Find the number of terms in the expansion of - 9 - 8 500 which are integers-

∴ General term _ #160;^ #160; T _ r+1 = _ #160;^ 500 C _ r ( 3 ^ 1/2 ) #160;^ 500 r ( 2 ^ 1/2 ) #160;^ r #160; = _ #1 ...

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Number of Terms in Binomial Expansion

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Question

Find the number of terms in the expansion of ${(\sqrt[4]{9} + \sqrt[6]{8})}^{500}$ which are integers.

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Solution

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Similar questions

{(9^{\frac{1}{4}} + 8^{\frac{1}{6}})}^{500}

{(9^{1 / 4} + 8^{1 / 6})}^{1000} .

{(9^{1 / 4} + 4^{1 / 6})}^{1000}

(9^{1 / 4} + 8^{1 / 6})^{1000}

List I	List II
A) lf $λ$ be the number of terms which are integers, in the expansion of $(5^{\frac{1}{6}} + 7^{\frac{1}{9}})^{1824}$ , then $λ$ is divisible by	P) 2
B) lf $λ$ be the number of terms which are rational in the expansion of $(5^{\frac{1}{6}} + 2^{\frac{1}{8}})^{100}$ , then $λ$ is divisible by	Q) 3
C) lf $λ$ be the number of terms which are irrational in the expansion of $(3^{\frac{1}{4}} + 4^{\frac{1}{3}})^{99}$ , then $λ$ is divisible by	R) 7
	S) 13
	T) 17

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