$^{25} C_{r}$ has its maximum value when $r$ has the value of

12

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

13

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

25

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A $13$
B $12$
Given
$n = 25$
Middle term of expansion when n is odd are $(\frac{n + 1}{2}), (\frac{n + 3}{2})$
Hence middle term are $13^{t h}, 14^{t h}$
Hence $^{25} C_{13} >^{25} C_{14}$
Hence maximum value of $r$ is $13$
But $^{25} C_{r} =^{25} C_{n - r}$
$^{25} C_{13} =^{25} C_{12}$
Hence $r$ has two value $12, 13$

Suggest Corrections

Similar questions

Q. The ratio of

^{24} C_{r} :^{25} C_{r}

when each of them has the greatest value possible is:

Q. What is the ratio of

^{20} C_{r}

^{25} C_{r}

when each of them has the greatest value possible?

Q. What is the value of

r

when

^{20} C_{r}

has its greatest value?

The wavefunction of a 2s electron is given by $ψ_{2 s} = \frac{1}{4 \sqrt{2} π} (\frac{1}{a_{0}})^{\frac{3}{2}} (2 - \frac{r}{a_{0}}) e^{\frac{- r}{a_{0}}}$
It has a node at $r = r_{0}$ . The value of $\frac{r_{0}}{a_{0}}$ is___

Q. The value of

sin Θ . cos Θ

has maximum value when

Θ

Join BYJU'S Learning Program

25Cr has its maximum value when r has the value of

The correct options are A 13 B 12Given n=25Middle term of expansion when n is odd are (n+12),(n+32)Hence middle term are 13th,14thHence 25C13>25C14Hence maximum value of r is 13But 25Cr=25Cn−r25C13=25C12Hence r has two value 12,13

$^{25} C_{r}$ has its maximum value when $r$ has the value of