The sixth term in the expansion of x1/3+y1/2n,if the binomial coefficient of the third term form theend is 45, is

The sixth term in the expansion of $(x^{1 / 3} +$ ${y^{1 / 2})}^{n}$ ,if the binomial coefficient of the third term form the
end is 45, is

A
$252 x^{5 / 3} y^{5 / 2}$
B
45
C
$45 x^{5 / 3} y^{5 / 2}$
D
none of these

Solution:

Binomial coefficients of the third term from the end in the expansion of ${(x^{1 / 3} + y^{1 / 2})}^{n}$ , is

$^{n} C_{2} = 45 \Rightarrow n (n - 1) - 90 = 0 \Rightarrow n = 10$ .

$∴$ Sixth term in the expansion of ${(x^{1 / 3} + y^{1 / 2})}^{n}$ is

$^{n} C_{5} {(x^{1 / 3})}^{n - 5} {(y^{1 / 2})}^{5} = 252 x^{5 / 3} y^{5 / 2}$

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