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  4. Number of rational terms in the expansion of (2(1/7)+3(1/4))198 is equal to

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Q. Number of rational terms in the expansion of $\left(2^{\frac{1}{7}}+3^{\frac{1}{4}}\right)^{198}$ is equal to

Binomial Theorem

Solution:

$ T_{r+1}={ }^{198} C_r(2)^{\frac{198- r }{7}}(3)^{\frac{r}{4}} $
$r =0,1,2 \ldots \ldots \ldots . .198$
$\therefore \text { For } r =16,44,72,100,128,156,184 \text { the terms in the expansion are rational. }$