COMEDK · Maths · 4. Permutation Combination
The range of the function \(f(x) = {}^{(7-x)}P_{(x-3)}\) is
- A \(\{1, 2, 3, 4\}\)
- B \(\{1, 2, 3, 4, 5\}\)
- C \(\{1, 2, 3\}\)
- D \(\{1, 2, 3, 4, 5, 6\}\)
Answer & Solution
Correct Answer
(C) \(\{1, 2, 3\}\)
Step-by-step Solution
Detailed explanation
For \(f(x) = {}^{(7-x)}P_{(x-3)}\) to be defined, the following conditions must be satisfied: \(7 - x \ge 0 \Rightarrow x \le 7\) \(x - 3 \ge 0 \Rightarrow x \ge 3\) \(7 - x \ge x - 3 \Rightarrow 2x \le 10 \Rightarrow x \le 5\) Also, \(x\) must be an integer. From the above…
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