NIMCET 2019 Question Paper with solutions

Question : 15 of 120

Marks: +1, -0

If a and b are the greatest values of

^{2n}C_r

^(2n-1)C_r

respectively, then

Solution:

We have,
a is the greatest value of

^{2n}C_r

∴ a=^{2n}C_n

b is the greatest value of

^{2n-1}C_n

∴b=^{2n-1}C_n

^{2n}C_{n}=\;\;{2n!}/{n!(2n-n)!}

=\;\;{2n(2n-1)!}/{n⋅(n-1)!(n)!}

^{2n}C_{n}=2⋅^{2n-1}C_{n}

∴a=2b

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