NIMCET 2012 Mathematics Question 23 with Solution

Question 23

Mathematics Binomial Theorem Medium

The sum of \({ }^{20} C_{8}+{ }^{20} C_{9}+{ }^{21} C_{10}+{ }^{22} C_{11}-{ }^{23} C_{11}\) is

(A) \({ }^{22} C_{12}\)

(B) \({ }^{23} C_{12}\)

(C) 0

(D) \({ }^{21} C_{10}\)

View Dynamic Solution & Explanation ▼

Correct Solution: Option C

Step-by-step Solution:

Using this formula \({ }^{n} C_{r}+{ }^{n} C_{r-1}={ }^{n+1} C_{r}\) \[\] \({ }^{20} C_{8}+{ }^{20} C_{9}+{ }^{21} C_{10}+{ }^{22} C_{11}-{ }^{23} C_{11}\) \[\] \({ }^{21} C_{9}+{ }^{21} C_{10}+{ }^{22} C_{11}-{ }^{23} C_{23}\) \[\] \({ }^{22} C_{10}+{ }^{22} C_{11}-{ }^{23} C_{11}\) \[\] \({ }^{23} C_{11}-{ }^{23} C_{11}=0\) \[\] Choice (C)