Explanation:

...First statement is incorrect. There is no clear definition of what shell company is in the Companies Act, or any other Act. But typically shell companies include multiple layers of companies that have been created for the purpose of diverting money or for money laundering.
Second statement is correct. They can be set up by business people for both legitimate and illegitimate purposes. Illegitimate purposes for registering a shell company include hiding particulars of ownership from the law enforcement, laundering unaccounted money and avoiding tax. With the shell company as a front, all transactions are shown on paper as legitimate business transactions, thereby turning black money into white.
Not all shell companies may be money laundering vehicles. There are many shell companies that work within legal limits and do not have financial irregularities. For example, a company may separate its HR function into another company altogether. The second one is a legal entity, which operates like any other company.
Third statement is incorrect. Not all the shell companies barred from carrying out business activities in India.