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The coefficient of t^(24) in (1+t^2)^(12...

The coefficient of `t^(24)` in `(1+t^2)^(12)(1+t^(12))(1+t^(24))` is

A

`.^(12)C_(6) + 3`

B

`.^(12)C_(6) + 1`

C

`.^(12)C_(6) `

D

`.^(12)C_(6) + 2`

Text Solution

Verified by Experts

The correct Answer is:
D
Hence ,Coefficient of `t^24` in `{(1+t^2)^12(1+t^12)(1+t^24)}`
=Coefficient of `t^24` in `{(1+t^2)^12.(1+t^12)+t^24+t^36)}`
=Coefficient of `t^24` in `{(1+t^2)^12+t^12(1+t^2)^12+t^12(1+t^2)^12},[Neglecting t^36 (1+t^2)^12]`
=Coefficient of `t^24 =(.^12C_12+.^12C_6+.12^C_0)=2+.^12C_6`.
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