As in the most of the papers around, what I wanted was to use symbols for the footnotes in the title page; and to use numbers for rest of the document. By,

\documentclass[11pt, twocolumn, titlepage]{article}

...

\maketitle

...

I was getting numbers for both. And by,

\documentclass[11pt, twocolumn]{article}

...

\maketitle

...

I got what I wanted, but with a numbered title page! So, after Googling a little, I found this trick:

\documentclass[11pt, twocolumn, titlepage]{article}

...

\renewcommand\thefootnote{\fnsymbol{footnote}}
\maketitle
\renewcommand\thefootnote{\arabic{footnote}}
...

Thank God, I am using TeX after ~30 years it’s been invented. Phew!