# If the number of integral terms in the expansion of $(3^{\frac{1}{2}}+5^{\frac{1}{8}})^{n}$ is excatly 33, then the least value of n is: Option: 1 264 Option: 2 128 Option: 3 256 Option: 4 248

$(3^{\frac{1}{2}}+5^{\frac{1}{8}})^{n}$

$T_{r+1}=^{n}C_{r}3^{\frac{n-r}{2}}.5^{\frac{r}{8}}$

Clearly r should be a multiple of 8.

There are exactly 33 integral terms possible values of r can be 0, 8, 16, ................, 32 × 8

Least value of n = 256.

n=256

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