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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 `^12 C_6+3` b. `^12 C_6+1` c. `^12 C_6` d. `^12 C_6+2`

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Verified by Experts

The correct Answer is:
99
`((1-x^(2))+x^(4))^(3)(1-x)^(7)`
`= ((1-x^(2))^(3)+3x^(4)(1-x^(2))^(3) +3x^(4)(1-x^(2))^(2)+3x^(8)(1-x^(2))+x^(12))xx(.^(7)C_(0) - .^(7)C_(1)x+.^(7)C_(2)x^(2)-"…….."-.^(7)C_(7)x^(7))`
`:.` Coefficient of `x^(12) = .^(7)C_(0) - 3 xx .^(7)C_(2) + 6 xx .^(7)C_(4) - 7 xx .^(7)C_(6)`
` = 99`
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