Number of rational terms in expansion of {left( {√ 2 ,, + ,,√[4]{3}} right)^{100}} i

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7.Binomial Theorem

normal

Number of rational terms in the expansion of ${\left( {\sqrt 2 \,\, + \,\,\sqrt[4]{3}} \right)^{100}}$ is :

A

$25$

B

$26$

C

$27$

D

$28$

Solution

$T_{r + 1} = ^{100}C_r . 3^{r/4}$

$\Rightarrow \,r$ must be even and divisible by $4$

$ \Rightarrow r = 0, 4, 8, …… , 100$

Standard 11

Mathematics

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