Coefficient of t24 in (1+t2)12(1+t12)(1+t24) is ?

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Question

Coefficient of

t^{24} i n (1 + t^{2})^{12} (1 + t^{12}) (1 + t^{24})

is ?

Options:

A . 12C6+3

B . 12C6+1

C . 12C6

D . 12C6+2

Answer: Option D
:
D
Here, Coefficient of

t^{24} i n {(1 + t^{2})^{12} (1 + t^{12}) (1 + t^{24})}

Coefficient of

t^{24} i n {(1 + t^{2})^{12} . (1 + t^{12} + t^{24} + t^{36})}

Coefficient of

t^{24} i n {(1 + t^{2})^{12} + t^{12} (1 + t^{2})^{12} + t^{24} (1 + t^{2})^{12}}

[Neglecting

t^{36} (1 + t^{2})^{12}]

Coefficient of

t^{24} = (^{12} C_{12} +^{12} C_{6} +^{12} C_{0}) = 2 +^{12} C_{6}

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