Question

The numerically greatest term in the expansion of $(3-2x{)}^4$, when $x=\frac{1}{3}$ is ?

• A. $216$
• B. $343$
• C. $512$
• D. $729$

Answer 1

The correct option is A $216$

The expression is $(3-2x{)}^4$

Here $n=4$

The greatest coefficient is ${}^n{C}_{n/2}$

The term is ${}^4{C}_2\left(3^3\right)(-2x{)}^{2}6(27)\left(4\left(\frac{1}{3}\right)\right)8\times 27=216$