Can the i2c data lines be stretched for about 75 feet, where my pi is master (placed in living room) and arduino(placed in some room) as slave

yes, but you need to adapt the pull up resistor

Check - Gammon Forum : Electronics : Microprocessors : I2C - Two-Wire Peripheral Interface - for Arduino - for all the details.

No. 75 feet is 22 meters.
Suppose the Raspberry Pi is the I2C Master, with three Slaves. The maximum total length of I2C can be 0.5 up to 2 meters. Let's assume you have luck and can do 1 meters of total length for the I2C bus. Each Slave should be at 33cm distance. That is 13 inch. Maybe that is enough for a small dollhouse.

The I2C is called a 'bus', but it was never designed to be used with a cable. It was designed to be used inside a television.

What about using wireless modules ?

it depends, see a.o. - Maximum I2C Bus Length? - Electrical Engineering Stack Exchange
and - http://www.nxp.com/documents/application_note/AN10658.pdf

Those links confirm what I wrote.

qutub, there are chips that turn the I2C bus into some kind of RS-485 signal. That signal can be used with a twisted pair cable. The normal I2C bus can not do that. Therefor you will need extra hardware for the 75 feet.
A common mistake with the normal I2C bus is that only the specification of 3mA and 400pF is used. However, crosstalk between SDA and SCL can be a bigger problem. If for example a change of the SDA causes a pulse in the SCL, some chips might see a clock pulse and other chips not, that will make the I2C bus unreliable.

Hi Koepel and Rob tillart,
thanks guys for the valuable info. This is for my home automation project. But koepel after converting i2c signals into rs485, shouldn’t i need to convert it back to origianl i2c signal, to feed it to slave(arduino).
and Koepel, using wireless modules with arduino uno is not that cost effective for me and also using another Pi (because even a Pi is costly as you know). So thought of using I2C to actuate the relay through arduino which is more than 50 feet from my master Pi.

I have another doubt, can i stretch GPIO pin of arduino upto this distance(i.e more than 50 feet), if yes then this will sove my problem.

Of course, you need those chips for long cables at both ends. At the Master and at the Slave.

A wireless module can be cost effective :wink:
A few dollars can be cheaper than a long cable (and perhaps drilling holes and so on).

A GPIO pin signal can be used. I would add a RC filter for protection.
The Raspberry Pi is 3.3V and if the Arduino is 5V, then it is more reliable if the signal is measured with an anlog input or some kind of level shifting is used.

The grounds will be connected. If both have different power supplies, then I would seperate them with an opto-coupler. That is the safest solution and solves also most noise and does level shifting.