I already said that I was new to exec() function. After doing some more digging, I came upon 2>&1 which needs to be added at the end of command in exec().
Thanks @mattosmat for pointing it out in the comments too. I did not try this at once because you said it is a Linux command, I am on Windows.
So, what I have discovered, the command is actually executing in the back-end. That is why I could not see it actually running, which I was expecting to happen.
For all of you, who had similar problem, my advise is to use that command. It will point out all the errors and also tell you info/details about execution.
exec('some_command 2>&1', $output);
print_r($output); // to see the response to your command
Thanks for all the help guys, I appreciate it ;)