The number of elements in the set {x in N : ^ | vedclass

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

Question

(C) For the binomial coefficient $^{n}C_{r}$ to be a natural number,we must have $n \geq r \geq 0$ and $n, r \in \mathbb{N}_0$.Given $^{20-2x}C_{x-3}

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) For the binomial coefficient $^{n}C_{r}$ to be a natural number,we must have $n \geq r \geq 0$ and $n, r \in \mathbb{N}_0$.Given $^{20-2x}C_{x-3} \in N$,the following conditions must be satisfied:$1) \; x-3 \geq 0 \Rightarrow x \geq 3$$2) \; 20-2x \geq x-3$ $\Rightarrow 23 \geq 3x$ $\Rightarrow x \leq \frac{23}{3} \approx 7.66$$3) \; 20-2x \geq 0 \Rightarrow x \leq 10$Combining these inequalities,we get $3 \leq x \leq 7.66$.Since $x \in N$,the possible values for $x$ are $3, 4, 5, 6, 7$.Thus,there are $5$ elements in the set.

The number of elements in the set $\{x \in N : ^{20-2x}C_{x-3} \in N\}$ is

Similar Questions

Out of $7$ consonants and $4$ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2$ vowels, is

$^{2n}C_4 : ^nC_3 = 99 : 4 \Rightarrow n = $

$A$ man has $7$ friends. In how many ways can he invite one or more of them for a tea party?

The total number of ways of selecting six coins out of $20$ one rupee coins,$10$ fifty paise coins,and $7$ twenty-five paise coins is:

In an election,there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

Vedclass Test Series

Exam Paper Generator

Online Exam Module