A) 1
B) \[-2\]
C) \[-1\]
D) 0
E) 2
Correct Answer: B
Solution :
\[f(x)=\left| \begin{matrix} x & 1+\sin x & \cos x \\ 1 & \log (1+x) & 2 \\ {{x}^{2}} & 1+{{x}^{2}} & 0 \\ \end{matrix} \right|\] \[=x\{-2(1+{{x}^{2}})\}-(1+\sin x)(-2{{x}^{2}})\] \[+\cos \{1+{{x}^{2}}-{{x}^{2}}\log (1+x)\}\] \[=-2x-2{{x}^{3}}+2{{x}^{2}}+2{{x}^{2}}\sin x\] \[+\cos x\{1+{{x}^{2}}-{{x}^{2}}\log (1+x)\}\] \[\therefore \]Coefficient of\[x\]in\[f(x)=-2\]You need to login to perform this action.
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