Find the sixth term of the expansion (y1/2 + x1/3)n, if the binomial coefficient of the third term from the end is 45.

Firstly,we have to find the power(n) of the binomial (y12+x13)nCoefficient of the third term from the end =45Cn-2n=45n!(n-(n-2))!(n-2)!=45n!2!(n-2)!=45n(n-1)2=45n2-n-90=0Soving,n=-b±b2-4ac2a=1±1+3602=1±192n= 10 or n=-9 (not possible)So n=10So T6=10C5(y12)(10-5)(x13)5=10C5y52x53

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