Free Topic-Wise General Studies MCQs
Test your spatial reasoning with Direction and Distance Sense MCQs. Step-by-step solutions for standard UPSC CSAT problems to ensure quick and accurate deductions.
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Explanation: At noon in the Northern Hemisphere, the sun lies due South, so shadows are cast due North. If the shadow falls directly behind the observer, the direction behind him is North; therefore, he must be facing South.
Explanation: The cyclist’s final position is 6 km East and 8 km North of the origin. The shortest return path is the straight-line hypotenuse of the right triangle with legs 6 km and 8 km. Distance = √(6² + 8²) = 10 km. Since he must travel both West and South, the direction is South-West.
Explanation: Using bearings measured clockwise from North: East = 90°. A 45° left (anticlockwise) turn gives 90° − 45° = 45° (North-East). A 90° right (clockwise) turn gives 45° + 90° = 135° (South-East). A final 135° left turn gives 135° − 135° = 0°, which is North.
Explanation: North-East is 45° from North. A 180° clockwise turn gives 45° + 180° = 225° (South-West). A 90° anticlockwise turn gives 225° − 90° = 135° (South-East). A final 45° clockwise turn gives 135° + 45° = 180° from North, which is South.
Explanation: A 270° clockwise turn is equivalent to three successive 90° right turns. Starting from South: first right turn points West, second points North, and the third points East. Alternatively, add 270° to the South bearing (180°): 180° + 270° = 450° ≡ 90°, which is East.
Explanation: Net East displacement = 10 − 5 = 5 km. Net North displacement = 13 − 1 = 12 km. These perpendicular components form a 5-12-13 right triangle. The minimum distance from the starting point is therefore 13 km.
Explanation: A 540° clockwise turn equals one full rotation (360°) plus an additional 180°. The full rotation brings her back to East, and the extra 180° reverses her to the opposite direction, which is West.
Explanation: Net East displacement = 20 − 5 = 15 km. Net North displacement = 22 − 2 = 20 km. These perpendicular components form a 15-20-25 right triangle (a 3-4-5 multiple). The shortest distance from the starting point is therefore 25 km.
Explanation: Net East displacement = 25 − 5 = 20 km. Net North displacement = 24 − 3 = 21 km. These perpendicular components form a 20-21-29 right triangle. The minimum distance from the starting point is therefore 29 km.
Explanation: The two legs of the journey form the perpendicular sides of a right triangle. Apply the Pythagorean theorem: displacement = √(8² + 6²) = √(64 + 36) = √100 = 10 km.
Explanation: 450° equals one full rotation (360°) plus an additional 90°. After the full rotation she is still facing East. The remaining 90° anticlockwise turn from East points to North.
Explanation: After 2 hours, cyclist A has reduced the East separation by 7 × 2 = 14 km, leaving 24 − 14 = 10 km East. Cyclist B has moved 12 × 2 = 24 km North. The positions form a right triangle with legs 10 km and 24 km. Apply the Pythagorean theorem: √(10² + 24²) = √(100 + 576) = √676 = 26 km.
Explanation: At 9 AM the sun is in the East, casting shadows West. If the shadow is to his left, his left side points West, so he faces North. At 3 PM the sun is in the West, casting shadows East. If the shadow is to his right, his right side points East, which again occurs when facing North. Since he walks the same straight line throughout, the direction is North.
Explanation: Track the cumulative displacement on each axis. East-West: 8 km East − 4 km West = 4 km East. North-South: 6 km North − 3 km South = 3 km North. The resultant forms a 3-4-5 right triangle, giving a displacement of 5 km in the North-East direction.
Explanation: Net East displacement = 15 − 7 + 4 = 12 km. Net North displacement = 8 − 3 = 5 km. These two perpendicular components form a 5-12-13 right triangle. The shortest distance from the starting point is therefore 13 km.
Explanation: At 2:00, the hour hand is at 60° from North (North-East). The direction exactly opposite to 60° is 60° − 180° = −120° ≡ 240° from North. A bearing of 240° lies between South-West (225°) and West (270°), so it falls in the South-West quadrant.
Explanation: Resolve the total displacement along the two axes. East-West: 6 km East − 3 km West = 3 km East. North-South: 8 km North − 4 km South = 4 km North. These perpendicular components form a 3-4-5 Pythagorean triple, so the shortest distance is 5 km.
Explanation: 765° equals two full rotations (2 × 360° = 720°) plus an additional 45°. After the two full rotations he is still facing South. The remaining 45° anticlockwise turn from South points to South-East (180° − 45° = 135°).
Explanation: West corresponds to 270° measured clockwise from North. An anticlockwise turn of 225° subtracts from this bearing: 270° − 225° = 45°. A bearing of 45° from North is the North-East direction.
Explanation: In the evening, the sun sets in the West, so shadows are cast towards the East. If the shadow falls to the person’s right, his right side points East. When facing North, the right hand points East. Therefore, he is facing North.
Explanation: At 10:00, the hour hand is at 10 × 30° = 300° from North, which lies between West (270°) and North (360°). The direction exactly opposite to 300° is 300° − 180° = 120° from North, which is the South-East direction.
Explanation: At sunrise, the sun rises in the East, so shadows fall towards the West. If the shadow is to the man’s left, his left side points West. When facing North, the left hand points West. Therefore, he is facing North.
Explanation: North-East corresponds to 45° measured clockwise from North. Adding a further 135° clockwise turn gives 45° + 135° = 180° from North, which is the South direction.
Explanation: Resolve the displacements on each axis. North-South: 7 km North + 5 km North = 12 km North. East-West: 24 km East − 8 km West = 16 km East. The final position is 16 km East and 12 km North of the origin, forming a 12-16-20 right triangle (a 3-4-5 multiple). Shortest distance = 20 km.
Explanation: At 11:00, the hour hand is at 330° from North (30° West of North). The direction exactly opposite to 330° is 330° − 180° = 150° from North. A bearing of 150° lies between South-East (135°) and South (180°), so it falls in the South-East quadrant.
Explanation: At 9:00, the hour hand points West (270°) and the minute hand points North (0° or 360°). When a person faces West, his right hand points North. Therefore, the minute hand lies to his right.
Explanation: At 2 PM the sun is in the West, so shadows are cast towards the East. If the shadow is to the man’s left, his left side points East. When facing South, the left hand points East. Therefore, he is facing South.
Explanation: At 10 AM the sun is in the South-East, so shadows are cast towards the North-West. If the shadow is to the man’s left, his left side points North-West. When facing North-East, the left hand points North-West. Therefore, he is facing North-East.
Explanation: Decompose each 60° slanted leg into East and North components using trigonometry: 6 km at 60° gives 6·cos(60°) = 3 km East and 6·sin(60°) = 3√3 km North (or South). The North-South components from the two slanted legs cancel each other (3√3 North minus 3√3 South), leaving only the 8 km due North. Total East displacement is 3 + 3 = 6 km. The resultant is a 6-8-10 right triangle, giving 10 km.
Explanation: The man’s net East displacement is 9 m − 4 m = 5 m, and his net North displacement is 12 m. These perpendicular displacements form a 5-12-13 right triangle. The shortest distance from the starting corner is therefore 13 m.
Explanation: Net East displacement = 6 − 2 = 4 km. Net North displacement = 8 − 5 = 3 km. The resultant displacement forms a 3-4-5 right triangle, giving 5 km in the North-East direction.
Explanation: 810° equals two full rotations (2 × 360° = 720°) plus an additional 90°. After the two full rotations he is still facing South. The remaining 90° clockwise turn from South points to West.
Explanation: Track the bearing step by step from North (0°). First right turn: 0° + 90° = East (90°). Second right turn: 90° + 90° = South (180°). First left turn: 180° − 90° = East (90°). Final left turn of 180°: 90° − 180° = −90° ≡ 270°, which is West.
Explanation: Net East displacement = 15 − 3 = 12 km. Net North displacement = 40 − 5 = 35 km. These perpendicular components form a 12-35-37 right triangle. The minimum distance from the starting point is therefore 37 km.
Explanation: At 4 PM the sun is in the West, so shadows point East. If the shadow is to his right, he is facing North. He walks 11 km North, then turns left (West) and walks 60 km. The final position is 11 km North and 60 km West of the origin, forming an 11-60-61 right triangle. Shortest distance = 61 km.
Explanation: Net East displacement = 12 − 3 = 9 km. Net North displacement = 15 − 3 = 12 km. These perpendicular components form a 9-12-15 right triangle (a 3-4-5 multiple). The shortest distance from the starting point is therefore 15 km.
Explanation: The second person is at (8 km East, 0 km North) and the third is at (0 km East, 6 km South). The separation forms a right triangle with legs 8 km (East-West) and 6 km (North-South). Distance = √(8² + 6²) = √100 = 10 km.
Explanation: At 6 AM the sun is in the East, so shadows point West. If the shadow is directly behind him, he is facing East. He walks 8 km East, then turns left (North) and walks 6 km. The final position is 8 km East and 6 km North of the origin, forming a 6-8-10 right triangle. Shortest distance = 10 km.
Explanation: A’s first leg is 6 km East. To reach B at (0 km East, 8 km North), A must travel from (6, 0) to (0, 8). The direct distance is √(6² + 8²) = 10 km in the North-West direction. From facing East, a North-West turn is a left turn. Total distance = 6 + 10 = 16 km.
Explanation: The positions of A and C relative to B form the two perpendicular legs of a right triangle. Apply the Pythagorean theorem: distance = √(20² + 21²) = √(400 + 441) = √841 = 29 km.
Explanation: Net East displacement = 9 − 4 = 5 km. Net North displacement = 12 km. These perpendicular components form a 5-12-13 right triangle. The shortest distance from the starting point is therefore 13 km.
Explanation: South-East corresponds to 135° measured clockwise from North. A 135° left (anticlockwise) turn subtracts from this bearing: 135° − 135° = 0° from North, which is the North direction.
Explanation: Each hour mark on the clock represents 30° from North. At 8:00, the hour hand is at 8 × 30° = 240°, which lies between South (180°) and West (270°). The direction exactly opposite to 240° is 240° − 180° = 60° from North, which is the North-East direction.
Explanation: At noon in Delhi, the sun lies South of the observer, so the shadow is cast towards the North. If the shadow falls to the man’s right, his right side points North. When facing West, the right hand points North. Therefore, he is facing West.
Explanation: Resolve the path into North-South and East-West components. North-South: 5 km North + 3 km North = 8 km North. East-West: 12 km East − 6 km West = 6 km East. The final position is 6 km East and 8 km North of the origin, forming a 6-8-10 right triangle. Shortest distance = √(6² + 8²) = 10 km.
Explanation: Combine the North-South components: 9 km North − 4 km South = 5 km North. The East-West component is 12 km East. These form a 5-12-13 right triangle. Minimum distance = √(5² + 12²) = √169 = 13 km.
Explanation: On a clock oriented with 12 at North, each hour represents 30°. At 7:30, the hour hand is halfway between 7 (210°) and 8 (240°), giving 225° (South-West). The minute hand at 6 points South (180°). The angular gap is 225° − 180° = 45°, with the hour hand lying to the West of the minute hand.
Explanation: Net East displacement = 10 − 2 = 8 km. Net North displacement = 18 − 3 = 15 km. These perpendicular components form an 8-15-17 right triangle. The shortest distance from the starting point is therefore 17 km.
Explanation: Starting from East (0°), a 90° left turn points to North (90°). A 180° right turn from North reverses to South (270°). A final 90° left turn from South returns to East (0°). Track cumulative angular displacement: +90° − 180° + 90° = 0°.
Explanation: Net East displacement = 10 − 3 = 7 km. Net North displacement = 25 − 1 = 24 km. These perpendicular components form a 7-24-25 right triangle. The minimum distance from the starting point is therefore 25 km.
Explanation: Resolve the displacements along the East-West and North-South axes. Net East displacement = 5 − 2 = 3 km East. Net North displacement = 3 − 1 = 2 km North. Since both components are positive (East and North), the resultant direction from the origin is North-East.
Explanation: At 8 AM the sun is in the East. For the sun to be on the man’s right, he must be facing North (right hand points East). He walks 12 km North, then turns left (West) and walks 5 km. The final position is 12 km North and 5 km West of the origin, forming a 5-12-13 right triangle. Shortest distance = 13 km.
Explanation: Net East displacement = 10 − 2 = 8 km. Net North displacement = 18 − 3 = 15 km. These perpendicular components form an 8-15-17 right triangle. The minimum distance from the starting point is therefore 17 km.
Explanation: 630° equals one full rotation (360°) plus an additional 270°. After the full rotation he is still facing North. The remaining 270° clockwise turn from North is equivalent to three 90° right turns, which ends at West.
Explanation: Net East displacement = 15 − 9 = 6 km. Net North displacement = 20 − 12 = 8 km. These two perpendicular components form a 6-8-10 right triangle. The minimum distance from the starting point is therefore 10 km.
Explanation: Treat the two displacements as perpendicular legs of a right triangle. Separation distance = √(4² + 3²) = 5 km. From the second person’s position (3 km East), the first person lies 4 km North and 3 km West, which is the North-West direction.
Explanation: Directions are mutual and opposite. If A lies North-West of B, then B must lie in the exactly opposite direction from A. The opposite of North-West is South-East, and the distance remains unchanged at 10 km.
Explanation: A 315° clockwise turn from North (0°) gives a bearing of 315°. Since 315° = 360° − 45°, this is 45° West of North, which is the North-West direction.
Explanation: The hiker’s final position is 9 km East and 40 km North of the origin. The shortest return path is the hypotenuse of the right triangle with legs 9 km and 40 km. Distance = √(9² + 40²) = √(81 + 1600) = √1681 = 41 km. Since she must travel both West and South, the direction is South-West.
Explanation: Coordinates: A = (12, 0), C = (0, 16). The midpoint D has coordinates ((12+0)/2, (0+16)/2) = (6, 8). The distance from the origin B to D is √(6² + 8²) = √100 = 10 km.