If the coefficients of the (2r + 3)^{th} and | vedclass

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(A) The general term $T_{k+1}$ in the expansion of $(1 + x)^n$ is given by $\binom{n}{k} x^k$.The $(2r + 3)^{th}$ term is $T_{(2r+2)+1}$,so its coeffi

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$5$

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(A) The general term $T_{k+1}$ in the expansion of $(1 + x)^n$ is given by $\binom{n}{k} x^k$.The $(2r + 3)^{th}$ term is $T_{(2r+2)+1}$,so its coefficient is $\binom{15}{2r+2}$.The $(r - 1)^{th}$ term is $T_{(r-2)+1}$,so its coefficient is $\binom{15}{r-2}$.Given that the coefficients are equal:$\binom{15}{2r+2} = \binom{15}{r-2}$.Using the property $\binom{n}{a} = \binom{n}{b}$,we have either $a = b$ or $a + b = n$.Case $1$: $2r + 2 = r - 2 \Rightarrow r = -4$ (Not possible as $r$ must be a positive integer for the term index).Case $2$: $(2r + 2) + (r - 2) = 15$$3r = 15$$r = 5$.

If the coefficients of the $(2r + 3)^{th}$ and $(r - 1)^{th}$ terms in the expansion of $(1 + x)^{15}$ are equal,then the value of $r$ is:

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