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Greatest Binomial Coefficients

If the coeffi...

Question

If the coefficient of $(2 r + 3)$ th and $(r - 3)$ th terms in the expansion of $(1 + x)^{18}$ are equal, then r is?

12

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10

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8

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6

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Solution

The correct option is C $6$
Given $(1 + x)^{18}$

$(2 r + 3) t h$ term of the given expression $=^{18} C_{2 r + 2}$

$(r - 3) t h$ term of the given expression $=^{18} C_{r - 2}$

Given, $^{18} C_{2 r + 2} =^{18} C_{r - 2}$

$2 r + 2 + r - 2 = 18 r = 6$

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