The coefficient of xr in the expansion of $$S=(x+3)n$$−$$1+(x+3)n$$−$$2(x+2)+(x+3)n$$−$$3(x+2)2+$$ …$$+(x+2)n$$−$$1$$ is

Correct option is 3nCr3n−r−2n−r

Questions

The coefficient of $x^{r}$ in the expansion of $\begin{array}{l} S = (x + 3)^{n - 1} + (x + 3)^{n - 2} (x + 2) + (x + 3)^{n - 3} (x + 2)^{2} + \dots + (x + 2)^{n - 1} \end{array}$ is

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3n−r−2n−r

nCr3r−2r

nCr3n−r−2n−r

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detailed solution

Correct option is C

We can write S=(x+3)n−11−x+2x+3n1−x+2x+3=(3+x)n−(2+x)n∴ Coefficient of xr=nCr3n−r−2n−r

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The coefficient of xr in the expansion of S=(x+3)n−1+(x+3)n−2(x+2)+(x+3)n−3(x+2)2+ …+(x+2)n−1 is

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The coefficient of $x^{r}$ in the expansion of $\begin{array}{l} S = (x + 3)^{n - 1} + (x + 3)^{n - 2} (x + 2) + (x + 3)^{n - 3} (x + 2)^{2} + \dots + (x + 2)^{n - 1} \end{array}$ is