Binomial Theorem And Its Simple Applications Question 25
Question: $ ^{10}C_1{{+}^{10}}C_3{{+}^{10}}C_5{{+}^{10}}C_7{{+}^{10}}C_9= $
[MP PET 1982]
Options:
A) $ 2^{9} $
B) $ 2^{10} $
C) $ 2^{10}-1 $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- We know that $ {2^{n-1}}={{,}^{n}}C_0+{{,}^{n}}C_2+{{,}^{n}}C_4+….={{,}^{n}}C_1+{{,}^{n}}C_3+{{,}^{n}}C_5+….. $ So, $ ^{10}C_1+{{,}^{10}}C_3+{{,}^{10}}C_5+…..+{{,}^{10}}C_9={2^{10-1}}=2^{9} $
BETA
