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Numerically Greatest Term

The numerical...

Question

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

A

216

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B

343

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C

512

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D

729

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Solution

The correct option is A $216$
The expression is $(3 - 2 x)^{4}$
Here $n = 4$
The greatest coefficient is $^{n} C_{n / 2}$
The term is $^{4} C_{2} (3^{3}) (- 2 x)^{2} 6 (27) (4 (\frac{1}{3})) 8 \times 27 = 216$

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