Greatest binomial coefficient for JEE

Formula

\(\text{Greatest value among }{}^nC_0,{}^nC_1,\dots,{}^nC_n\text{ occurs at }r=\lfloor n/2\rfloor\text{ and also at }r=\lceil n/2\rceil\text{ if }n\text{ is odd.}\)

Variables: \(n\) is a non-negative integer.

Conditions: For even \(n\), unique greatest coefficient is \({}^nC_{n/2}\); for odd \(n\), two equal greatest coefficients are \({}^nC_{(n-1)/2}\) and \({}^nC_{(n+1)/2}\).

Maximum term/coefficient questions.