Q260 / 270 · NDA 2013 (Phase 2) · Mathematics

If $\mathrm{C}(28,2 r)=\mathrm{C}(28,2 r-4)$, then what is $r$ equal to?

  • A
    7
  • Correct answer
    B
    8
  • C
    12
  • D
    16

Solution

$\begin{aligned} & { }^{28} \mathrm{C}_{2 r}={ }^{28} \mathrm{C}_{2 r-4} \\ & \Rightarrow 2 r+2 r-4=28 \\ & \Rightarrow 4 r=32 \\ & r=8 \end{aligned}$

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

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