Correct option is A
The correct answer is (a) by the Central Government.
Explanation
The Delhi Special Police Establishment (DSPE) was constituted under the Delhi Special Police Establishment Act, 1946. Although the name includes "Delhi," its administrative and legal origin is tied strictly to the Union.
Why (a) is correct: According to Section 2(1) of the DSPE Act, the Central Government may constitute a special police force for the investigation of certain offences in any Union Territory. It is a federal agency under the administrative control of the Ministry of Personnel, Public Grievances and Pensions (specifically the Department of Personnel and Training - DoPT).
Why (b) is incorrect: The Government of the National Capital Territory (NCT) of Delhi has no role in the constitution or administration of the DSPE. "Police" in Delhi is a subject that falls under the Union List, not the State/UT list.
Why (c) is incorrect: While it was initially constituted for the Union Territories, Section 5 of the Act allows the Central Government to extend its powers and jurisdiction to any area in a State (subject to the consent of that state under Section 6). Thus, it is a pan-India agency, not limited to Delhi.
Why (d) is incorrect: The DSPE does not investigate "all" criminal cases. It can only investigate offences that are specifically notified by the Central Government under Section 3 of the Act.