Number of terms in the expansion of $(x^{1 / 3} + x^{2 / 5})^{40}$ with integral power of x is equal to

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Solution

$T_{r + 1} =^{40} C_{r} x^{\frac{40 - r}{3}} . x^{\frac{2 r}{5}}$
$=^{40} C_{r} x^{\frac{200 + r}{15}}$
$r = 10, 25, 40$
$\Rightarrow$ Number of such terms = 3

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