Let $f(x)=1+2 x^2+2^2 x^4+\ldots+2^{10} x^{20}$. Then, f(x) has

more than one minimum exactly one minimum at least one maximum none of these

exactly one minimum

We have, $f(x)=1+2 x^2+2^2 x^4+...+2^{10} x^{20}$ $\Rightarrow f'(x)=x\left(4+4 . 2^2 . x^2+...+20 . 2^{10} x^{18}\right)$ Clearly, f'(x) = 0 at x = 0 only and f''(0) > 0 Hence, f(x) has exactly one minimum.