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

5

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6

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4

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3

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Solution

The correct option is A $5$
Coefficient of
$\begin{matrix} T_{2 r + 2 + 1} =^{2 n} C_{2 r + 2} {(1)}^{2 r + 2} T_{r - 2 + 1} =^{2 n} C_{2 r - 2} {(1)}^{r - 1} U s i n g f o r m u l a^{n} C_{x} =^{n} C_{y} n = x = y g i v e n 2^{2 n} C_{2 r + 2} =^{2 n} C_{2 - r} 2 r + 2 + r - 2 = 15 3 r = 15 r = 5 \end{matrix}$

Hence, this is the answer.

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Similar questions

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

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

{(1 + x)}^{15}

{(2 r + 3)}^{th} and {(r - 1)}^{th}

(2 r + 3)^{t h}

(r - 1)^{t h}

(1 + x)^{18}

r

(2 r + 3)^{t h}

(r - 1)^{t h}

{(1 + x)}^{18}

r

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