The problem asks to identify the incorrect statement based on the seating arrangement of five persons: A, B, C, D, and E.
Analyzing Seating Constraints
- There are 5 positions in the row: 1, 2, 3, 4, 5.
- C is in the middle: C is at position 3. Arrangement: $_ _ C _ _$
- D is at an extreme end: D is either at position 1 or position 5.
- At least two persons between B and E: The number of positions between B and E must be 2 or more. This implies the difference in their positions must be at least 3 (e.g., position 1 and 4, or 1 and 5, or 2 and 5). Mathematically, $|Pos(B) - Pos(E)| \ge 3$.
Determining Possible Arrangements
We consider the two cases for D's position:
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Case 1: D is at position 1.
Arrangement: $D _ C _ _$
Positions available for B and E are 2, 4, 5. To satisfy $|Pos(B) - Pos(E)| \ge 3$, B and E must occupy positions 2 and 5. The remaining person, A, takes position 4.
- Subcase 1a: B at 2, E at 5. Arrangement: $D B C A E$. (Positions 3 and 4 are between B and E).
- Subcase 1b: E at 2, B at 5. Arrangement: $D E C A B$. (Positions 3 and 4 are between E and B).
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Case 2: D is at position 5.
Arrangement: $_ _ C _ D$
Positions available for B and E are 1, 2, 4. To satisfy $|Pos(B) - Pos(E)| \ge 3$, B and E must occupy positions 1 and 4. The remaining person, A, takes position 2.
- Subcase 2a: B at 1, E at 4. Arrangement: $B A C E D$. (Positions 2 and 3 are between B and E).
- Subcase 2b: E at 1, B at 4. Arrangement: $E A C B D$. (Positions 2 and 3 are between E and B).
The possible valid arrangements are: $D B C A E$, $D E C A B$, $B A C E D$, $E A C B D$.
Evaluating the Statements
Now, let's check each statement against these arrangements:
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Statement 1: E can be on extreme left.
This is true in arrangement $E A C B D$, where E is at position 1.
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Statement 2: E can be on extreme right.
This is true in arrangement $D B C A E$, where E is at position 5.
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Statement 3: A cannot be on extreme left.
In all derived arrangements (A is at position 4 or 2), A is never at the extreme left (position 1). This statement is true.
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Statement 4: A is always a neighbour of B or D.
- In $D B C A E$: A is at position 4. Neighbours are C (3) and E (5). A is not adjacent to B (2) or D (1). This contradicts the statement.
- In $D E C A B$: A is at position 4. Neighbours are C (3) and B (5). A is adjacent to B. Statement holds.
- In $B A C E D$: A is at position 2. Neighbours are B (1) and C (3). A is adjacent to B. Statement holds.
- In $E A C B D$: A is at position 2. Neighbours are E (1) and C (3). A is not adjacent to B (4) or D (5). This contradicts the statement.
Since the statement "A is *always* a neighbour of B or D" is false for arrangements $D B C A E$ and $E A C B D$, the statement itself is incorrect.
Conclusion
The statement that is incorrect is "A is always a neighbour of B or D".
Important Questions from Seating Arrangement (Notes)
Read the directions carefully and give the answer from the given options.
P, Q, R, S, T, K, L, M and N are sitting around a circle facing the centre.
K is $4^{th}$ to the right of P and P is $3^{rd}$ to the right of Q.
N is $4^{th}$ to the left of Q and $3^{rd}$ to the right of S.
R is $2^{nd}$ to the right of M and M is the immediate neighbour of P.
T is $2^{nd}$ to the left of L.
Who is to the immediate left of K?
Seven people, F, J, M, L, R, V and X, are sitting in a row, facing north.
Only three people sit to the left of X. Only M sits to the right of R. Only three people sit between R and V. J sits at some place to the left of L but at some place to the right of F.
How many people sit to the left of V?Seven boxes, A, B, C, D, E, F and G, are kept one over the other but not necessarily in the same order. Only A is kept above F. Only D is kept between F and C. Only E is kept below B. How many boxes are kept below C?
P, Q, R, S, T, U and V are sitting in a row, facing north. No one sits to the left of U. Only four people sit between U and R. Only three people sit to the right of V. P sits to the immediate left of S. Q is not an immediate neighbour of V. How many people sit between P and T?
Six people, B, C, D, I, J and K, are sitting around a circular table facing the centre. Only two people sit between B and I when counted from the right of I. K sits to the immediate left of J. I sits to the immediate right of C. Who among the following are the immediate neighbours of D?
