what is the order and the degree of the given diff. equation? the given diff. equation is $$y=1+ \frac{dy}{dx}+\frac{1}{2!}\left(\frac{dy}{dx}\right)^2+\cdots+\frac{1}{n!}\left(\frac{dy}{dx}\right)^n$$
it is given that the order is $1$ and the degree is also $1$. But how it happens because the the highest order $1$ has degree is $n$. so how the given degree is possible?

If you really do mean that those (first) derivatives are raised to powers from $1$ to $n$, then it is a first order differential equation. However, it would be $n$th degree.
Here are the definitions of order and degree for an ODE.
