Q77 / 225 · JEE Main 2004 · Mathematics

The range of the function $f(x)={ }^{7-x} P_{x-3}$ is

  • Correct answer
    A
    $\{1,2,3\}$
  • B
    $\{1,2,3,4,5\}$
  • C
    $\{1,2,3,4\}$
  • D
    $\{1,2,3,4,5,6\}$

Solution

$f(x)={ }^{7-x} P_{x-3}$ $7-x \geq 0 \Rightarrow x \leq 7$ $x-3 \geq 0 \Rightarrow x \geq 3$, and $7-x \geq x-3 \Rightarrow x \leq 5$ $\Rightarrow 3 \leq x \leq 5 \Rightarrow x=3,4,5 \Rightarrow$ Range is $\{1,2,3\}$

Hence, the correct answer is option: 'A'.

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