Question

The power of $x$ in the term with the greatest coefficient in the expansion of $\left(1+\frac{x}{2}\right)^{10}$ is:

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

3

Answer 2

$\left(1+\frac{x}{2}\right)^{10}=1+{ }^{10} C_{1} \frac{1}{2} x$
$+{ }^{10} C_{2}\left(\frac{1}{2} x\right)^{2}+{ }^{10} C_{3}\left(\frac{1}{2} x\right)^{3}+{ }^{10} C_{4}\left(\frac{1}{2} x\right)^{4}+\ldots$
By inspection, ${ }^{10} C_{3} \cdot \frac{1}{8}$ is the highest coefficient.
So, power of the $x$ is 3 .