Explanation:

This question pertains to international agreements and current affairs regarding cooperation in disaster management. - **Option (A) Japan:** This is the correct answer. The Union Cabinet of India, under the chairmanship of the Prime Minister, approved the signing of a Memorandum of Understanding (MoU) between India and Japan. This MoU specifically focuses on strengthening cooperation in the field of Disaster Management. The agreement aims to enhance collaboration through the exchange of information, technology, and personnel, and to foster mutual assistance in disaster risk reduction and response. Both India and Japan are highly susceptible to various natural disasters, making such bilateral cooperation critically important. - **Option (B) Bangladesh:** India and Bangladesh maintain extensive cooperation, including in disaster management, particularly concerning floods and cyclones in the Bay of Bengal region. However, the specific MoU approved by the Cabinet for cooperation in disaster management, as referenced in the question, was with Japan, not Bangladesh. - **Option (C) Sri Lanka:** India and Sri Lanka also engage in collaboration on disaster management, especially in areas like maritime safety and tsunami warning systems. Despite this, the particular Cabinet approval for an MoU in the context of the question was with Japan, not Sri Lanka. - **Option (D) Nepal:** India and Nepal share a long border and face similar risks from seismic activity and floods. They have ongoing cooperation in disaster relief and preparedness. However, the specific MoU approval mentioned in the question was with Japan.\nThus, the correct country with which India's Cabinet approved an MoU on cooperation in disaster management is Japan.