While exam-style questions are a fundamental educational tool serving a variety of purposes, manual construction of questions is a complex process that requires training, experience and resources. Automatic question generation (QG) techniques can be utilized to satisfy the need for a continuous supply of new questions by streamlining their generation. However, compared to automatic question answering (QA), QG is a more challenging task. In this work, we fine-tune a multilingual T5 (mT5) transformer in a multitask setting for QA, QG and answer extraction tasks using Turkish QA datasets. To the best of our knowledge, this is the first academic work that performs automated text-to-text question generation from Turkish texts. Experimental evaluations show that the proposed multitask setting achieves state-of-the-art Turkish question answering and question generation performance on TQuADv1, TQuADv2 datasets and XQuAD Turkish split. The source code and the pretrained models are available at https://github.com/obss/turkish- question-generation.