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
Let (5 + 2√6)n = p + f, where n ∈ N and p ∈ N and 0 < f < 1, then the value of f2 - f + pf - p i...The number 101100 - 1 is divisible by -...If the sum of coefficients in the binomial expansion of (x + y)n is 4096 then greatest coefficient in the expansion is -...If (1 + x)n = C0 + C1x + C2 x2 + ...+ Cnxn, then the value of 12 C1 + 22 C2 + 32 C3 + ...+ n2 Cn is -...79 + 97 is divisible by :...