Q. If $\ ^{n}C_{r - 1} = 36,\ \ ^{n}C_{r} = 84$ and $\ ^{n}C_{r + 1} = 126$, then the value of $r$ is
A) 1
B) 2
C) 3
D) None of these
Explanation
(c)
Here, $\frac{\ ^{n}C_{r - 1}}{\ ^{n}C_{r}} = \frac{36}{84}$ and $\frac{\ ^{n}C_{r}}{\ ^{n}C_{r + 1}} = \frac{84}{126}$
$\Rightarrow \ \ \ 3n - 10r = - 3$
and $4n - 10r = 6$
On solving, we get $n = 9$ and $r = 3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.