Is Expenditure by government in providing free eduction included/excluded in National Income?

Yes,

It will be included in the national income as it is a part of the government final consumption expenditure.

Explanation:-

The government spends generally for the welfare of the society. It includes maintaining law and order, security and providing free services to the poor.

It comes under the government’s final consumption expenditure.

Government final consumption expenditure is included in national income through the expenditure method.