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Question

If (1+x−2x2)6=1+a1x+a2x2+...+a12x12, then a2+a4+a6+...+a12=

A
21
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B
11
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C
31
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D
None of the above
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Solution

The correct option is C 31
(1+x2x2)6=1+a1x+a2x2+...+a12x12

Putting x=1, we get 0=1+a1+a2+...+a12 ....(1)

Putting x=1, we get 64=1a1+a2...+a12 ...(2)

Adding (1) and (2), we get

64=2(1+a2+a4+...)

a2+a4+a6+...+a12=31

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