First slide

Binomial theorem for positive integral Index

Question

Coefficient of t ²⁴ in the expansion of ${(1 + t^{2})}^{12} (1 + t^{12}) (1 + t^{24})$ is

Moderate

A

$^{12} C_{6} + 2$
B

$^{12} C_{6} + 1$
C

$^{12} C_{6}$
D

$^{12} C_{6} + 3$

Solution

Coefficient of t ²⁴ in ${(1 + t^{2})}^{12} (1 + t^{12}) (1 + t^{24})$
= Coefficient of t ²⁴ in $(1 +^{12} C_{1} t^{2} +^{12} C_{2} t^{4} + \dots) (1 + t^{12} + t^{24})$
$=^{12} C_{12} +^{12} C_{6} + 1 =^{12} C_{6} + 2$

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