If ^nC_{r-1} = 36,^nC_r = 84,and ^nC_{r+1} = | vedclass

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

Question

(C) We are given the following equations:$(1)$ $\frac{^nC_{r-1}}{^nC_r} = \frac{36}{84} = \frac{3}{7}$Using the formula $\frac{^nC_{r-1}}{^nC_r} = \fr

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) We are given the following equations:$(1)$ $\frac{^nC_{r-1}}{^nC_r} = \frac{36}{84} = \frac{3}{7}$Using the formula $\frac{^nC_{r-1}}{^nC_r} = \frac{r}{n-r+1}$,we get $\frac{r}{n-r+1} = \frac{3}{7} \implies 7r = 3n - 3r + 3 \implies 3n - 10r = -3$.$(2)$ $\frac{^nC_r}{^nC_{r+1}} = \frac{84}{126} = \frac{2}{3}$Using the formula $\frac{^nC_r}{^nC_{r+1}} = \frac{r+1}{n-r}$,we get $\frac{r+1}{n-r} = \frac{2}{3} \implies 3r + 3 = 2n - 2r \implies 2n - 5r = 3$.Multiplying the second equation by $2$,we get $4n - 10r = 6$.Subtracting the first equation $(3n - 10r = -3)$ from this,we get $n = 9$.Substituting $n = 9$ into $2n - 5r = 3$,we get $18 - 5r = 3 \implies 5r = 15 \implies r = 3$.

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

Similar Questions

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class,if there are two specific boys $A$ and $B$ who refuse to be members of the same team,is

The number of ways in which $3$ identical balls can be distributed into $7$ distinct bins is

$A$ student has to answer $10$ out of $13$ questions in an examination. The number of ways in which he can answer if he must answer at least $3$ of the first $5$ questions is:

If set $A$ contains $8$ elements,then the number of subsets of $A$ which contain at least $6$ elements is

The least value of $n$ such that ${ }^{(n-1)} C_3 + { }^{(n-1)} C_4 > { }^n C_3$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module