Binomial Theorem And Its Simple Applications Question 210
Question: If the sum of the coefficients in the expansion of $ {{(1-3x+10x^{2})}^{n}} $ is a and if the sum of the coefficients in the expansion of $ {{(1+x^{2})}^{n}} $ is b, then
Options:
A) $ a=3b $
B) $ a=b^{3} $
C) $ b=a^{3} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] We have a = sum of the coefficient in the expansion of $ {{(1-3x+10x^{2})}^{n}}={{(1-3+10)}^{n}} $
$ ={{(8)}^{n}} $
$ \Rightarrow {{(1-3x+10x^{2})}^{n}}={{(2)}^{3n}}, $
[Putting $ x=1 $ ] Now, b = sum of the coefficient in the expansion of $ {{(1+x^{2})}^{n}}={{(1+1)}^{n}}=2n. $ clearly, $ a=b^{3} $
BETA
