If there are 62 onto mapping from a set X containing n elements to the set $Y=\{-1,1\}$, then $n$ is equal to 

Let $X=\left\{x_1,x_2,\dots ,x_{\mathrm{n}}\right\}$

Each $x_i$ can have two images $viz – 1$ and 1. Thus, there are $2^n$ mappings from $X$ to $Y$.

 But there are exactly two map ping which are not onto. 

These are when all the elements are mapped to – 1 or when all the elements are mapped to 1.

 $\therefore$there are $2^n-2$ onto mapping from $X$ to $Y$

$\begin{array}{l}\text{ Set }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{2}^n-2=62=\Rightarrow 2^n=64=2^6\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}n=6\end{array}$