If ${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$, then find $k$

If ${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$, then find $k$
  1. 3
  2. 6
  3. 9
  4. 4

Solution

It is given that, $ { }^{12} C_{2 k-1}={ }^{12} C_{k+1} $ So, either $2 k-1=k+1$ or $ \begin{aligned} & 2 k-1+k+1=12 \\ \Rightarrow \quad k=2 \text { or } k & =4 . \\ \{\therefore & \text { If } \left.{ }^n C_x={ }^n C_y \text { then either, } x=y \text { or } x+y=n\right\} \end{aligned} $ Hence, option (4) is correct

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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