The number of irrational terms in the expansion of ${(5^{1 / 6} + 2^{1 / 8})}^{100}$ is

96

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97

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98

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99

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Solution

The correct option is B $97$

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(2^{1 / 5} + 3^{1 / 10})^{55}

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