If he does not draw pictures he will fail the exam
Drawing animate beings such as people and animals is haraam, and is in fact a major sin. We have already quoted the evidence for that in question no. 7222. We have also stated in question no. 9473that if a picture is drawn without the head, then it is no longer haraam.
If a student is required to draw something and he is able to draw a permissible image, then he should do that. In this case it is not permissible to draw a haraam image. Examples of permissible images include trees, rivers and other inanimate things, or he can draw people without heads.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked:
Some students have to draw some animals for the purpose of study. What is the ruling on that? He replied:
It is not permissible to make images of these animals because the Prophet (peace and blessings of Allaah be upon him) cursed the image-makers and said: “The most severely punished of the people on the Day of Resurrection will be the image-makers.” This indicates that making images is a major sin, because this curse only applies to major sins, and the warning of severe punishment only applies to major sins. But it is possible to draw part of the body such as a hand or foot, etc, because these parts cannot live independently, and the apparent meaning of the texts is that what is forbidden is that which could live (independently), because the Prophet (peace and blessings of Allaah be upon him) said in some ahaadeeth: “He (the image maker) will be told to breathe life into it and he will not be able to do so.”
Fataawa Ibn ‘Uthaymeen, 2/272.
He also said:
If a student is told to draw and has no other option, then he should draw an animal without a head.
Fataawa Ibn ‘Uthaymeen, 2/274, 272
If a student is obliged to draw a complete picture, and not doing so may cause him to fail, then Shaykh Ibn ‘Uthaymeen said:
If this is the case then the student may regarded as being forced to do this thing, so the sin will be on the one who told him to do that. But I hope that those in charge will not go to this extent and force the slaves of Allaah to disobey Allaah.
Majmoo’ Fataawa Ibn ‘Uthaymeen, 2/274
And Allaah knows best.