Question

If the polynomial $f(x)=\left|\begin{array}{ccc}(1+x)^{a} & (2+x)^{b} & 1 \\ 1 & (1+x)^{a} & (2+x)^{b} \\ (2+x)^{b} & 1 & (1+x)^{a}\end{array}\right|$, then the constant term of $f(x)$ is
(A) $2-3.2^{\mathrm{b}}+2^{3 \mathrm{~b}}$
(B) $2+3.2^{b}+2^{3 b}$
(C) $2+3.2^{\mathrm{b}}-2^{3 \mathrm{~b}}$
(D) $2-3.2^{\mathrm{b}}-2^{3 \mathrm{~b}}$

Answer 1

Ans: (A)
Hint $: f(0)=\left|\begin{array}{rrr}1 & 2^{b} & 1 \\ 1 & 1 & 2^{b} \\ 2^{b} & 1 & 1\end{array}\right|=2-3.2^{b}+2^{3 b}$

Answer 2

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Answer 3

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