If the coefficients of $(2 r + 4)$ th term and $(r - 2)$ th term in the expansion of $(1 + x)^{18}$ are equal, then $r =$

4

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6

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Solution

The correct option is B $6$
In the expansion of $(1 + x)^{18}$

coefficient of $T_{2 r + 4} =^{18} C_{2 r + 3}$

coefficient of $T_{r - 2} =^{18} C_{r - 3}$

Given,

$^{18} C_{2 r + 3} =^{18} C_{r - 3}$

$\Rightarrow 2 r - 3 = r + 3$ or $2 r + 3 + r - 3 = 18$

$\Rightarrow r = - 6$ or $3 r = 18 \Rightarrow r = 6$

but $r$ cannot be negative

$∴ r = 6$

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Similar questions

(2 r + 4)

(r - 2)

{(1 + x)}^{18}

r =

The value of r if the coefficients of (2r+4)th and (r -2)th terms in the expansion of(1+x)¹⁸are equal.

If the coefficient of (2r + 4)th term is equal to the coefficient of (r – 2)th term in the expansion of $(1 + x)^{18}$ then r =

(r + 4)

(2 r + 1)

{(1 + x)}^{18}

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(2 r + 3)

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