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+1 vote
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in Binomial Theorem by (46.2k points)
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If in the expansion of (1 + x)18, coefficients of (2r + 4)th and (r – 2)th terms are equal then value of r is:

(A) 5

(B) 6

(C) 7

(D) 8

1 Answer

+1 vote
by (47.9k points)
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Best answer

Answer is (B) 6

In the expansion of (1 + x)18 coefficients of (2r + 4)th and (r – 2)th terms are 18C2r + 3 and 18Cr – 3 respectively

Given :

These are equal

Then, 18C2r + 318Cr – 3

⇒ 2r + 3 = r – 3

or 2r+ 3= 18 -(r – 3)

For using the statement if

nCr = nCp or nCn-p

⇒ 2r – r = -3 – 3

or 2r + 3 = 18 – r + 3

⇒ r = -6 or r = 6

r is a natural number, so r = – 6 is not possible, then x = 6. 

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