If the ratio of the 7 th term from the beginning to the 7 th term from the end in the expansion of ( [3] 2 + 1 [3] 3 )^n is 1 6 , then n=

Step-by-step solution

Since, the general term in the expansion of ( [3] 2 + 1 [3] 3 )^n is T_ r+1 = ^n C_r (2^ 1 / 3 )^ n-r ( 1 3^ 1 / 3 )^r Now, the 7 th term from beginning = ^n C₆ 2^ n-6 3 3⁻² and the 7 th term from end = ^n C₆ ( 1 3^ 1 / 3 )^ n-6 (2^ 1 / 3 )^6 It is given that, ^n C₆ 2^ n-6 3 3⁻² ^n C₆ 3^ 6-n 3 2^2 = 1 6 1 6^ 6-n 3 +2 = 1 6 array ll & 6-n 3 +2=1 6-n 3 =-1 & 6-n=-3 n=9 array Hence, option (c) is correct.