In which of the given pairs of people, is odd number of people sitting between them?

As many people sit to the left of E as to the right of E, => E sits in the middle.

Only one person sits between E and O

Case 1 : O sits second to the left of E.

L sits third to the left of P and P is not an Immediate neighbour of O. Also, P does not sit at any end.

=> L sits to the immediate left of E and P sits second to the right of E.

Only three persons sits between B and C and B is not an Immediate neighbour of E, => C sits to the immediate right of E and B sits fourth to the left of C.

Since, D does not sit at any end, => D sits to the immediate right of P.

Also, there are two people between B and E, => there should be only 1 person sitting between E and N, which is not possible as shown :

Case 2 : O sits second to the right of E.

L sits third to the left of P and P is not an Immediate neighbour of O. Also, P does not sit at any end.

=> P sits to the immediate left of E and L sits at extreme left end.

Only three persons sits between B and C and B is not an Immediate neighbour of E, => C sits to the immediate right of E and B sits fourth to the left of C.

The number of people sitting between B and E is 2, so number of people sitting between E and N should be 1, => N sits second to the left of E.

Since, D does not sit at any end, => M sits at right end and D to its immediate left. The arrangement :

Number of people sitting between E and M = 3   (odd)

B and M = 6

L and C = 4

L and P = 2

P and O = 2

=> Ans - (A)