Question
Question: The coefficient of x<sup>4</sup> in the expansion of (1 + x + x<sup>2</sup> + x<sup>3</sup>)<sup>11<...
The coefficient of x4 in the expansion of (1 + x + x2 + x3)11 is
A
990
B
605
C
810
D
None of these
Answer
990
Explanation
Solution
(1 + x + x2 + x3)11 = (1 + x)11 . (1 + x2)11
= (1 + 11C1x + 11C2x2 + 11C3x3 + 11C4x4 + ……..) .
(1 + 11C1x2 + 11C2x4 + …….)
The numbers of terms which give x4.
= 11C2 + 11C2 × 11C1 + 11C4 = 990