( x ) = 7 x 10 + 9 x 8 ( 1 + x 2 + 2 x 9 ) 2 d x , x 0 , lim x 0 f ( x ) = 0 and f ( 1 ) = 1 4 . If A = [ 0 0 1 1 4 f ( 1 ) 1 2 4 1 ] and B = adj ( adj A ) be such that | B | = 81 , then 2 is equal to [2026]

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Solution

Q.
Let $f (x) = \int \frac{7 x^{10} + 9 x^{8}}{{(1 + x^{2} + 2 x^{9})}^{2}} d x, x > 0,$ $\lim_{x \to 0} f (x) = 0$ and $f (1) = \frac{1}{4}$ .

If $A = [\begin{matrix} 0 & 0 & 1 \\ \frac{1}{4} & f' (1) & 1 \\ α^{2} & 4 & 1 \end{matrix}]$ and $B = adj (adj A)$ be such that $| B |$ $= 81$ , then $α^{2}$ is equal to [2026]

1 1

2 4

3 2

4 3

Ans.
(2)

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