Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least.

In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.

Question: If B scores the least, the rank of C will be

The correct option is Second or third.

Let us break down the solution step-by-step based on the rules and conditions provided:

1. Identify the student who scores the highest and the least:
We are given that either C or F scores the highest.
Condition 1: If C scores the highest, then E scores the least.
Condition 2: If F scores the highest, then B scores the least.
The question states that B scores the least. Since B scores the least, C cannot be the highest scorer (because if C were the highest, E would have to be the least). Therefore, F must be the highest scorer.
So, we have:
Rank 1 (Highest): F
Rank 6 (Least): B

2. Analyze the relative positions of the remaining students:
The remaining students to be ranked from Rank 2 to Rank 5 are A, C, D, and E.
We are given the following rules:
- D scores higher than A, but they are close competitors. This means D is ranked immediately above A (they form an adjacent pair, DA).
- C scores higher than A (C $>$ A, meaning C has a better rank than A).

3. Determine the possible ranks for C:
Since D and A are close competitors, they must occupy adjacent ranks. Let us test the possible positions for the pair (D, A) within the ranks 2, 3, 4, and 5:

Case 1: D is Rank 2 and A is Rank 3.
If A is Rank 3, then C (who must score higher than A) must be Rank 2. However, Rank 2 is already occupied by D. Therefore, this case is not possible.

Case 2: D is Rank 3 and A is Rank 4.
The remaining ranks for C and E are Rank 2 and Rank 5.
Since C must score higher than A (Rank 4), C must occupy Rank 2, and E will occupy Rank 5.
This gives the valid ranking order: F (1), C (2), D (3), A (4), E (5), B (6).
In this arrangement, the rank of C is Second.

Case 3: D is Rank 4 and A is Rank 5.
The remaining ranks for C and E are Rank 2 and Rank 3.
Since both Rank 2 and Rank 3 are higher than A's rank (Rank 5), C can occupy either of these ranks:
- If C is Rank 2 and E is Rank 3, the ranking order is: F (1), C (2), E (3), D (4), A (5), B (6). Here, C is Second.
- If E is Rank 2 and C is Rank 3, the ranking order is: F (1), E (2), C (3), D (4), A (5), B (6). Here, C is Third.

Thus, the rank of C will be either Second or third.