# Find the sixth term of the expansion $(y^{\Large\frac{1}{2}}+x^{\Large\frac{1}{3}})^n$.If the binomial coefficient of the third term from the end is 45.

$\begin{array}{1 1}(A)\;252 y^{\Large\frac{5}{2}}x^{\Large\frac{5}{3}}\\(B)\;252\\(C)\;y^{\Large\frac{5}{2}}x^{\Large\frac{5}{3}}\\(D)\;200y^{\Large\frac{5}{2}}\end{array}$

The correct answer is A. The given expansion is (y^1/2 + x^1/3)^n T6=T5+1=nC5(y^1/2)^n-5(x^1/3)^5 Now, nC2=45 N(n-1)(n-2)!/2!(n-2)!=45 N(n-1)=90 On solving by splitting the term method, we get N=10 So, T6 = 252 y^5/2 x^5/3 Hope it helps....