A) \[50\]
B) \[-50\]
C) \[68\]
D) None of these
Correct Answer: B
Solution :
[b] \[{{(1-x+{{x}^{2}})}^{6}}={{[1-x(1-x)]}^{6}}\] \[{{=}^{6}}{{C}_{0}}{{-}^{6}}{{C}_{1}}x(1-x){{+}^{6}}{{C}_{2}}{{x}^{2}}{{(1-x)}^{2}}{{-}^{6}}{{C}_{3}}{{x}^{3}}{{(1-x)}^{3}}+\]???.up to 7 terms \[{{=}^{6}}{{C}_{0}}{{-}^{6}}{{C}_{1}}x(1-x){{+}^{6}}{{C}_{2}}{{x}^{2}}(1-2x+{{x}^{2}})\] \[{{-}^{6}}{{C}_{3}}{{x}^{3}}(1-3x+3{{x}^{2}}-{{x}^{3}})+\]... up to 7 terms \[\therefore \] Coefficient of \[{{x}^{3}}=-2{{\times }^{6}}{{C}_{2}}{{-}^{6}}{{C}_{3}}\] \[=-2\frac{6!}{2!4!}-\frac{6!}{3!3!}=-50\]
You need to login to perform this action.
You will be redirected in
3 sec
