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Q.

The sum of the last eight coefficients in the expansion of (1+x)15 is.

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a

216

b

215

c

214

d

none of these

answer is C.

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Detailed Solution

We have,(1+x)15=15C0+15C1x+15C2x2+…+15C15x15We have to find the value of  15C8+15C9+15C10+…+15C15=122×15C8+2×15C9+2×15C10+…+2×15C15=12 15C7+15C8+ 15C6+15C9+ 15C5+15C10+…+…………..+ 15C0+15C15∵nCr=nCn−r=12 15C0+15C1+15C2+…+15C15=12×215=214
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