How many questions are there in the question paper?

In a question paper there are twelve questions, out of which only six are to be answered, six questions have one alternative each. Each question has four parts only three of which are to be answered.

Yes, it's the correct choice.

There are 12 questions
In them 6 questions have one alternative each, means there are two questions. So, total 12 questions, remaining 6 questions have no alternative. Only 6 questions are there. Total 12 + 6 questions means there are 18 are questions. Each question has 4 parts. 18 * 4 = 72 questions.