Explanation:

• The Cabinet Secretariat is responsible for the administration of the Government of India (Transaction of Business) Rules, 1961 and the Government of India (Allocation of Business) Rules 1961, facilitating smooth transaction of business in Ministries/ Departments of the Government.
• This Secretariat provides Secretarial assistance to the Cabinet and its Committees, and also assists in decision-making in Government by ensuring Inter-Ministerial coordination, ironing out differences amongst Ministries/ Departments, and evolving consensus through the instrumentality of the standing/ Adhoc Committees of Secretaries. Through this mechanism, new policy initiatives are also promoted.
• The Cabinet Secretariat ensures that the President, the Vice President, and Ministers are kept informed of the major activities of all Ministries/Departments by means of a monthly summary of their activities.
• Hence, statement 1 is correct.
• Management of major crisis situations in the country and coordinating activities of various Ministries in such a situation is also one of the functions of the Cabinet Secretariat.
• The Cabinet Secretariat functions directly under the Prime Minister.
• Hence, statement 2 is correct.
• The administrative head of the Secretariat is the Cabinet Secretary who is also the ex-officio Chairman of the Civil Services Board.
• The business allocated to the Cabinet Secretariat under Government of India (Allocation of Business) Rules, 1961 includes (i) Secretarial assistance to the Cabinet and Cabinet Committees; and (ii) Rules of Business.