The domain of the function f(x) = ^{16 - x}C_ | vedclass

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

Question

(A) For $f(x)$ to be defined,the following conditions must be satisfied:$(i)$ For the combination $^{16-x}C_{2x-1}$:$16-x \ge 2x-1 \ge 0$ and $16-x, 2

Vedclass · Accepted Answer

{$2, 3$}

Vedclass · Answer

(A) For $f(x)$ to be defined,the following conditions must be satisfied:$(i)$ For the combination $^{16-x}C_{2x-1}$:$16-x \ge 2x-1 \ge 0$ and $16-x, 2x-1$ must be non-negative integers.$16-x \ge 2x-1 \Rightarrow 3x \le 17 \Rightarrow x \le 5.66$$2x-1 \ge 0 \Rightarrow x \ge 0.5$(ii) For the permutation $^{20-3x}P_{4x-5}$:$20-3x \ge 4x-5 \ge 0$ and $20-3x, 4x-5$ must be non-negative integers.$20-3x \ge 4x-5 \Rightarrow 7x \le 25 \Rightarrow x \le 3.57$$4x-5 \ge 0 \Rightarrow x \ge 1.25$(iii) Combining all inequalities:$x \ge 0.5$,$x \le 5.66$,$x \ge 1.25$,$x \le 3.57$.Thus,$1.25 \le x \le 3.57$.(iv) Since $x$ must be an integer for the binomial coefficient and permutation to be defined,the possible integer values for $x$ are $2$ and $3$.Therefore,the domain is ${2, 3}$.

The domain of the function $f(x) = ^{16 - x}C_{2x - 1} + ^{20 - 3x}P_{4x - 5}$,where the symbols have their usual meanings,is the set

Similar Questions

If $f(n) = n! (31-n)!$,where $n \in \{0, 1, 2, \ldots, 31\}$,then the minimum value of $f(n)$ is

$A$ question paper contains $4$ questions,each having $4$ alternative answers. The number of ways that a candidate can answer one or more questions is

Among the inequalities below,which ones are true for all natural numbers $n > 1000$?
$I. n! \leq n^n$
$II. (n!)^2 \leq n^n$
$III. 10^n \leq n!$
$IV. n^n \leq (2n)!$

$^{80}C_{40}$ is not divisible by -

The number of $4$-letter permutations formed using the English alphabet such that the number of distinct vowels is equal to the number of distinct consonants,when repetition is allowed,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module