The answer is simple, NO! The sequential order is not necessary to be followed in the exam. Instead, you must adopt the style of answering as you find it most comfortable and favourable for yourself. Any examiner or the marker would like to read the right answers, of course! You tend to put a fine impression at the examiner when writing all the correct answers and getting a good score. If you know all your answers, go with the serial order of the questions. However, if you are dicey about certain aspects, prefer going with the correct answers at the initial.
Alternative approach to support my reason would be to save your time. As you know exam stands on two aspects, accuracy and time management. In case, you believe certain answers are going to take huge chunk of time, save them for the last. The questions for which the answers are in your mind or are easy to attempt, kindly attempt those first. This will not only save your score but you will be relaxed while attempting the complicated problems.
But remember if you started say Q No. 2 in starting then all parts of Q No. 2 must be at one place. Say there are three parts in Q No 2 i.e. 2(a), 2(b) and 2(c). You must solve all parts before starting next Q. But you may solve in any sequence like 2(b), 2(c) and 2(a) etc. internal sequence is not required. Now what if you are dicey about answer of Q 2(b) or 2(c) or 2(a) then leave space for that part and start next Q.
In the nutshell, order is not a priority. The sequence is your choice as this will not only get you marks but also save your time.
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