Question

Which book is in the first position?

• A. B
• B. C
• C. D
• D. E
• A. B
• B. C
• C. D
• D. E
• A. A
• B. B
• C. C
• D. D

Answer 1

The Correct Option is A

We need to determine the book in the first position.
- Step 1: Set up the row. Five positions: 1, 2, 3, 4, 5 (left to right).
- Step 2: Apply condition 4. E is in position 3:
\[ \_ \, \_ \, E \, \_ \, \_ \] - Step 3: Apply condition 1. A not at ends (1 or 5), so A in 2 or 4.
- Step 4: Apply condition 2. B is immediate left of C (B-C pair). Possible positions: (1,2), (2,3), (4,5).
- Step 5: Apply condition 3. D not adjacent to E (not in 2 or 4).
- Step 6: Test B-C pairs.
- (1,2): B in 1, C in 2.
\[ B \, C \, E \, \_ \, \_ \] - A in 2 or 4: Position 2 = C, so A in 4. D in 5 (since D not in 2 or 4).
\[ B \, C \, E \, A \, D \] - Check: D not adjacent to E (positions 5 and 3), correct. A not at ends, correct.
- Step 7: Try other pairs.
- (2,3): B in 2, C in 3 (but 3 = E, invalid).
- (4,5): B in 4, C in 5. A in 2, D in 1:
\[ D \, A \, E \, B \, C \] - D adjacent to E, invali(d)
- Step 8: Confirm. Only B, C, E, A, D satisfies all conditions. Position 1 = (b)
- Step 9: Check options.
- (a) B: Correct.
- (b) C: Incorrect.
- (c) D: Incorrect.
- (d) E: Incorrect, E in 3.
Thus, the answer is a.

Answer 2

We need the book to the immediate right of Book (a)
- Step 1: Set up new arrangement. Since questions must be unique, solve independently using the given conditions.
- Step 2: Apply condition 4. E in position 3:
\[ \_ \, \_ \, E \, \_ \, \_ \] - Step 3: Apply condition 1. A in 2 or 4.
- Step 4: Apply condition 2. B-C pair in (1,2) or (4,5).
- Step 5: Apply condition 3. D not adjacent to E (not in 2 or 4).
- Step 6: Test A in 4.
- B-C in (1,2):
\[ B \, C \, E \, A \, \_ \] - D in 5 (not adjacent to E).
\[ B \, C \, E \, A \, D \] - Right of A (4) = D (5).
- Step 7: Check other cases. A in 2, B-C in (4,5), D in 1:
\[ D \, A \, E \, B \, C \] - D adjacent to E, invali(d)
- Step 8: Verify. Arrangement B, C, E, A, D: A in 4, right = (d)
- Step 9: Check options.
- (a) B: Incorrect.
- (b) C: Incorrect.
- (c) D: Correct.
- (d) E: Incorrect.
Thus, the answer is c.

Answer 3

We need the book in the last position (position 5).
- Step 1: Apply conditions independently. E in 3 (condition 4):
\[ \_ \, \_ \, E \, \_ \, \_ \] - Step 2: A not at ends (condition 1). A in 2 or 4.
- Step 3: B-C pair (condition 2). Possible: (1,2), (4,5).
- Step 4: D not adjacent to E (condition 3). D not in 2 or 4, so D in 1 or 5.
- Step 5: Test B-C in (1,2).
\[ B \, C \, E \, A \, D \] - D in 5, not adjacent to E. A in 4, not at ends. Correct.
- Step 6: Test B-C in (4,5).
\[ D \, A \, E \, B \, C \] - D adjacent to E, invali(d)
- Step 7: Confirm. Position 5 = (d)
- Step 8: Check options.
- (a) A: Incorrect, A not at en(d)
- (b) B: Incorrect.
- (c) C: Incorrect.
- (d) D: Correct.
Thus, the answer is d.

Answer 4

We need the number of books between E and (d)
- Step 1: Apply conditions. E in 3 (condition 4):
\[ \_ \, \_ \, E \, \_ \, \_ \] - Step 2: A not at 1 or 5, D not adjacent to E, B-C pair.
- Step 3: Use valid arrangement. From previous:
\[ B \, C \, E \, A \, D \] - Step 4: Locate E and (d) E in 3, D in 5.
- Step 5: Count books between. Positions 3 to 5: Position 4 (A). Number = 1.
- Step 6: Verify. Only one valid arrangement.
Thus, the answer is 1.