The two given sentences suggest a contrasting idea. 'Though it was difficult, I managed to solve it'. Hence, conjunctions like 'though', 'but', etc.. can present the idea meaningfully. The use of 'as' or 'for' distorts the meaning.

Conjunctions 'but' and 'however' can be used to combine the two sentences with out changing their meaning.

Because she is an excellent teacher she is liked by all her students. This meaning is conveyed by all the three starters.

He deserves to be well-paid, though he is not. Hence, conjunctions like but, though, although, in spite of the fact that, etc. can be used to effectively put forth the idea while combining the two sentences.

The two sentences imply that in order to overcome the adversities of life a positive attitude is necessary. This meaning is conveyed using all the three probable starters.

The reason for him being incarcerated is that he was proved guilty of committing the crime, this is conveyed by all the three sentences.

Inspite of being almost eighty years old he has a zest for life, this is implied in A and C.

The two sentences imply that inspite of the government imposing a ban on child labour, it still continuous surreptitiously. This meaning is conveyed when the two sentences are combined using 'despite' and 'although'.

A and B convey the meaning implied in the two sentences.

Students are busy burning the midnight oil because the examinations are fast approaching. This is conveyed through A and C.