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Binomial Coefficients

If the coeffi...

Question

If the coefficient of $(2 r + 3)^{t h}$ term and $(r - 1)^{t h}$ terms in the expansion of ${(1 + x)}^{18}$ are equal, find $r$ .

r = 6

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r = 7

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r = 11

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r = 12

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Solution

The correct option is A $r = 6$
Since the two coefficients are equal
$^{18} C_{r - 2} =^{18} C_{2 r + 2}$
$18 - (r - 2) = 2 r + 2$
$18 + 2 - r = 2 r + 2$
$3 r = 18$
$r = 6$

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