Q. The sum of the coefficients in the expansion of ${(x + y)}^{n}$ is 4096. The greatest coefficient in the expansion is
A) 1024
B) 924
C) 824
D) 724
Explanation
(b)
By hypothesis, $2^{n} = 4096 = 2^{12} \Rightarrow n = 12$
Since, $n$ is even, hence greatest coefficient
$= \ ^{n}C_{\frac{n}{2}} = \ ^{12}C_{6} = \frac{12 \bullet 11 \bullet 10 \bullet 9 \bullet 8 \bullet 7}{1 \bullet 2 \bullet 3 \bullet 4 \bullet 5 \bullet 6} = 924$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.