Coefficient of y 3- x 6 in the binomial expansion x -2 y 9A- 276B- 672C- 762D- 267

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Standard XI

Mathematics

Binomial Expression

Coefficient o...

Question

Coefficient of $y^{3} . x^{6}$ in the binomial expansion $(x + 2 y)^{9}$

276

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672

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762

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267

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Solution

The correct option is B
672

$T_{r + 1}$ = $^{n} C_{r}$ $x^{n - r} y^{r}$ = $^{9} C_{r}$ $x^{9 - r} (2 y)^{r}$

r = 3 ⇒ coeff = $^{9} C_{3}$ $2^{3}$ = 672

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Prove that the coefficient of $x^{n}$ in the binomial expansion of $(1 + x)^{2 n}$ is twice the coefficient of $x^{n}$ in the binomial expansion of $(1 + x)^{2 n - 1}$ .

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Coefficient of y3.x6 in the binomial expansion (x+2y)9

The correct option is B 672 Tr+1 = nCrxn−ryr = 9Crx9−r(2y)r r = 3 ⇒ coeff = 9C323 = 672

Coefficient of $y^{3} . x^{6}$ in the binomial expansion $(x + 2 y)^{9}$

The correct option is B
672

$T_{r + 1}$ = $^{n} C_{r}$ $x^{n - r} y^{r}$ = $^{9} C_{r}$ $x^{9 - r} (2 y)^{r}$

r = 3 ⇒ coeff = $^{9} C_{3}$ $2^{3}$ = 672