If n C r -1-36- n C r -84 and n C r -1-126 then r isA- 1B- 2C- 3D- none of these

The correct option is C 3^nC_r 1=36, ^nC_r=84 and ^nC_r+1=126 We know that ^nC_r 1/^nC_r = r/n r+1 ∴36/84 = r/n r+1 or r/n r+1=3/7 or 3n 10r + 3 = 0 Also, ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

nCr Definitions and Properties

If n C r -1=3...

Question

If $^{n} C_{r - 1} = 36,^{n} C_{r} = 84 a n d^{n} C_{r + 1} = 126$ then r is

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

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

none of these

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

Open in App

Solution

The correct option is C 3
$^{n} C_{r - 1} = 36,^{n} C_{r} = 84 a n d^{n} C_{r + 1} = 126$
We know that
$\frac{^{n} C_{r - 1}}{^{n} C_{r}} = \frac{r}{n - r + 1} ∴ \frac{36}{84} = \frac{r}{n - r + 1} o r \frac{r}{n - r + 1} = \frac{3}{7} o r 3 n - 10 r + 3 = 0 A l s o, \frac{^{n} C_{r}}{^{n} C_{r + 1}} = \frac{r + 1}{n - r} = \frac{84}{126} = \frac{2}{3} o r 2 n - 5 r - 3 = 0 S o l v i n g (1) a n d (2), w e g e t n = 9 a n d r = 3$

Suggest Corrections

Similar questions

Q. If

^{n} C_{r - 1} = 36,^{n} C_{r} = 84 a n d^{n} C_{r + 1} = 126

then r is

If $^{n} C r - 1$ = 36, $^{n} C r$ = 84 and $^{n} C r + 1$ = 126, then the value of r is

Q. If

^{n} C_{r - 1} = 36,^{n} C_{r} = 84,^{n} C_{r + 1} = 126

, then

(n, r)

=

Q. If ⁿC_r_{– 1} = 36, ⁿC_r = 84 and ⁿC_r_{+ 1} = 126, then r = ____________.

Q. If

^{n} C_{r - 1} = 36,^{n} C_{r} = 84

and

^{n} C_{r + 1} = 126,

then find

r

Join BYJU'S Learning Program

If nCr−1=36, nCr=84 and nCr+1=126 then r is

The correct option is C 3nCr−1=36, nCr=84 and nCr+1=126 We know that nCr−1nCr=rn−r+1∴3684=rn−r+1or rn−r+1=37or 3n−10r+3=0Also,nCrnCr+1=r+1n−r=84126=23or 2n−5r−3=0Solving (1) and (2), we get n=9 and r=3

If $^{n} C_{r - 1} = 36,^{n} C_{r} = 84 a n d^{n} C_{r + 1} = 126$ then r is