If, in the course of proceedings to obtain letters of administration under the provisions of section 9 or section 10, and within such period as to the High Court seems reasonable, no person appears and establishes his claim to probate of a will, or to a grant of letters of administration as next-of-kin of the deceased, or satisfies the High Court that he has taken and is prosecuting with due diligence other proceedings for the protection of the estate, the case being one in which the obtaining of such probate or letters of administration is not obligatory under the provisions of the Indian Succession Act, 1925 (39 of 1925), and the High Court is satisfied that there is apprehension of misappropriation, deterioration, or waste of the assets or that the grant of letters of administration in such proceedings is other wise necessary for the protection of the assets;
or if a person who has established his claim to a grant of letters of administration as next-of-kin of the deceased fails to give such security as may be required of him by law;
the High Court may grant letters of administration to the Administrator-General.