UPSC NDA Math Model Paper 7

Given: (x−

1

x

)12
As we know that, in the expansion of (a + b)‌n , the r th term from the end is [(n+1)–r+1]=(n–r+2) th term from the beginning.
Here, n = 12 and r = 5
So, the 5th term from the = [(12 + 1) - 5 + 1] = 9th term from the beginning.
T9=T(8+1)=‌12C8.(x)4.(−1∕x)8
⇒T9=T(8+1)=(−1)8.‌12C8.(x)4 .(1∕x)8
⇒T9=

495

x4