Binomial Theorem And Its Simple Applications Question 121
Question: The coefficient of the middle term in the binomial expansion in powers of x of $ {{(1+ax)}^{4}} $ and of $ {{(1-ax)}^{6}} $ is the same, if $ \alpha $ equals
Options:
A) $ -\frac{5}{3} $
B) $ \frac{10}{3} $
C) $ -\frac{3}{10} $
D) $ \frac{3}{5} $
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Answer:
Correct Answer: C
Solution:
- [c] Middle term of $ {{(1+\alpha x)}^{4}} $ is $ T_3 $ .
Its coefficient is $ ^{4}C_2{{(\alpha )}^{2}}=6{{\alpha }^{2.}} $ Middle term of $ {{(1-\alpha x)}^{6}} $ is $ T_4 $ .
Its coefficient is $ ^{6}C_3{{(-\alpha )}^{3}}=-20{{\alpha }^{3}} $ .
According to question, $ 6{{\alpha }^{2}}=-20{{\alpha }^{3}} $ or $ 3{{\alpha }^{2}}+10{{\alpha }^{2}}=0 $ or $ {{\alpha }^{2}}(3+10\alpha )=0 $ or $ \alpha =-\frac{3}{10} $
BETA
