Binomial Theorem And Its Simple Applications Question 5
Question: The value of $\begin{aligned} & \left({ }^{10} C_0\right)+\left({ }^{10} C_0+{ }^{10} C_1\right)+\left({ }^{10} C_0+{ }^{10} C_1 +{ }^{10} C_2\right)+\ldots \ldots+\left({ }^{10} C_0+{ }^{10} C_1 { }^{10} C_2+\ldots+{ }^{10} C_9\right) \text { is }\end{aligned}$
Options:
A) $ 2^{10} $
B) $ {{10.2}^{9}} $
C) $ {{10.2}^{10}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ {{(}^{10}}C_0)+{{(}^{10}}C_0+{{}^{10}}C_1)+{{(}^{10}}C_0+{{}^{10}}C_1+{{}^{10}}C_2) $
$ +….+{{(}^{10}}C_0+{{}^{10}}C_1+{{}^{10}}C_2+…+{{}^{10}}C_9) $
$ =10{{}^{10}}C_0+9{{}^{10}}C_1+8{{}^{10}}C_2+…+{{}^{10}}C_9 $
$ ={{}^{10}}C_1+2{{}^{10}}C_2+3{{}^{10}}C_3+…10{{}^{10}}C_{10} $
$ =\sum\limits_{r=1}^{10}{r^{10}C_{r}=10\sum\limits_{r=1}^{10}{^{9}{C_{r-1}}={{10.2}^{9}}}} $
BETA
