UPSC NDA Math Model Paper 7

We have to find term independent of x in (x2−

1

x

)9
As we know, T(r+1)=‌nCr×xn−r×yr
⇒T(r+1)=‌9Cr×(x2)9−r×(

−1

x2

)r
=(−1)r9Crx18−2rx−r
=(−1)r9Crx18−3r
For the term independent of x, power of x should be zero
Therefore, 18−3r=0
∴r=6
Hence the value term independent of x is (−1)69C6=84