If in the expansion of (1 + x)²⁰, the coefficients of rth and (r + 4)th terms are equal, then r is equal to
(a) 7
(b) 8
(c) 9
(d) 10

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Solution

(c) 9
$Coefficients of the r th and (r + 4) th terms in the given expansion are {}^{20}C_{r - 1} and^{20} C_{r + 3} . Here, {}^{20}C_{r - 1} =^{20} C_{r + 3} \Rightarrow r - 1 + r + 3 = 20 [∵ if^{n} C_{x} =^{n} C_{y} \Rightarrow x = y or x + y = n] \Rightarrow r = 2 or 2 r = 18 \Rightarrow r = 9$

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