If n is the number of irrational terms in the | vedclass

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(A) The general term in the expansion of $(3^{1/4} + 5^{1/8})^{60}$ is given by $T_{r+1} = {}^{60}C_r (3^{1/4})^{60-r} (5^{1/8})^r = {}^{60}C_r (3)^{(

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$26$

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(A) The general term in the expansion of $(3^{1/4} + 5^{1/8})^{60}$ is given by $T_{r+1} = {}^{60}C_r (3^{1/4})^{60-r} (5^{1/8})^r = {}^{60}C_r (3)^{(60-r)/4} (5)^{r/8}$.For the term to be rational,the exponents of $3$ and $5$ must be integers.Thus,$r$ must be a multiple of $8$ such that $0 \leq r \leq 60$.The possible values for $r$ are $0, 8, 16, 24, 32, 40, 48, 56$.There are $8$ rational terms.The total number of terms in the expansion is $60 + 1 = 61$.Therefore,the number of irrational terms $n = 61 - 8 = 53$.We need to check divisibility for $(n - 1) = 53 - 1 = 52$.Since $52 = 26 	imes 2$,$(n - 1)$ is divisible by $26$.

If $n$ is the number of irrational terms in the expansion of $(3^{1/4} + 5^{1/8})^{60}$,then $(n - 1)$ is divisible by

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