Q. If the sum of the coefficient in the expansion of $(a^{2}x^{2} - 6ax + 11)^{10}$, where $a$ is constant is 1024, then the value of $a$ is
A) 5
B) 1
C) 2
D) 3
Explanation
(d)
$(a^{2} - 6a + {11)}^{10} = 1024$
$\Longrightarrow \ \ \ \ \ (a^{2} - 6a + 11)^{10} = 2^{10}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ a^{2} - 6a + 11 = 2$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ a^{2} - 6a + 9 = 0$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (a - 3)^{2} = 0$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a = 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.