Answers:
(i)
If (r + 1)th term in the given expression is independent of x.
Tr+1 = nCr xn-r ar
For this term to be independent of x,
18 – 3r = 0
3r = 18
r = 18/3
r = 6
The term is 7th term.
T7 = T6+1
= 9C6 × (39-12)/(29-6)
= (9×8×7)/(3×2) × 3-3 × 2-3
= 7/18
Term independent of x is 7/18.
(ii)
If (r + 1)th term in the given expression is independent of x.
Tr+1 = nCr xn-r ar
For this term to be independent of x,
9 – 3r = 0
3r = 9
r = 9/3
r = 3
The term is 4th term.
T4 = T3+1
= 9C3 × (26)/(33)
= 9C3 × 64/27
Term independent of x is 9C3 × 64/27.