IT is very strange that you forgot to mention the date in class 10th answer sheet because there are  invigilators just  to sign your answer scripts to ensure that you have filled all the necessary details in the answer script however if that happened to then I don't think that there would be any problem because the exams are conducted altogether and they already have the details for schedule of the exam and also it is the fault of invigilator to not to recognise that you have not mention the date so so you can just ask for your exam centre and narrate the problem otherwise schools might also help you in that case. This is more subjective aspect because every schools treated differently so you should contact your school staff.