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Question

If (1+x)(1+x2)(1+x4)...(1+x128)=nr=0xr then n is

A
255
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B
127
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C
63
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D
none of these
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Solution

The correct option is A 255
The problem is to find the greatest power of x in the expansion
The greatest power is obtained when all the powers of x in all the brackets add up
Thus, n=1+2+4+..+128
=1(281)21=2561=255
Hence, A is correct.

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