BITSAT Mathematics Question (2024) — Solution

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 C_4 ( 1 3 )^6 x^2 \\ Coefficient of x^2 & = ^ 10 C_4 ( 1 3 )^6 \\ & = 10 9 8 7 4 3 2 1 1 3^6 = 70 243 aligned