Binomial TheoremHard
Question
The co-efficient of x4 in the expansion of (1 - x + 2x2)12 is:
Options
A.12C3
B.13C3
C.14C4
D.12C3 + 3 13C3 + 14C4
Solution
(1 - x + 2x2)12
General term =
(1)r1 (-x)r2 (2x2)r3
r2 + 2r3 = 4 ⇒ r3 = 0, r2 = 4, r1 = 8
r3 = 1, r2 = 2, r1 = 9
r3 = 2, r2 = 0, r1 = 10
Co-efficient of x4 =
(2)2 + 
× (2)
= 12C8 + 4 .12C10 + 6 . 12C9
= 12C3 + 3 .13C3 + 14C4 (after solving)
General term =
(1)r1 (-x)r2 (2x2)r3r2 + 2r3 = 4 ⇒ r3 = 0, r2 = 4, r1 = 8
r3 = 1, r2 = 2, r1 = 9
r3 = 2, r2 = 0, r1 = 10
Co-efficient of x4 =
(2)2 + × (2)= 12C8 + 4 .12C10 + 6 . 12C9
= 12C3 + 3 .13C3 + 14C4 (after solving)
Create a free account to view solution
View Solution FreeMore Binomial Theorem Questions
If x4 occurs in the rth term in the expansion of , then r equals-...If (1 + x)n =ar xr and br = 1 + andbr =, then n equals to :...If (1 + x)n = 1 + C1x + C2x2 +......+ Cnxn, then C1 + C3 + C5 + ..... is equal to-...If the middle term in the expansion of is 924 x6, then n =...The number of integral terms in the expansion of (51/2 + 71/6)642 is -...