a) ​The teacher’s absent. Should be The teacher is absent. Using an apostrophe is not correct. All the other examples show that the 'object' is owned by the 'subject'. The teacher's absent could be used as slang, if you put it into speech marks, but it shows the contraction of two words into one. Other examples would be could not = couldn't can not = can't b) The trains collided by a river. The sentence makes no sense when compared to the other sentences which all show something affecting something else. In this case it was two trains that collided and it occurred by a river. But following the meaning of the other sentences it would imply that the river collided with the train. c) This is a tricky one. I would go for I must have something to drink. As it is in the future tense. All the others are in the past tense. Would be interesting to hear others opinions on which is odd one out for this and why.

a. ​The baby’s bottle. ​The nation’s struggle. ​The teacher’s absent.<== ​The nurse’s pay. ​The government’s defeat. b.​The plane was hijacked by a woman. ​The tourists were attacked by a gang. ​The soldier was hit by a bullet. ​The trains collided by a river. <== ​Three hundred people were killed by the earthquake. c.​She must have lost the address. ​Alan must have been there too. ​That must have been awful. <= ​The thieves must have got in through the window. ​I must have something to drink.

I agree with Neil's answers