Seating Arrangement - Beginner Level: relative positions BEGINNER

Solution Approach:

Step 1: Apply the fixed condition
- W sits second from the left → W at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with W at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
• V W Z Y X
• V W Z X Y
• Z W X Y V
• Y W V Z X
• X W V Z Y
• X W Z V Y
(shown up to 6)

Step 3: Test each MCQ option

- "W sits at position 2": ✓ Possible in at least one valid arrangement
- "X sits at position 4": ✓ Possible in at least one valid arrangement
- "X sits at position 1": ✓ Possible in at least one valid arrangement
- "V sits at position 2": ✗ NEVER possible → must be FALSE

Step 4: Conclusion
"V sits at position 2" is impossible in ALL 7 valid arrangement(s) — it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "V sits at position 2" must be FALSE.

Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) → M1(2) → C2(3) → M2(4) → C3(5) → M3(6) → C4(7) → M4(8) → back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7

Step 2: Place persons systematically
- D sits at a corner → pos 1
- E sits second to the RIGHT of D: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- B sits OPPOSITE D (pos 1) → pos 5 ✓
- H at midpoint, NOT adjacent to D(pos 1):
Adjacent to pos 1: pos 8 and pos 2
H → pos 6 (midpoint, not adjacent) ✓
- A sits at corner immediately to the RIGHT of H(pos 6):
1 CW from pos 6 → pos 7 (corner) ✓

Step 3: Remaining persons
Remaining: C, F, G
Fill remaining seats: pos2=C, pos8=F, pos4=G

Final Arrangement (clockwise):
pos1:D → pos2:C → pos3:E → pos4:G → pos5:B → pos6:H → pos7:A → pos8:F

Step 4: Count from LEFT of D to B
Left = anti-clockwise direction from D(pos 1):
pos1(D) → pos8(F) → pos7(A) → pos6(H) → pos5(B)
Persons between (excluding D and B): pos8(F), pos7(A), pos6(H)
Count = 3 person(s)

Answer: Three person(s) sit between D and B.

Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) — all occupied.
Outer circle: 6 positions O1–O6 clockwise — 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- D sits immediately to the right of A (inner circle, facing center: right=CW)
→ A and D are adjacent. Possible: A=I1, D=I2 or A=I2, D=I3, etc.
- B sits opposite to D:
If D=I2, then B=I4. Then A=I1 (left of I2), C=I3 (remaining).
All constraints consistent ✓.

Inner: I1=A, I2=D, I3=C, I4=B

Step 4: Place outer circle persons
- Q faces A(I1) → Q at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- P second to right of R (outer, facing center: right=CW, step 2):
Remaining outer persons: P,R,S at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ R=O2, P=O4, S=O5 ✓
- S(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(P) — NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) ✓.

Step 5: Answer the question
D is at I2. Opposite of I2 = I4 = B.

Final Arrangements:
Inner (CW): I1=A, I2=D, I3=C, I4=B
Outer (CW): O1=Q, O2=R, O3=empty, O4=P, O5=S, O6=empty

Verification:
✓ Q faces A (I1↔O1)
✓ D immediately right of A (I2 is CW from I1)
✓ B opposite D (I4 opposite I2)
✓ P second right of R (O4 = O2 + 2 CW)
✓ S(O5) immediately left of empty O6

Answer: B sits opposite to D.

Solution Approach:

Step 1: Draw rectangular table
Positions 1–10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) — actually:
Bottom traversed right→left: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. ✓
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)

Step 2: Place persons
- A at middle of longer side → pos 7 (mid-bottom)
- I at middle of shorter side → pos 4 (mid-right)
- H second to the RIGHT of A (pos 7):
right(center-facing)=CW: pos7+2 = pos9 → H ✓
- B at a corner → pos 1
- J at corner OPPOSITE to B: pos5 → J ✓
- G second to the LEFT of I (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 → G ✓

Step 3: Fill remaining positions
Remaining persons: D, F, E, C
Remaining seats: [3, 6, 8, 10]

Final Arrangement (clockwise):
pos1:B | pos2:G | pos3:D | pos4:I | pos5:J | pos6:F | pos7:A | pos8:E | pos9:H | pos10:C

Find second to the left of I (pos 4):
Left (anti-CW): pos4 → pos3 → pos2 = G

Answer: G sits second to the left of I.

Solution Approach:

Step 1: Mark total positions
Seats: 1 2 3 4 5 6 7 8 9 10
Total: 10 seats, 8 persons, 2 empty.

Step 2: Place definite positions
- A at seat 3
- F at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

Seat: 1(_) 2(_) 3(A) 4(_) 5(_) 6(_) 7(_) 8(F) 9(_) 10(_)

Step 3: Apply empty seat adjacency
- B sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = B ✓

Seat: 1(_) 2(B) 3(A) 4(_) 5(_) 6(_) 7(_) 8(F) 9(_) 10(_)

Step 4: Apply "fourth to the left" condition
- G sits fourth to the LEFT of F (seat 8)
- Fourth to left: 8 → 7 → 6 → 5 → 4
- G at seat 4 ✓

Seat: 1(_) 2(B) 3(A) 4(G) 5(_) 6(_) 7(_) 8(F) 9(_) 10(_)

Step 5: Locate second empty seat
Remaining persons: E, D, C, H → fill seats 5, 6, 7, 9, 10 minus one empty.
After placing E(5), D(6), C(7), H(10): seat 9 is empty.

Step 6: Final arrangement
Seat: 1(_) 2(B) 3(A) 4(G) 5(E) 6(D) 7(C) 8(F) 9(_) 10(H)

Count persons between empty seats (seat 1 and seat 9):
Seats 2 through 8: B, A, G, E, D, C, F = 7 persons

Verification:
✓ A at seat 3
✓ F at seat 8
✓ Empty at seat 1 (extreme end)
✓ B immediately right of empty seat 1
✓ G fourth to left of F (seat 4 = seat 8 - 4)

Answer: 7 persons sit between the two empty seats.

Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- C sits at one extreme end → Place C at position 1
- D sits second to the right of C → D at position 3
- B sits immediately to the left of D → B at position 2

Position: C B D _ _

Step 3: Apply constraint conditions
- A is not at any extreme end → remaining positions are 4 and 5; A cannot be at 5, so A at position 4
- Only E remains → E at position 5

Final Arrangement (all facing North ↑):
Position: C B D A E

Verification:
✓ C at extreme end (pos 1)
✓ D second to the right of C (pos 3)
✓ B immediately to the left of D (pos 2)
✓ A not at extreme end (pos 4)

Answer: E sits at the other extreme end (position 5).

Solution Approach:

Step 1: Create position-person-profession grid
Position: 1 2 3 4 5 6
Person: _ _ _ _ _ _
Profsn: _ _ _ _ _ _

Step 2: Apply direct conditions
- Amit is Architect, sits at position 3
- The Teacher sits second from the left → position 2
(Which person is the Teacher? Must be Chetan, the only one unassigned here — verified below.)
- Falguni sits second to the right of the Teacher (pos 2): 2+2 = pos 4 → Falguni at position 4

Position: _ [Teacher] Amit Falguni _ _
Profsn: _ Teacher Architect _ _ _

Step 3: Apply adjacency and profession constraints
- The Engineer sits immediately to the RIGHT of Amit(pos 3) → pos 4 = Falguni
∴ Falguni is the Engineer ✓
- The Lawyer sits at right extreme → position 6

Position: _ [Teacher] Amit Falguni _ [law]
Profsn: _ Teacher Architect Engineer _ Lawyer

Step 4: Identify the Engineer
Persons left for pos1,2,5,6: Chetan, Eshaan, Divya, Bina
The Teacher is at pos2. Which person?
Not Amit(pos3), not Falguni(pos4). Try each remaining:
Chetan at pos2 → Chetan=Teacher ✓ (no other constraint violated)

Position: _ Chetan Amit Falguni _ _
Profsn: _ Teacher Architect Engineer _ _

Step 5: Place E, D, F
Remaining persons: Divya,Eshaan,Bina → positions 1, 5, 6.
- Divya is Banker and NOT adjacent to Amit(pos3): adjacent = pos2,pos4.
Divya not at pos2(taken) or pos4(taken). Remaining: pos1, pos5, pos6. All satisfy adjacency ✓.
- Bina sits at an extreme end: pos1 or pos6.
- Eshaan is NOT at an extreme end: Eshaan not at pos1 or pos6 → Eshaan at pos5.
- Bina at extreme: pos1 or pos6.
- Lawyer at pos6. If F=Lawyer, F at pos6. Otherwise F at pos1.
After placing D=pos5: remaining Divya and Bina at pos1 and pos6.
F at extreme → F at pos1 or pos6 (both extreme).
Who is the Lawyer (pos6)? Not Amit(doc), Falguni(ban), Chetan(eng), Eshaan(remaining profsn), Divya(tea).
Lawyer must be Bina. So Bina at pos6 = Lawyer. Divya at pos1 = Banker ✓ (not adjacent to Amit).

Final Arrangement:
Position: 1 2 3 4 5 6
Person: Divya Chetan Amit Falguni Eshaan Bina
Profsn: Banker Teacher Architect Engineer ? Lawyer

Step 6: Determine Eshaan's profession
Professions assigned: Architect(Amit), Engineer(Falguni), Teacher(Chetan), Banker(Divya), Lawyer(Bina)
Remaining profession: Doctor → Eshaan is the Doctor

Verification:
✓ Amit=Doctor at pos 3
✓ Engineer(Chetan) at pos 2
✓ Falguni second right of Engineer (pos 4)
✓ Banker(Falguni) immediately right of Amit
✓ Divya=Teacher at pos 1 (not adjacent to Amit)
✓ Lawyer(Bina) at right extreme (pos 6)
✓ Bina at extreme end (pos 6)
✓ Eshaan not at extreme end (pos 5)

Answer: Eshaan's profession is Doctor.

Solution Approach:

Step 1: Draw rectangular table
Positions 1–10 clockwise:
- Top (longer, 3 persons): pos1(corner-TL), pos2(mid-top), pos3(corner-TR)
- Right (shorter, 2 persons): pos4(mid-right), pos5(corner-BR)
- Bottom (longer, 3 persons): pos6(mid-bot), pos7(corner-BL-ish... wait, pos7 is mid-bottom)
Correction: pos6(mid-bot), pos7(mid-bot2), pos8(corner-BL) — actually:
Bottom traversed right→left: pos6(mid), pos7(mid2)? For 3 persons: corner is shared with adjacent side.
In competitive exams: the 3 bottom persons are at pos6(mid), pos7, pos8(corner-BL).
Actually pos6,7,8 with pos8=BL-corner and pos5=BR-corner. ✓
- Left (shorter, 2 persons): pos9(mid-left), pos10(mid-left2)
- Corners: pos1(TL), pos3(TR), pos5(BR), pos8(BL)
- Longer-side midpoints: pos2(top), pos7(bottom)
- Shorter-side midpoints: pos4(right), pos9(left)

Step 2: Place persons
- D at middle of longer side → pos 7 (mid-bottom)
- J at middle of shorter side → pos 4 (mid-right)
- B second to the RIGHT of D (pos 7):
right(center-facing)=CW: pos7+2 = pos9 → B ✓
- F at a corner → pos 1
- H at corner OPPOSITE to F: pos5 → H ✓
- E second to the LEFT of J (pos 4):
left(center-facing)=anti-CW: pos4-2 = pos2 → E ✓

Step 3: Fill remaining positions
Remaining persons: I, C, G, A
Remaining seats: [3, 6, 8, 10]

Final Arrangement (clockwise):
pos1:F | pos2:E | pos3:I | pos4:J | pos5:H | pos6:C | pos7:D | pos8:G | pos9:B | pos10:A

Find second to the left of J (pos 4):
Left (anti-CW): pos4 → pos3 → pos2 = E

Answer: E sits second to the left of J.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix N at position 1.
- O sits second to the LEFT of N: left(outward)=CW, so O is 2 CW from N.
pos[O] = 3
- K sits opposite O (pos 3): pos 6
- L sits immediately to the RIGHT of K (pos 6):
right(outward)=anti-CW → pos 5
- M sits opposite N (pos 1): pos 4
- Remaining P fills pos 2.

Final Arrangement (clockwise):
pos1:N → pos2:P → pos3:O → pos4:M → pos5:L → pos6:K
(All facing outward ↗)

Find immediate left of O (pos 3):
Left (outward) = clockwise → pos 4 = M

Verification:
✓ O second to left of N (CW direction)
✓ K opposite O
✓ L immediately right (anti-CW) of K
✓ M opposite N

Answer: M sits immediately to the left of O.

Solution Approach:

Step 1: Mark total positions
Seats: 1 2 3 4 5 6 7 8 9 10
Total: 10 seats, 8 persons, 2 empty.

Step 2: Place definite positions
- E at seat 3
- F at seat 8 (seat 8)
- One empty seat at extreme end → seat 1 is empty

Seat: 1(_) 2(_) 3(E) 4(_) 5(_) 6(_) 7(_) 8(F) 9(_) 10(_)

Step 3: Apply empty seat adjacency
- A sits immediately to the RIGHT of an empty seat
- Empty at seat 1 → seat 2 = A ✓

Seat: 1(_) 2(A) 3(E) 4(_) 5(_) 6(_) 7(_) 8(F) 9(_) 10(_)

Step 4: Apply "fourth to the left" condition
- C sits fourth to the LEFT of F (seat 8)
- Fourth to left: 8 → 7 → 6 → 5 → 4
- C at seat 4 ✓

Seat: 1(_) 2(A) 3(E) 4(C) 5(_) 6(_) 7(_) 8(F) 9(_) 10(_)

Step 5: Locate second empty seat
Remaining persons: H, B, D, G → fill seats 5, 6, 7, 9, 10 minus one empty.
After placing H(5), B(6), D(7), G(10): seat 9 is empty.

Step 6: Final arrangement
Seat: 1(_) 2(A) 3(E) 4(C) 5(H) 6(B) 7(D) 8(F) 9(_) 10(G)

Count persons between empty seats (seat 1 and seat 9):
Seats 2 through 8: A, E, C, H, B, D, F = 7 persons

Verification:
✓ E at seat 3
✓ F at seat 8
✓ Empty at seat 1 (extreme end)
✓ A immediately right of empty seat 1
✓ C fourth to left of F (seat 4 = seat 8 - 4)

Answer: 7 persons sit between the two empty seats.

Solution Approach:

Step 1: Understand the setup
Position: 1(Left) 2 3 4(Right)
Row 1 (↓): _ _ _ _
Row 2 (↑): _ _ _ _
Row 3 (↓): _ _ _ _

Facing: Row 1 pos i faces Row 2 pos i; Row 2 pos i faces Row 3 pos i.
(Using viewer's perspective: left=position 1, right=position 4)

Step 2: Apply facing relationships
- A faces R who faces Y: all three in the SAME vertical column.
Place at position 2:
Row1: _ A _ _
Row2: _ R _ _
Row3: _ Y _ _

Step 3: Apply left-right conditions
- C sits to the left of A(pos 2) in Row 1 → C at position 1
Row1: C A _ _

Step 4: Second facing relationship
- S faces C(Row1 pos1) → S at Row2 position 1
- S faces Z → Z at Row3 position 1
Row1: C A _ _
Row2: S R _ _
Row3: Z Y _ _

Step 5: Apply relative positioning in Row 2
- Q sits second to the right of S(pos1): 1+2=3 → Q at Row2 position 3
Row2: S R Q _
Q faces Row1 pos3 → B at Row1 pos3 ✓
Q faces Row3 pos3 → X at Row3 pos3 ✓

Step 6: Fill remaining positions
Remaining: Row1 pos4=D, Row2 pos4=P, Row3 pos4=W

Final Arrangement:
Position: 1 2 3 4
Row 1 (↓): C A B D
Row 2 (↑): S R Q P
Row 3 (↓): Z Y X W

Right extreme of Row 3 = position 4 = W

Answer: W

Solution Approach:

Step 1: Draw square table diagram
Positions clockwise (C=Corner, M=Midpoint):
C1(1) → M1(2) → C2(3) → M2(4) → C3(5) → M3(6) → C4(7) → M4(8) → back to C1
Corner positions: 1, 3, 5, 7
Midpoint positions: 2, 4, 6, 8
Opposite corners: pos1↔pos5, pos3↔pos7

Step 2: Place persons systematically
- H sits at a corner → pos 1
- C sits second to the RIGHT of H: right(center-facing)=CW
2 CW from pos 1 → pos 3 ✓ (corner)
- D sits OPPOSITE H (pos 1) → pos 5 ✓
- E at midpoint, NOT adjacent to H(pos 1):
Adjacent to pos 1: pos 8 and pos 2
E → pos 6 (midpoint, not adjacent) ✓
- A sits at corner immediately to the RIGHT of E(pos 6):
1 CW from pos 6 → pos 7 (corner) ✓

Step 3: Remaining persons
Remaining: B, F, G
Fill remaining seats: pos2=B, pos8=F, pos4=G

Final Arrangement (clockwise):
pos1:H → pos2:B → pos3:C → pos4:G → pos5:D → pos6:E → pos7:A → pos8:F

Step 4: Count from LEFT of H to D
Left = anti-clockwise direction from H(pos 1):
pos1(H) → pos8(F) → pos7(A) → pos6(E) → pos5(D)
Persons between (excluding H and D): pos8(F), pos7(A), pos6(E)
Count = 3 person(s)

Answer: Three person(s) sit between H and D.

Solution Approach:

Step 1: Draw circular diagram
6 persons facing center. Opposite positions are 3 seats apart.
Number positions 1–6 clockwise.

Step 2: Place definite positions
- Fix B at position 1 (reference point)
- B is second to the LEFT of A → A is 2 clockwise from B
pos[A] = 3
- E sits OPPOSITE B (pos 1) → pos 4
- F sits immediately to the right of E (pos 4) → pos 5

Step 3: Resolve remaining positions
Remaining persons: C, D → remaining seats: [2, 6]
C is NOT adjacent to F (pos 5).
Adjacent to pos 5: pos 4 and pos 6.
Therefore C → pos 2, and D → pos 6.

Final Arrangement (clockwise):
pos1:B → pos2:C → pos3:A → pos4:E → pos5:F → pos6:D
(All facing center)

Opposite pairs: pos1↔pos4, pos2↔pos5, pos3↔pos6

A is at pos 3 → opposite = pos 6 = D

Answer: D sits opposite to A.

Solution Approach:

Step 1: Understanding facing outward
When facing outward (away from center):
- LEFT = CLOCKWISE direction
- RIGHT = ANTI-CLOCKWISE direction
- Opposite positions are still n/2 = 3 seats apart.

Step 2: Draw diagram (positions 1–6 clockwise)

Step 3: Apply conditions
- Fix M at position 1.
- O sits second to the LEFT of M: left(outward)=CW, so O is 2 CW from M.
pos[O] = 3
- N sits opposite O (pos 3): pos 6
- P sits immediately to the RIGHT of N (pos 6):
right(outward)=anti-CW → pos 5
- L sits opposite M (pos 1): pos 4
- Remaining K fills pos 2.

Final Arrangement (clockwise):
pos1:M → pos2:K → pos3:O → pos4:L → pos5:P → pos6:N
(All facing outward ↗)

Find immediate left of O (pos 3):
Left (outward) = clockwise → pos 4 = L

Verification:
✓ O second to left of M (CW direction)
✓ N opposite O
✓ P immediately right (anti-CW) of N
✓ L opposite M

Answer: L sits immediately to the left of O.

Solution Approach:

Step 1: Identify genders
Males: Rohan, Kunal, Varun
Females: Swati, Sita, Meera

Step 2: Apply no-adjacent-males constraint
With 3 males and 3 females in a circle of 6, "no two males adjacent" forces strict alternation:
M, F, M, F, M, F (clockwise)

Step 3: Build the arrangement
Position 1: a Male. Let Rohan at pos 1.
Then: pos2=Female, pos3=Male, pos4=Female, pos5=Male, pos6=Female.

Step 4: Apply the mother-grandmother constraint
Sita sits second to the RIGHT of Swati (right=CW):
Female positions: 2, 4, 6.
- If Swati=pos2 → Sita=pos4 ✓ (or pos2+2=pos4)
- If Swati=pos4 → Sita=pos6 ✓
- If Swati=pos6 → Sita=pos8%6=pos2 ✓

Step 5: Apply father-not-adjacent-to-mother (wife) constraint
Kunal's wife = Sita.
Kunal not adjacent to Sita.
Male positions: 1, 3, 5. Female positions: 2, 4, 6.
Testing Swati=pos4 → Sita=pos6:
- Father options: pos1, pos3, pos5.
Adjacent to pos6: pos5, pos1. So father ≠ pos5 and ≠ pos1 → Kunal=pos3 ✓.
Remaining males: Rohan(1), Varun(5). Meera and Swati fill pos2, pos4.
Swati=pos4 (as set). Meera=pos2 ✓.

Final Arrangement:
pos1:Rohan → pos2:Sita → pos3:Varun → pos4:Meera → pos5:Kunal → pos6:Swati

Verification:
✓ No adjacent males: Rohan(1)-Meera(2), Kunal(3)-Swati(4), Varun(5)-Sita(6) — all M-F pairs
✓ Sita(pos6) second right of Swati(pos4): CW 2 from pos4 = pos6 ✓
✓ Kunal(pos3) not adjacent to Sita(pos6): pos3 and pos6 are not adjacent ✓

Find immediately to the right of Meera:
Meera at pos 4. Right (CW) = pos 5 = Kunal.

Answer: Kunal sits immediately to the right of Meera.

Solution Approach:

Step 1: Apply the fixed condition
- Z sits second from the left → Z at position 2 (fixed)

Step 2: Enumerate all valid arrangements
Testing all 120 possible arrangements with Z at pos 2, applying all conditions.
7 valid arrangement(s) found.

Valid arrangement(s):
• V Z W Y X
• V Z W X Y
• W Z X Y V
• Y Z V W X
• X Z V W Y
• X Z W V Y
(shown up to 6)

Step 3: Test each MCQ option

- "V sits at position 2": ✗ NEVER possible → must be FALSE
- "X sits at position 3": ✓ Possible in at least one valid arrangement
- "V sits at position 5": ✓ Possible in at least one valid arrangement
- "X sits at position 5": ✓ Possible in at least one valid arrangement

Step 4: Conclusion
"V sits at position 2" is impossible in ALL 7 valid arrangement(s) — it must be FALSE.
All other options occur in at least one valid arrangement.

Answer: "V sits at position 2" must be FALSE.

Solution Approach:

Step 1: Create the basic diagram
Draw 5 positions in a row, all facing North (↑):
Position: 1 2 3 4 5

Step 2: Apply direct conditions
- C sits at one extreme end → Place C at position 1
- A sits second to the right of C → A at position 3
- B sits immediately to the left of A → B at position 2

Position: C B A _ _

Step 3: Apply constraint conditions
- D is not at any extreme end → remaining positions are 4 and 5; D cannot be at 5, so D at position 4
- Only E remains → E at position 5

Final Arrangement (all facing North ↑):
Position: C B A D E

Verification:
✓ C at extreme end (pos 1)
✓ A second to the right of C (pos 3)
✓ B immediately to the left of A (pos 2)
✓ D not at extreme end (pos 4)

Answer: E sits at the other extreme end (position 5).

Solution Approach:

Step 1: Create position-person-profession grid
Position: 1 2 3 4 5 6
Person: _ _ _ _ _ _
Profsn: _ _ _ _ _ _

Step 2: Apply direct conditions
- Divya is Teacher, sits at position 3
- The Architect sits second from the left → position 2
(Which person is the Architect? Must be Chetan, the only one unassigned here — verified below.)
- Bina sits second to the right of the Architect (pos 2): 2+2 = pos 4 → Bina at position 4

Position: _ [Architect] Divya Bina _ _
Profsn: _ Architect Teacher _ _ _

Step 3: Apply adjacency and profession constraints
- The Banker sits immediately to the RIGHT of Divya(pos 3) → pos 4 = Bina
∴ Bina is the Banker ✓
- The Engineer sits at right extreme → position 6

Position: _ [Architect] Divya Bina _ [law]
Profsn: _ Architect Teacher Banker _ Engineer

Step 4: Identify the Engineer
Persons left for pos1,2,5,6: Chetan, Eshaan, Falguni, Amit
The Architect is at pos2. Which person?
Not Divya(pos3), not Bina(pos4). Try each remaining:
Chetan at pos2 → Chetan=Architect ✓ (no other constraint violated)

Position: _ Chetan Divya Bina _ _
Profsn: _ Architect Teacher Banker _ _

Step 5: Place E, D, F
Remaining persons: Falguni,Eshaan,Amit → positions 1, 5, 6.
- Falguni is Doctor and NOT adjacent to Divya(pos3): adjacent = pos2,pos4.
Falguni not at pos2(taken) or pos4(taken). Remaining: pos1, pos5, pos6. All satisfy adjacency ✓.
- Amit sits at an extreme end: pos1 or pos6.
- Eshaan is NOT at an extreme end: Eshaan not at pos1 or pos6 → Eshaan at pos5.
- Amit at extreme: pos1 or pos6.
- Engineer at pos6. If F=Engineer, F at pos6. Otherwise F at pos1.
After placing D=pos5: remaining Falguni and Amit at pos1 and pos6.
F at extreme → F at pos1 or pos6 (both extreme).
Who is the Engineer (pos6)? Not Divya(doc), Bina(ban), Chetan(eng), Eshaan(remaining profsn), Falguni(tea).
Engineer must be Amit. So Amit at pos6 = Engineer. Falguni at pos1 = Doctor ✓ (not adjacent to Divya).

Final Arrangement:
Position: 1 2 3 4 5 6
Person: Falguni Chetan Divya Bina Eshaan Amit
Profsn: Doctor Architect Teacher Banker ? Engineer

Step 6: Determine Eshaan's profession
Professions assigned: Teacher(Divya), Banker(Bina), Architect(Chetan), Doctor(Falguni), Engineer(Amit)
Remaining profession: Lawyer → Eshaan is the Lawyer

Verification:
✓ Divya=Doctor at pos 3
✓ Engineer(Chetan) at pos 2
✓ Bina second right of Engineer (pos 4)
✓ Banker(Bina) immediately right of Divya
✓ Falguni=Teacher at pos 1 (not adjacent to Divya)
✓ Lawyer(Amit) at right extreme (pos 6)
✓ Amit at extreme end (pos 6)
✓ Eshaan not at extreme end (pos 5)

Answer: Eshaan's profession is Lawyer.

Solution Approach:

Step 1: Draw concentric circles
Inner circle: 4 positions I1(12 o'clock), I2(3), I3(6), I4(9) — all occupied.
Outer circle: 6 positions O1–O6 clockwise — 4 occupied, 2 empty.
Facing alignment: I1↔O1, I2↔O2, I3↔O4, I4↔O5 (O3 and O6 are empty).

Step 2: Inner circle opposite pairs
In a 4-person circle, opposite pairs are 2 seats apart:
I1 opposite I3, I2 opposite I4.

Step 3: Place inner circle persons
- A sits immediately to the right of B (inner circle, facing center: right=CW)
→ B and A are adjacent. Possible: B=I1, A=I2 or B=I2, A=I3, etc.
- C sits opposite to A:
If A=I2, then C=I4. Then B=I1 (left of I2), D=I3 (remaining).
All constraints consistent ✓.

Inner: I1=B, I2=A, I3=D, I4=C

Step 4: Place outer circle persons
- P faces B(I1) → P at O1 ✓
- Outer occupied seats: O1, O2, O4, O5. Empty: O3, O6.
- Q second to right of S (outer, facing center: right=CW, step 2):
Remaining outer persons: Q,S,R at O2, O4, O5.
R=O2 → Q=O4, S=O5 ✓
R=O4 → Q=O6(empty) ✗
R=O5 → Q=O1=P ✗
∴ S=O2, Q=O4, R=O5 ✓
- R(O5) immediately to the LEFT of an empty:
Left(CW) of O5 = O4(Q) — NOT empty.
RIGHT(CW) of O5 = O6(empty). So O5 is immediately to the LEFT of O6(empty) ✓.

Step 5: Answer the question
A is at I2. Opposite of I2 = I4 = C.

Final Arrangements:
Inner (CW): I1=B, I2=A, I3=D, I4=C
Outer (CW): O1=P, O2=S, O3=empty, O4=Q, O5=R, O6=empty

Verification:
✓ P faces B (I1↔O1)
✓ A immediately right of B (I2 is CW from I1)
✓ C opposite A (I4 opposite I2)
✓ Q second right of S (O4 = O2 + 2 CW)
✓ R(O5) immediately left of empty O6

Answer: C sits opposite to A.

Solution Approach:

Step 1: Draw hexagonal arrangement
6 corners H1–H6 clockwise.
Opposite pairs: H1↔H4, H2↔H5, H3↔H6.

Step 2: Place definite positions
- Fix Deepak at H1 (pos 1).
- Deepak opposite Bhanu: opp(pos1) = pos4 → Bhanu at H4

Step 3: Apply relative positioning
- Farhan second to the right of Deepak(pos1):
CW 2: pos1→pos2→pos3
→ Farhan at H3

- Esha second to the right of Charu:
This means F is somewhere and E is 2 CW from F.
We need to find where F and E land.
After placing Deepak=1, Bhanu=4, Farhan=3,
remaining seats: [2, 5, 6].
Esha = 2 CW from Charu: pos5 is 2 clockwise [solver-verified].
→ Charu at pos6, Esha at pos2

Step 4: Apply constraint
- Aman not adjacent to Deepak(pos1):
Adjacent to pos1: pos6 and pos2
→ Aman at pos5 (not adjacent) ✓

Final Arrangement (clockwise):
H1:Deepak → H2:Esha → H3:Farhan → H4:Bhanu → H5:Aman → H6:Charu

Step 5: Find Aman's position relative to Farhan
Farhan at pos3, Aman at pos5.
pos5 is 2 clockwise from pos3.

Verification:
✓ Deepak opposite Bhanu
✓ Farhan second to right of Deepak
✓ Esha second to right of Charu
✓ Aman not adjacent to Deepak

Answer: Aman sits to the second to the right of Farhan.