A patient presented with his head tilted towards left. On examination, he was having left hypertropia which increased on looking towards right or medially. The muscle which is most likely paralyzed
All of you know following three facts -


In extraocular muscle paralysis, the eye is deviated opposite to the action of the paralysed muscle.
Diplopia is maximum in the direction of action of paralysed muscle.
The patient shifts the head in such direction so that the eye lies in the direction of action of paralysed muscle.


Now see the action of various extraocular musles


Iam taking example of two muscles, one which acts only in horizontal direction(left lateral rectus) and one which acts in 3 different planes (left superior oblique) :


 Left lateral rectus causes abduction of left eye so, in left lateral rectus palsy, the left eye will be deviated towards the right, diplopia will be maximum on looking horizontally left side (left lateral), and the head will be turned towards the left.
In left superior oblique palsy :- i) The left eye will be deviated superiorly and medially (heterotropia, i.e. superior deviation); ii) Diplopia will be maximum while looking right side (left nasal) and inferiorly, i.e. in the direction of left superior oblique action; and iii) The head will be tilted to the left and turned to the right.


Point (iii) requires some explanation. In paralysis of horizontaly acting muscles (medial or lateral rectus) the head is only turned. However, in muscles which acts in multiple planes, the head is turned and tilted.
For example, take the example of left superior oblique in above figure. Left superior oblique causes depression and inward movement of left eye. So, in its paralysis the patient will require position of head which will compensate for this movement. For depression of left eye, the patient will bend (tilt) the head on left side so that left eye will be in lower (depressed) position. For inward movement, the patient will turn the head to the right side. Now, you can easily understand that in superior oblique palsy, the head will be bend (tilted) on left side and turned towards the right side.
Left superior oblique
Left inferior oblique
Right superior oblique
Right inferior oblique