If coefficient of {(2r + 3)^{th}} and {(r - 1)^{th}} terms in expansion of {(1 + x)^{15}} are equal,

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7.Binomial Theorem

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

A

$5$

B

$6$

C

$4$

D

$3$

Solution

(a) $^{15}{C_{2r + 2}}{ = ^{15}}{C_{r – 2}}$

But $^{15}{C_{2r + 2}} = {\,^{15}}{C_{15 – (2r + 2)}} = {\,^{15}}{C_{13 – 2r}}$

==> $^{15}{C_{13 – 2r}} = \,{\,^{15}}{C_{r – 2}}$

$\Rightarrow r = 5$.

Standard 11

Mathematics

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