Binomial Theorem And Its Simple Applications Question 149
Question: The coefficient of $ x^{100} $ in the expansion of $ \sum\limits_{j=0}^{200}{{{(1+x)}^{j}}} $ is
[UPSEAT 2004]
Options:
A) $ ( \begin{aligned} & 200 \\ & 100 \\ \end{aligned} ) $
B) $ ( \begin{aligned} & 201 \\ & 102 \\ \end{aligned} ) $
C) $ ( \begin{aligned} & 200 \\ & 101 \\ \end{aligned} ) $
D) $ ( \begin{aligned} & 201 \\ & 100 \\ \end{aligned} ) $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ {T_{r+1}}={{,}^{200}}C_{r}{{(1)}^{200-r}}.{{(x)}^{r}} $
Hence coefficient of $ x^{100}={{,}^{200}}C_{100}=( \begin{aligned} & 200 \\ & 100 \\ \end{aligned} ) $ .
BETA
