Coefficient of {t^{12}} in {left( {1 + {t^2}} right)^6}left( {1 + {t^6}} right)left( {1 + {t^

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7.Binomial Theorem

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Coefficient of ${t^{12}}$ in ${\left( {1 + {t^2}} \right)^6}\left( {1 + {t^6}} \right)\left( {1 + {t^{12}}} \right)$ is-

A

$24$

B

$21$

C

$22$

D

$23$

Solution

$\left(1+t^{2}\right)^{6}\left(1+t^{2}+t^{12}+t^{18}\right)$

coeff of $t^{12}$ in $\left(1+t^{2}\right)^{6}+$ coeff of $t^{6}$ in $\left(1+t^{2}\right)^{6}+$

coeff. of $t^{\circ}$ in $\left(1+t^{2}\right)^{6}$

$^{6} \mathrm{C}_{6}+^{6} \mathrm{C}_{3}+^{6} \mathrm{C}_{0}$

$22$

Standard 11

Mathematics

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