Question:
Given the integers r > 1, n > 2, and coefficient of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then
(a) n = 2r
(b) n = 3r
(c) n = 2r + 1
(d) none of these
Solution:
Given r > 1 and n > 2
and coefficient of T3r = coefficient of Tr+2 is expansion of (1 + x)2n
i.e. ${ }^{2 n} C_{3 r-1}={ }^{2 n} C_{r+1}$
i. e. $3 r-1=r+1$ (using property of combination)
and $2 n-3 r+1=r+1$
i. e. $2 r=2$ and $2 n=4 r$
i. e. $r=1$ and $n=2 r$
Hence, the correct answer is option A.
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