(a) A diode valve can be used as a rectifier.
(b) A triode valve can be used as a rectifier.
(d) A triode valve can be used as an amplifier.
A diode valve and a triode valve allow current to flow only in one direction. Since a rectifier is a device that converts alternating current (bi-directional) into direct current (uni-directional), a diode valve and a triode valve can be used as rectifiers.
A triode valve can control its output in proportion to the input signal. That is, it can act as an amplifier, whereas a diode valve cannot control its output in proportion to the input signal. So, it cannot be use as an amplifier.