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 $S_n = \sum_{r=0}^n \frac{1}{^nC_r}$ and $T_n = \sum_{r=0}^n \frac{r}{^nC_r}$,then $\frac{T_n}{S_n}$ is equal to

In how many ways can $n$ prizes be distributed among $n$ boys such that no boy gets all the prizes?

Consider the following two statements:
$I.$ If $n$ is a composite number,then $n$ divides $(n-1)!$.
$II.$ There are infinitely many natural numbers $n$ such that $n^3+2n^2+n$ divides $n!$.

Words with or without meaning are to be formed using all the letters of the word $EXAMINATION$. The probability that the letter $M$ appears at the fourth position in any such word is:

The number of ways in which four letters of the word '$MATHEMATICS$' can be arranged is given by

Vedclass Test Series

Exam Paper Generator

Online Exam Module