The value of −15C1+2×15C2−3×15C3+...−15×15C15+14C1+14C3+14C5+...+14C11 is :
A
214
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B
213−13
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C
216−1
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D
213−14
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Solution
The correct option is D213−14 S1=−15C1+2×15C2−3×15C3+...−15×15C15 =15∑r=1(−1)r×r×15Cr=1515∑r=1(−1)r14Cr−1=15(−14C0+14C1−14C2+⋯−14C14)=15(0)=0S2=14C1+14C3+14C5+⋯+14C11=(14C1+14C3+14C5+⋯+14C11+14C13)−14C13=213−14∴S1+S2=213−14