The domain of the function f(x) = {}^{7-x}P_{ | vedclass

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

Question

(A) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r$ must be non-negative integers.Here,$n = 7-x$ and $r = x-1$

Vedclass · Accepted Answer

$x \in \{1, 2, 3, 4\}$

Vedclass · Answer

(A) For the permutation ${}^{n}P_{r}$ to be defined,we must have $n \ge r \ge 0$ and $n, r$ must be non-negative integers.Here,$n = 7-x$ and $r = x-1$.Condition $1$: $n \ge r \implies 7-x \ge x-1 \implies 8 \ge 2x \implies x \le 4$.Condition $2$: $r \ge 0 \implies x-1 \ge 0 \implies x \ge 1$.Condition $3$: $n \ge 0 \implies 7-x \ge 0 \implies x \le 7$.Combining these,we get $1 \le x \le 4$.Since $x$ must be an integer for the permutation notation,the domain is $\{1, 2, 3, 4\}$.

The domain of the function $f(x) = {}^{7-x}P_{x-1}$ is:

Similar Questions

How many numbers can be formed using the digits $0, 1, 2, 3, 4, 5$ that are greater than $3000$ (repetition is not allowed)?

Find the number of different $8$-letter arrangements that can be made from the letters of the word $DAUGHTER$ such that all vowels occur together.

How many numbers can be formed using the digits $1, 2, 3, 4$ if repetition of digits is not allowed?

Find the total number of arrangements of the letters of the word $EAMCET$ such that no two vowels are together.

The number of $3$ digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition of digits is allowed is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module