Paid up Capital

This word is going to keep reappearing in next few articles, so better understand it in advance.
You already saw that there are two ways to finance a company: Debt + Equity.
Paid up Capital means the amount of money contributed via Equity (shareholders)

Private company

It has a minimum paid-up capital of Rs.1 lakh
It needs minimum to members and maximum 50 members (i.e. The persons who hold its 'equity')
This company is to use the word "Private Limited" at the end of its name.
It cannot have more than 50 members
It cannot borrow for general public.
For example Balaji Telefilms private ltd= Ektaa Kapoor's company, involved in making those boring Saas Bahu serials.
Another example: Neela telefilms private ltd. = Asit Modi's company, they produce the comedy serial Tarak Mehta Kaa oolta Chashmaa.
Flipkart.com : the online shopping website is also a private company, started by Sachin and Binni Bansal.

It has minimum paid-up capital of Rs.5 lakh.
Requires minimum seven members to start a public company.
It has to hold annual general meeting of shareholders.
It can borrow from general public via IPOs and Bonds.
For example, Infosys started as a private ltd company in 1981, but in 1992, it re-registered itself as a Public Ltd company and launched the IPO in 1993.

If company A holds more than 50% Shares of company B then,
Company A is a holding company
Company B is a subsidiary company
Example: Coal India is a holding company. Bharat Coking ltd, Mahanadi CoalFields ltd are its subsidiary companies.
Similarly, Konkan Railway is a subsidiary company of Indian Railways. Although Indian Railways is not a 'Holding Company', it is a Departmental undertaking.

They are involved in some commercial activity such as engineering, manufacturing etc. But
They're directly controlled by the government, just like any other department
For example: Indian Railways, postal Department.
They are not registered as companies under the companies act
They are wholly financed by

Source : mrunal's blog on civils