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If ${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$, then find $k$
Options:
Solution:
1077 Upvotes
Verified Answer
The correct answer is:
4
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.
$$
{ }^{12} C_{2 k-1}={ }^{12} C_{k+1}
$$
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.
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