The responsible agency for conducting the Census in India is:

Office of the Registrar General & Census Commissioner
Ministry of Home Affairs
NITI Aayog
Election Commission of India

The correct answer is: Office of the Registrar General & Census Commissioner.

The Office of the Registrar General & Census Commissioner is the nodal agency for conducting the Census in India. It is a statutory body under the Ministry of Home Affairs. The Office is responsible for planning, organizing, and conducting the Census every 10 years. It also publishes the results of the Census.

The Ministry of Home Affairs is the ministry of the Government of India that is responsible for the maintenance of internal security, law and order, and border management. It is also responsible for the administration of the Union Territories.

NITI Aayog is a policy think tank of the Government of India. It was set up in 2015 to replace the Planning Commission. NITI Aayog is responsible for providing strategic and policy advice to the Government on matters of national importance.

The Election Commission of India is an independent constitutional body responsible for conducting elections to the Parliament of India, the legislative assemblies of the states, and the offices of the President and Vice-President of India. It is also responsible for regulating political parties and ensuring that elections are conducted in a free and fair manner.