Is the historical Volatility of a stock always greater than the "Implied Volatility" of the options of that particular stock?

Algos, strategies, code
2

Not really. They can take any value. Also, you could take a look at this chapter to appriciate different types of volatility -

Refer section 19.1.

3

Thanks for your opinion Karthik . I went through the link however the query still remains. Let me refresh it a bit.
As we near expiry does the Implied Volatility start converging near the Annual Volatility ?

4

Implied volatility will be different for each option and it depends on particular strike.
Implied volatlity will not converge to annual volatility at expiry.