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Question

If (1+x)10=a0+a1x+a2x2+.....+a10x10, then value of (a0a2+a4a6+a8a10)2+(a1a3+a5a7+a9)2 is

A
210
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B
2
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C
220
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D
230
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Solution

The correct option is A 210
Here ai=10Ci
ie,(a0a2+a4a6+a8a10)2+(a1a3+a5a7+a9)2
=(10C010C2+10C410C6+10C810C10)2+(10C110C3+10C510C7+10C9)2
((10C010C10)+(10C810C2)+(10C410C6))2+((1)(2)102)2=210
Since [n/2]i=0nC2i=0,Ifn+24Integers(1)[(n+2)/4]2[n/2]
and [n/2]i=0nC2i+1=0,Ifn4Integers(1)[n/4]2[n/2]
Option A is correct

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