Which of the following statements is/are correct ?

• Box A is at the extreme right (Position 6), is Orange, and contains Tennis.

• Box C is 5th from the right (Position 2), is Green, and contains Cricket.

• Box C is next to Box B, so Box B is at Position 1 or 3. Since Box A is at 6, and C is at 2, B must be at Position 1 (left of C) or Position 3 (right of C). However, the box with Hockey is between Golf and Volleyball (B). Let's determine positions first.

• The sequence of boxes is 1, 2, 3, 4, 5, 6. A is at 6. C is at 2. B is next to C, so B is at 1 or 3.

• The box with Hockey is between Golf and Volleyball (B). This implies the order is Golf-Hockey-B or B-Hockey-Golf.

• If B is at 1, Hockey cannot be between B and another box to its left. So B must be at 3. Thus, C is at 2, B is at 3.

• Since B (Volleyball) is at 3, and Hockey is between Golf and B, the order must be Golf (Pos 4) - Hockey (Pos 5) - B (Pos 3)? No, 'between' usually implies immediate adjacency in these puzzles or just positional. Let's look at the remaining boxes: 1, 4, 5. Boxes are A(6), C(2), B(3). Remaining boxes: 1, 4, 5.

• Hockey is not in D or E. Hockey is not in Blue or Yellow.

• Golf is in Violet and not in D.

• Let's place the 'Golf-Hockey-B' or 'B-Hockey-Golf' sequence. B is at 3. So Hockey is at 2 or 4? No, C is at 2. So Hockey cannot be at 2. Therefore, Hockey must be at 4 or 5? Wait, 'between' means the box with Hockey is physically located between the box with Golf and the box with Volleyball (B). Since B is at 3, the boxes are 1, 2, 3, 4, 5, 6. The only way a box is 'between' B(3) and another box is if the other box is at 1 (Hockey at 2) or 5 (Hockey at 4) or 6 (Hockey at 4 or 5). But C is at 2. So Hockey cannot be at 2. Thus, the sequence must be B(3) - Hockey(4) - Golf(5) OR Golf(1) - Hockey(2) - B(3) [Impossible as C is at 2]. So it must be B(3) - Hockey(4) - Golf(5). Or Golf(1) is not possible because Hockey would be at 2 which is C. So the order is B(3), Hockey(4), Golf(5). This means Box 4 has Hockey, Box 5 has Golf.

• So: Pos 1: ?, Pos 2: C (Green, Cricket), Pos 3: B (Volleyball), Pos 4: Hockey, Pos 5: Golf (Violet), Pos 6: A (Orange, Tennis).

• Remaining boxes for labels: D, E, F. Positions 1, 4, 5 are occupied by unknown labels? No, we have labels A, B, C, D, E, F. We placed A(6), C(2), B(3). Remaining labels D, E, F for positions 1, 4, 5.

• Golf is in Violet box and not in D. Golf is at Pos 5. So Pos 5 is not D. Pos 5 is either E or F.

• Hockey is at Pos 4. Hockey is not in D or E. So Pos 4 is not D and not E. Therefore, Pos 4 must be F.

• So F is at Pos 4. F contains Hockey.

• Remaining labels D and E for Pos 1 and Pos 5.

• Golf is at Pos 5. Golf is not in D. So Pos 5 is not D. Therefore, Pos 5 is E. Consequently, Pos 1 is D.

• So: Pos 1: D, Pos 2: C, Pos 3: B, Pos 4: F, Pos 5: E, Pos 6: A.

• Colors: C(2) is Green. A(6) is Orange. Golf(5/E) is Violet.

• Remaining colors: Indigo, Blue, Yellow for D(1), B(3), F(4).

• Hockey is in F(4). Hockey is not in Blue or Yellow. So F(4) is not Blue or Yellow. Therefore, F(4) must be Indigo.

• So F is painted Indigo. This matches option (b).

• Remaining colors for D(1) and B(3) are Blue and Yellow.

• We need to check if D is Yellow or B is Blue. The question asks which statement is correct. We established F is Indigo. Let's check the other options. Is D Yellow? We don't have enough info to distinguish D and B between Blue and Yellow yet? Wait, 'Hockey ball is neither in the box painted blue nor in the box painted yellow'. We used this to say F is Indigo. Does it constrain D or B? No. But let's re-read carefully. 'The hockey ball is neither in box D nor in box E'. We used this to say Pos 4 (Hockey) is not D or E. 'The hockey ball is neither in the box painted blue nor in the box painted yellow'. We used this to say F (Hockey) is not Blue or Yellow. So F is Indigo. This is solid. What about D and B? One is Blue, one is Yellow. Is there a constraint? 'Golf ball is in violet box'. 'Box A... orange'. 'Box C... green'. No other color constraints. So D and B can be Blue/Yellow in either order? Let's check the options. (a) D is yellow. (c) B is blue. If D is Yellow, B is Blue. If D is Blue, B is Yellow. Both are possible based on the given info? Wait, usually these puzzles have a unique solution. Let me re-check 'Hockey ball is neither in box D nor in box E'. This was used to identify F. 'Hockey ball is neither in the box painted blue nor in the box painted yellow'. This was used to identify F as Indigo. There is no constraint linking D or B to specific colors other than they are the remaining two. However, option (b) 'F is painted indigo' is definitely true. Options (a) and (c) depend on the arbitrary assignment of Blue/Yellow to D/B unless I missed a clue. Let's re-read. 'Six boxes... arranged from left to right'. 'Golf... not in D'. 'A... orange... extreme right'. 'Hockey... not in D or E'. 'C... green'. 'Hockey... not in Blue or Yellow'. 'C is 5th from right (Pos 2) and next to B'. 'B contains volleyball'. 'Hockey is between Golf and Volleyball'.

• My deduction: Pos 1(D), 2(C), 3(B), 4(F), 5(E), 6(A). Colors: 2(Green), 6(Orange), 5(Violet). Remaining: 1, 3, 4 need Indigo, Blue, Yellow. F(4) has Hockey. Hockey not in Blue/Yellow. So F(4) is Indigo. This is certain. D(1) and B(3) are Blue and Yellow. No constraint distinguishes them. Thus (a) and (c) are not necessarily true, but (b) is always true. Therefore, (b) is the correct answer.