If n is even and the value of ^n{C_r} is maxi | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

The binomial coefficient series is

${ }^n C_0,{ }^n C_1,{ }^n C_2, \ldots,{ }^n C r, \ldots .,{ }^n C_{n-2},{ }^n C_{n-1},{ }^n C_n$

the task is

Vedclass · Accepted Answer

$\frac{n}{2}$

Vedclass · Answer

The binomial coefficient series is

${ }^n C_0,{ }^n C_1,{ }^n C_2, \ldots,{ }^n C r, \ldots .,{ }^n C_{n-2},{ }^n C_{n-1},{ }^n C_n$

the task is to find maximum value of ${ }^{ n } Cr$

The value of coefficients increasing initially and reaches its maximum and then start reducing value in middle is maximum

total term are $=n+1$

${ }^n Cr$ is $r +1$ th term

middle term $=(n+1+1) / 2=n / 2+1$

$r+1=n / 2+1$

$r=n / 2$

If $n$ is even and the value of ${ }^n C r$, is maximum, when $r=n / 2$

if $n$ is odd, the maximum occurs at $r=(n-1) / 2$ and at $r=(n+1) / 2$.

$r=n / 2$ if $n$ is Even

If $n$ is even and the value of $^n{C_r}$ is maximum, then $r = $

Similar Questions

The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is

The value of $\sum\limits_{r = 1}^{15} {{r^2}\,\left( {\frac{{^{15}{C_r}}}{{^{15}{C_{r - 1}}}}} \right)} $ is equal to

If $\sum\limits_{i = 0}^4 {^{4 + 1}} {C_i} + \sum\limits_{j = 6}^9 {^{3 + j}} {C_j} = {\,^x}{C_y}$ ($x$ is prime number), then which one of the following is incorrect

What is the number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these

four cards belong to four different suits,

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :