Q43 / 100 · BITSAT 2024 (Memory Based Paper 2) · Mathematics

If ${ }^{22} P_{r+1}:{ }^{20} P_{r+2}=11: 52$, then $r$ is equal to

  • A
    $3$
  • B
    $5$
  • Correct answer
    C
    $7$
  • D
    $9$

Solution

${ }^{22} P_{r+1}:{ }^{20} P_{r+2}=11: 52$ or $(21-r)(20-r)(19-r)=52 \times 2 \times 21$ $\Rightarrow(21-r)(20-r)(19-r)=14 \times 13 \times 12$ $\begin{aligned} & \Rightarrow(21-r)(20-r)(19-r)=(21-7)(20-7)(19 \\ & -7)\end{aligned}$ $\Rightarrow r=7$

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

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