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Q.
The power of ' $x$ ' which has the greatest coefficient in the expansion of $\left(1+\frac{x}{2}\right)^{10}$ is
Binomial Theorem
Solution:
$C _{ r +1}={ }^{10} C _{ r } \frac{ x ^{ r }}{2^{ r }}$
For $ r =2 ; { }^{10} C _2 \frac{ x ^2}{2^2} \Rightarrow $ coefficient of $x ^2=\frac{45}{4}=11 \frac{1}{4}$
For $ r =3 ; { }^{10} C _3 \frac{ x ^3}{2^3} \Rightarrow $ coefficient of $x ^3=15$
For $ r =4 ; { }^{10} C _4 \frac{ x ^4}{2^4} \Rightarrow $ coefficient of $x ^4=\frac{210}{16}=\frac{105}{8}=13 \frac{1}{8} \Rightarrow r =3 \Rightarrow$ (B)