Infra-red rays are A. Longitudinal waves B. Transverse waves C. Mechanical waves D. Electromagnetic waves

Infrared rays are part of the electromagnetic spectrum, with wavelengths just longer than red light. Like all electromagnetic waves they are transverse (the electric and magnetic fields vibrate at right angles to the direction of travel) and need no medium. They are not longitudinal or mechanical waves, so the correct pair is B and D.