Starter A gives a reason. It can ideally begin the sentence as the first given sentence is the cause/reason. Starter B can also begin the sentence, as the reason is implied.

If you do not think well before you take a decision, you will repent for it later. This is conveyed in A and B.

All the three starters convey the meaning intended in the two given sentences.

The idea given in the second sentence is a continuation of the idea expressed in the first. Hence conjunctions like 'and', 'or', 'that' can be used to combine the sentences meaningfully.

The first sentence is a statement. The second sentence makes an 'observation' on this statement. The use of 'though' 'although', 'yet' 'despite the fact that', can all be used to combine the sentences without changing their meaning. The use of 'since' is incorrect.

The two sentences bring out the contrast between Lakshman and his brother. This contrast is brought out in A and B.

The second sentence suggests the purpose or a condition for the action mentioned in the first sentence. Hence conjunctions like 'in order that', 'so that', 'if' or 'unless' can be used to combine the given sentences.

The sentences are connected with the idea of cause and effect / result. 'As' and 'on hearing' can be used to combine the sentences meaningfully. The use of 'while', distorts the meaning implied.

The second sentence expresses a contrast and so conjunctions like 'through', 'although', 'yet' 'nevertheless' can be used to combine the sentences meaningfully.

The two sentences are linked with an action and the purpose of the action. 'In order to', 'so as to', 'as', 'so ... that' etc. can be used to combine the sentences.