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'Take over' in this context means to require or consume an extended period, while 'take on' means to accept responsibility, and 'take in' or 'take along' don't convey temporal meaning. 'Nambiar took ages over the project' means he spent an extremely long time working on it. The idiom 'take [time] over' is less common but valid in this usage.

'Absorbed in' is the correct idiom meaning deeply engrossed or completely focused on something, especially studies or work. The preposition 'in' is standard with 'absorbed' to indicate concentration. 'Absorbed on', 'absorbed of', 'absorbed along', and 'absorbed besides' are not correct collocations with this verb.

Among is used when someone is part of a group or surrounded by people. Among friends means being in the company of friends.

Sorry for is used to express regret about someone or something. I am sorry for your nephew expresses sympathy for him.

Believe in means to have faith in the existence of something. Believe in angels means to believe that angels exist.

Good at is used to describe someone's skill or ability in an activity. Good at sky diving means skilled in that activity.

Nobody but means nobody except. Nobody but Jobin knows the way means only Jobin knows the way.

Got off is the correct phrasal verb for dismounting from a vehicle or cycle. Got off the cycle means dismounted from it.

Lived on can mean subsisting on a particular thing. Lived on water suggests surviving only by consuming water, likely in a survival context.

Under stress is the correct prepositional phrase. Under is used to describe being affected by pressure or difficult conditions.

Point in is used in phrases like what's the point in doing something, though point of is more common. Point in is grammatically acceptable.

Did nothing but means did nothing except. Did nothing but smashed him implies the only action taken was smashing him.

Since is used with present perfect tense to indicate when an action began. Have been here since January shows the starting point.

Under can indicate position below something. Live under us likely means they live in the apartment directly below.

The correct answer is 'beside' because it indicates position next to or at the side of the lake. 'Over' means above something, 'along' means following the length of something, 'off' means away from, and 'but' is a conjunction.