India is considered a `Republic` mainly because the head of state is elected. This means that the President of India, who holds the highest position in the country, is elected by the people. This is in contrast to a monarchy, where the position of the head of state is passed down through hereditary succession.
The other options provided do not fully explain why India is considered a Republic, as they focus on other aspects. Option 2 mentions India gaining independence on 15th August 1947, which is an important historical event but not directly related to India being a Republic. Option 3 mentions India having its own written constitution, which is true but does not inherently make it a Republic. Option 4 mentions India having a parliamentary form of government, which is true but not the main reason for it being considered a Republic.
Therefore, the correct answer is option 1.