Five children namely 1, 2, 3, 4, and 5 are sitting in a

Solution

 Since one person sits between 2 and 3 and one person sits between 2 and 4, it means 2 must be sitting at the center and 3 at the extreme right end.  One person sits between 5 and 1, means 5 and 1 sit on the immediate left and right of 2 respectively.  5 sits to the immediate right of 4, means 4 is at the extreme left end. Final arrangement is shown below: From above it is clear that 3 and 4 sit at the extreme ends. Hence, the correct answer is (B).