JEE Main Solved Paper 2017 Question 19
Question: The value of $ ({{,}^{21}}C _1-{{,}^{10}}C _1)+({{,}^{21}}C _2-{{,}^{10}}C _2)+ $ $ ({{,}^{21}}C _3-{{,}^{10}}C _3)+({{,}^{21}}C _4-{{,}^{10}}C _4)+….+ $ $ ({{,}^{21}}C _{10}-{{,}^{10}}C _{10}) $ is:- JEE Main Solved Paper-2017
Options:
A) $ 2^{20}-2^{10} $
B) $ 2^{21}-2^{11} $
C) $ 2^{21}-2^{10} $
D) $ 2^{20}-2^{9} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ ({{,}^{21}}C _1{{+}^{21}}C _2…..+{{,}^{21}}C _{10}) $ $ -({{,}^{10}}C _1{{+}^{10}}C _2…..{{,}^{10}}C _{10}) $ $ =\frac{1}{2}[({{,}^{21}}C _1+….+{{,}^{21}}C _{10})+({{,}^{21}}C _{11}+….{{,}^{21}}C _{20})] $ $ -(2^{10}-1) $ $ =\frac{1}{2}[2^{21}-2]-(2^{10}-1) $ $ =(2^{20}-1)-(2^{10}-1)=2^{20}-2^{10} $
