UPSC NDA Math Model Paper 5

Given: (x+3)6
Here, n = 6
∵ n = 6 and it as even number
As we know that, in the expansion of (a+b)n the middle term is (

n

2

+1)th term if n is even.
So, (

6

2

+1)th=4 th term is the middle term in the expansion of (x+3)6
As we know that, the general term is given by: Tr+1=‌nCr.an−r.br
Here, n=6,r=3,a=x and b=3
T4=T(3+1)=‌6C3.x3.(3)3=540x3
Hence, option D is the correct answer.