Free Topic-Wise General Studies MCQs
Challenge your logical deduction with Seating Arrangements MCQs. Practice linear and circular arrangement problems mapped to the latest UPSC CSAT reasoning trends.
Your Total Marks
Syncing Benchmark...
Want to redo this specific test later?
REF ID (Save this!):
Explanation: The number of handshakes equals the number of ways to choose 2 persons from 12, which is C(12, 2) = 12 × 11 / 2 = 66.
Explanation: With boys and girls alternating starting with a boy, odd positions are boys and even positions are girls. A is 15th from the left (odd position), so A is a boy. There are 45 − 15 = 30 students to his right, starting from position 16 (a girl). In 30 alternating positions, exactly half are girls, giving 15 girls.
Explanation: B is 44 − 16 + 1 = 29th from the left. After interchange, A moves to position 29 and B moves to position 20. Persons between = 29 − 20 − 1 = 8.
Explanation: Maximum persons between occurs when the total is minimized while still accommodating both positions. With total = 25, B is 1st from the left and A is 20th from the left, giving 20 − 1 − 1 = 18 persons between them.
Explanation: B's position from the left = (Position of A + Position of C) / 2 = (12 + 38) / 2 = 25. B's position from the right = 55 − 25 + 1 = 31.
Explanation: Position from right = Total number of persons − Position from left + 1. Here, 45 − 18 + 1 = 28.
Explanation: Adding students to the right end does not change A's position from the left. The new total is 32 + 6 = 38. A's new position from the right = 38 − 14 + 1 = 25.
Explanation: Students to the left of A: 12 − 1 = 11. B is 36 − 18 + 1 = 19th from the left. Students between A (12) and B (19): 19 − 12 − 1 = 6. Including B himself (1), total facing South = 11 + 6 + 1 = 18.
Explanation: Facing the centre, left is clockwise and right is counter-clockwise. With B at 0, A is at position 4. C is 6th to the right (counter-clockwise) of B, so C is at position 9. The shorter path between A (4) and C (9) is clockwise, passing through positions 5, 6, 7, and 8, giving 4 persons between.
Explanation: Total persons = New position of Ram + Old position of Shyam − 1 = 17 + 14 − 1 = 30. Shyam's new position = Total − Ram's old position + 1 = 30 − 9 + 1 = 22.
Explanation: In a circular arrangement, each person has 2 immediate neighbors. Each handshake involves 2 persons, so total handshakes = 15 × 2 / 2 = 15.
Explanation: Facing the centre, right is counter-clockwise and left is clockwise. With B at 0, A is at position 8. C is immediately to B's left (clockwise), so C is at position 1. D is 2nd to the left (clockwise) of C, so D is at position 3. The shortest path between A (8) and D (3) is clockwise, passing through positions 7, 6, 5, and 4, giving 4 persons between.
Explanation: Minimum total with overlap and at least 5 persons between: Total = Position of A from left + Position of B from right − Persons between − 2 = 14 + 19 − 5 − 2 = 26.
Explanation: Let the total be T. Using the non-overlap formula: T = A's position from left + Persons between + B's position from right = 12 + T/3 + 18. Solving: 2T/3 = 30, so T = 45.
Explanation: Persons between = Total − (Position from left + Position from right). Here, 50 − (15 + 12) = 23.
Explanation: Facing the centre, right is counter-clockwise. With B at 0, A is at position 6. C diametrically opposite B is at position 10. From the left of A (clockwise), the path from 6 to 10 passes through positions 5, 4, 3, 2, 1, 0, 19, 18, 17, 16, 15, 14, 13, 12, and 11, giving 15 persons between.
Explanation: Total persons in a row = (Position from left + Position from right) − 1. Here, 17 + 14 − 1 = 30.
Explanation: First convert B's position to the left direction: 40 − 22 + 1 = 19. The midpoint between positions 15 and 19 is (15 + 19) / 2 = 17.
Explanation: The number of handshakes equals the number of ways to choose 2 persons from 20, which is C(20, 2) = 20 × 19 / 2 = 190.
Explanation: Maximum total occurs when A is to the left of B (no overlap): Total = Position of A from left + Persons between + Position of B from right = 15 + 6 + 18 = 39.
Explanation: Assign positions with C at 0. A is 3rd to the right (counter-clockwise), so A is at position 13. A is 5th to the left (clockwise) of B, so B is at position 8. Persons between B (8) and C (0) = 8 − 0 − 1 = 7.
Explanation: Original position from right = 50 − 18 + 1 = 33. After 5 students leave from the right, the new position from right = 33 − 5 = 28. Alternatively, new total = 45, so 45 − 18 + 1 = 28.
Explanation: Students to the left of A = 7 − 1 = 6. Persons between A and B = 6 / 2 = 3. Using the non-overlap formula: Total = A's position from left + Persons between + B's position from right = 7 + 3 + 12 = 22.
Explanation: First convert both positions to the same direction. Sita is 9th from the right. Persons between = 20 − 9 − 1 = 10.
Explanation: Facing the centre, left is clockwise. With B at 0, A is at position 4. D is 2nd to the right (counter-clockwise) of A, so D is at position 2. C opposite D is at position 2 + 5 = 7. Clockwise from B (0) to C (7), the persons strictly between are at positions 1 through 6, giving 6 persons.
Explanation: Maximum total occurs when A is to the left of B (no overlap): Total = Position of A from left + Persons between + Position of B from right = 12 + 4 + 16 = 32.
Explanation: C is 4th to the right of A, so C is 14 + 4 = 18th from the left. C is 7th to the left of B, so B is 18 + 7 = 25th from the left. Total = B's position from left + B's position from right − 1 = 25 + 16 − 1 = 40.
Explanation: Minimum persons between occurs when the total is just large enough for A and B to be adjacent. With total = 43, B is 19th from the left and A is 20th from the left, so there are 0 persons between them.
Explanation: After 8 students leave from the left, A's position from the left becomes 25 − 8 = 17. The new total is 60 − 8 − 6 = 46. A's new position from the right = 46 − 17 + 1 = 30.
Explanation: Facing the centre, left is clockwise and right is counter-clockwise. With B at 0, A is at position 4. C is 5th to the right (counter-clockwise) of A, so C is at position 17. D opposite C is at position 17 + 9 = 8 (mod 18). From the right of B (counter-clockwise), the persons strictly between B (0) and D (8) are at positions 17, 16, 15, 14, 13, 12, 11, 10, and 9, giving 9 persons.
Explanation: B is 49 − 16 + 1 = 34th from the left. C is exactly midway: (16 + 34) / 2 = 25th from the left. D is 3rd to the left of C, so D is 25 − 3 = 22nd from the left. D's position from the right = 49 − 22 + 1 = 28.
Explanation: Facing the centre, left is clockwise and right is counter-clockwise. With B at 0, A is at position 4. C is 6th to the right (counter-clockwise) of A, so C is at position 9. From the right of B (counter-clockwise), the path from B (0) to C (9) passes through positions 12, 11, and 10, giving 3 persons between.
Explanation: Facing the centre, left is clockwise and right is counter-clockwise. With B at 0, A is at position 8. C is 5th to the right (counter-clockwise) of A, so C is at position 3. D opposite C is at position 15. From the left of B (clockwise), the persons strictly between B (0) and D (15) are at positions 1 through 14, giving 14 persons.
Explanation: With B at position 0 and right being clockwise, A is at position 3. C opposite A is at position 3 + 6 = 9. From the left of B (counter-clockwise), the path is 0 to 11 to 10 to 9, with 2 persons between.
Explanation: B is 64 − 20 + 1 = 45th from the left. C is 5th to the right of A, so C is 24 + 5 = 29th from the left. D is 6th to the left of B, so D is 45 − 6 = 39th from the left. Persons between C (29) and D (39) = 39 − 29 − 1 = 9.
Explanation: Facing outward, left is counter-clockwise and right is clockwise. With B at 0, A is at position 7. C is 2nd to the right (clockwise) of A, so C is at position 9. D opposite B is at position 5. From the right of C (clockwise), the path is 9 to 0 to 1 to 2 to 3 to 4 to 5, with 5 persons between.
Explanation: Facing the centre, right is counter-clockwise and left is clockwise. With B at 0, A is at position 5. C is 3rd to the left (clockwise) of A, so C is at position 2. D opposite B is at position 7. From the left of C (clockwise), the persons between C (2) and D (7) are at positions 3, 4, 5, and 6, giving 4 persons.
Explanation: Facing outward, right is clockwise and left is counter-clockwise. With B at position 0, A is 3rd to the right (clockwise), so A is at position 3. C is immediately to A's left (counter-clockwise), so C is at position 2. From C, 2nd to the left (counter-clockwise) is position 0, which is B.
Explanation: After interchange, A moves to B's original position, which is 20th from the left. Position from the right = Total − Position from left + 1 = 30 − 20 + 1 = 11.
Explanation: Facing outward, right is clockwise. With B at 0, A is at position 5. C opposite A is at position 5 + 7 = 12. From the left of B (counter-clockwise), the path from B (0) to C (12) passes through position 13, giving 1 person between.
Explanation: For an odd number of persons, the middle position = (Total + 1) / 2. Here, (37 + 1) / 2 = 19.
Explanation: Persons between two positions = Difference in positions − 1. Here, 23 − 12 − 1 = 10.
Explanation: Facing the centre, left is clockwise. With B at 0, A is at position 10. C is 12th to the right (counter-clockwise) of B, so C is at position 8. D opposite C is at position 8 + 10 = 18. From the left of A (clockwise), the path from A (10) to D (18) passes through positions 11, 12, 13, 14, 15, 16, and 17, giving 7 persons between.
Explanation: After adding 4 students to the left of A, A's position from the left becomes 10 + 4 = 14. The new total is 25 + 4 = 29. A's position from the right = 29 − 14 + 1 = 16.
Explanation: After interchange, A occupies B's original position, which is 15th from the left. B occupies A's original position, and B is 12th from the right, so B is 40 − 12 + 1 = 29th from the left. Therefore, A was originally 29th from the left.
Explanation: Students to the left of A: 12 − 1 = 11. B is 36 − 18 + 1 = 19th from the left. Between A (12) and B (19): 19 − 12 − 1 = 6. Including B (1), total facing South = 11 + 6 + 1 = 18.
Explanation: For an even number of persons, the two middle positions are Total/2 and (Total/2) + 1. Here, 42/2 = 21 and 22.
Explanation: Students to the left of A: 18 − 1 = 17 face North. B is 52 − 24 + 1 = 29th from the left. Between A and B: 29 − 18 − 1 = 10 face North. Students to the right of B: 52 − 29 = 23 face North. Including A (1), total facing North = 17 + 1 + 10 + 23 = 51.
Explanation: Facing the centre, left is clockwise and right is counter-clockwise. With B at 0, A is at position 2. C is immediately to B's right (counter-clockwise), so C is at position 11. From the right of A (counter-clockwise), the path is 2 to 1 to 0 to 11, with 2 persons between.
Explanation: Maximum total with no overlap and at most 8 persons between: Total = Position of A from left + Persons between + Position of B from right = 18 + 8 + 22 = 48.
Explanation: If A is 3rd to the right of B, there are 2 persons between B and A in the clockwise direction. In a circle of 8, the remaining persons between A and B in the counter-clockwise direction (left of A) = 8 − 2 − 2 = 4.
Explanation: Since B is equidistant from A and C, the distance from A to B equals the distance from B to C. A is 8th and B is 22nd, so C is 22 + (22 − 8) = 36th from the left. C's position from the right = 50 − 36 + 1 = 15.
Explanation: Minimum total occurs when A is to the right of B (overlap): Total = Position of A from left + Position of B from right − Persons between − 2 = 12 + 16 − 4 − 2 = 22.
Explanation: Let A's position from the left be x. Students to the left = x − 1, students to the right = 31 − x. Given 31 − x = 1.5(x − 1), solving gives 31 − x = 1.5x − 1.5, so 32.5 = 2.5x, and x = 13.
Explanation: When persons to the left leave, the position from the left decreases by the number of persons who left. New position = 18 − 5 = 13.
Explanation: Facing the centre, right is counter-clockwise. With B at 0, A is at position 4. C opposite A is at position 4 + 8 = 12. From the left of B (clockwise), the persons strictly between B (0) and C (12) are at positions 1 through 11, giving 11 persons.
Explanation: C is 5th to the right of A with 5 students between, so C is 16 + 5 + 1 = 22nd from the left. C's position from the right = 48 − 22 + 1 = 27.
Explanation: Minimum total with overlap and at least 3 persons between: Total = Position of A from left + Position of B from right − Persons between − 2 = 18 + 22 − 3 − 2 = 35.
Explanation: A's position from the left = 48 × 3/8 = 18. A's position from the right = 48 − 18 + 1 = 31.
Explanation: After 4 students to the left leave, A's position from the left becomes 15 − 4 = 11. After 3 new students join at the left end, A's position becomes 11 + 3 = 14. The new total is 40 − 4 + 3 = 39. A's new position from the right = 39 − 14 + 1 = 26.