In the context of Indian history, the principle of 'Dyarchy (diarchy)' refers to

1. A

   Division of the central legislature into two houses.

   Division of the central legislature into two houses is bicameralism, introduced in a different sense by the Government of India Act, 1919 at the centre. That is not what dyarchy means. This option is not the key.

2. B

   Introduction of double government i.e., Central and State governments.

   Double government as Centre and provinces is a federal or devolutionary arrangement, not the technical meaning of dyarchy in Indian constitutional history. This option is therefore wrong.

3. C

   Having two sets of rulers; one in London and another in Delhi.

   Two sets of rulers in London and Delhi describes the Secretary of State / Governor-General dual control in a loose way, not the 1919 dyarchy device. This option is not the key.

4. D

   Division of the subjects delegated to the provinces into two categories.

   Dyarchy under the Government of India Act, 1919 split provincial subjects into transferred (ministers responsible to the legislature) and reserved (Governor and executive council). That division of provincial subjects into two categories is the official key.

Summary. Official key is (d) Division of the subjects delegated to the provinces into two categories. Dyarchy (Montagu–Chelmsford) put some provincial heads under Indian ministers and kept others reserved to the Governor. Bicameralism, Centre–province duality, and London–Delhi dual control are different ideas. The 1935 Act ended provincial dyarchy and introduced provincial autonomy. Only (d) is the textbook definition.