The coefficient of x^2 term in the binomial expansion of ( 1 3 x^ 1 2 +x^ -1 4 )¹⁰ is

Step-by-step solution

General term of given binomial expansion is aligned T_ r+1 & = ¹⁰ C_r ( 1 3 x^ 1 2 )^ 10-r (x^ - 1 4 )^r & = ¹⁰ C_r ( 1 3 )^ 10-r x^ 10-r 2 - r 4 aligned We have to find coefficient of x^2 aligned 10-r 2 - r 4 & =2 r=4 T_ 4+1 & = ¹⁰ C₄ ( 1 3 )^6 x^2 Coefficient of x^2 & = ¹⁰ C₄ ( 1 3 )^6 & = 10 9 8 7 4 3 2 1 1 3^6 = 70 243 aligned