If n is an odd natural number and ^nC_0 ^nC_ r+1 > ^nC_ r+2 > > ^nC_n, then r=

JEE Main Mathematics question

If is an odd natural number and {}^nC_0<{}^nC_1<{}^nC_2<\cdots<{}^nC_r>{}^nC_{r+1}>{}^nC_{r+2}>\cdots>{}^nC_n, then

(A)
(B)
(C)
(D)Does not existCorrect

Answer: (D)

Solution

For odd the two middle binomial coefficients are equal, , and they are the greatest. A chain with strict inequalities on both sides needs a single greatest coefficient, so neither (then fails) nor

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Question ID VK-021243