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JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Binomial Theorem

The Coefficient of

x^{- 6}

, in the expansion of

(\frac{4 x}{5} + \frac{5}{2 x ^{2}})^{9}

, is

Answer: 5040

Solution

The general term is

T_{r + 1} =^{9} C_{r} (\frac{4 x}{5})^{9 - r} (\frac{5}{2 x ^{2}})^{r} =^{9} C_{r} (\frac{4}{5})^{9 - r} (\frac{5}{2})^{r} x^{9 - 3 r} .

For the power

x^{- 6}

,

9 - 3 r = - 6

gives

r = 5.

The coefficient is

^{9} C_{5} (\frac{4}{5})^{4} (\frac{5}{2})^{5} = 126 \cdot \frac{256}{625} \cdot \frac{3125}{32} = 126 \cdot 40 = 5040.

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Integer answer

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