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  4. In the expansion of (4-3x)7, when x=(2/3), the numerically greatest term is

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Q. In the expansion of $ {{(4-3x)}^{7}}, $ when $ x=\frac{2}{3}, $ the numerically greatest term is

JamiaJamia 2013

Solution:

$ {{(4-3x)}^{7}}={{4}^{7}}{{\left( 1-\frac{3x}{4} \right)}^{2}} $ Consider, $ {{\left( 1-\frac{3x}{4} \right)}^{7}} $ $ \frac{{{T}_{r+1}}}{{{T}_{r}}}=\frac{7-r+1}{r}.\frac{3}{4}.\frac{2}{3}\ge 1 $ $ \Rightarrow $ $ r\le 2.66 $ $ \therefore $ $ r=2 $ Hence, the greatest term is $ {{T}_{3}} $ .