Binomial Theorem And Its Simple Applications Question 200
Question: The coefficient of $ x^{53} $ in the expansion $ \sum\limits_{m=0}^{100}{^{100}C_{m}{{(x-3)}^{100-m}}2^{m}} $ is
Options:
A) $ ^{100}C_{47} $
B) $ ^{100}C_{53} $
C) $ {{-}^{100}}C_{53} $
D) $ {{-}^{100}}C_{100} $
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Answer:
Correct Answer: C
Solution:
- [c] The given sigma is the expansion of $ [(x-3)+2]100=(x-1)100=(1-x)100 $
Therefore, $ x^{53} $ will occur in $ T_{54} $ . $ T_{54}={{,}^{100}}C_{53}{{(-x)}^{53}} $
Therefore, the coefficient is $ {{-}^{100}}C_{53} $
BETA
