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 (1 + x)n = C0 + C1 x + C2 x2 + ...+ Cnxn, then the value of C0 + 2C1 + 3C2 + ....+(n +1)Cn is -...If |x| < 1, then the co-efficient of xn in the expansion of (1 + x + x2 + x3 +....)2 is...The numerically greatest term in the expansion of (2x + 5y)34, when x = 3 & y = 2 is :...Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by...is equal to -...