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JEE MATHEMATICS MCQ: COMBINATIONS

1 Easy

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Understanding +4 | -1

If

n

is even and

^n{C_0}{ < ^n}{C_1}{ < ^n}{C_2} < ....{ < ^n}{C_r}{ > ^n}{C_{r + 1}}{ > ^n}{C_{r + 2}} > ....{ > ^n}{C_{n'}}

then,

r =

View answer and explanation

Correct option: A

\frac{n}{2}

Option A (

\frac{n}{2}

) is correct because the binomial coefficients

^{n}C_r

are maximized when

r

is closest to

\frac{n}{2}

, and since

n

is even,

r = \frac{n}{2}

gives the maximum value.

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{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}

n