Question 1

Direction sense: Find M's direction from K on a compass grid.  Given: K is 40 m to the South-West of L. Also: M is 40 m to the South-East of L. Question: In which direction is M located with respect to K? Choose the correct option.

Accepted Answer

Given dataK is 40 m South-West of L.M is 40 m South-East of L.Concept/ApproachPlace L at the origin. Take East = +x and North = +y. South-West is (−, −) from L; South-East is (+, −). Only relative direction between K and M is asked.Step-by-stepK ≈ (−40, −40)M ≈ (+40, −40)Vector K→M = (80, 0) ⇒ due East.Common pitfallProjecting diagonals with √2 factors is unnecessary for direction; the sign pattern suffices.Final AnswerEast

Question 2

Relative positions of villages: Determine S's direction from R.  Facts: Q is to the North of P. R is to the East of Q. S is to the left of P (map-view; i.e., West of P). Question: In which direction is village S with respect to village R? Choose the…

Accepted Answer

Place points on a mapLet P = (0,0).Q is North of P ⇒ Q = (0, +1).R is East of Q ⇒ R = (+1, +1).S is left of P (West) ⇒ S = (−1, 0).Direction from R to SVector R→S = (−2, −1) ⇒ quadrant (−x, −y) = South-West.Final AnswerSouth-West

Question 3

Sun–shadow reasoning (morning): Find Suresh's facing direction.  Scenario: One morning after sunrise, Suresh faced a pole. Observation: The pole's shadow fell exactly to Suresh's right. Question: Toward which direction was Suresh facing? Choose the …

Accepted Answer

Key ideaIn the morning, the Sun is in the East, so shadows are cast toward the West.ReasoningIf Suresh sees the pole's shadow on his right, then West must be on his right-hand side.Facing South ⇒ right side is West (fits the observation).ChecksFacing East ⇒ right is South (≠ West).Facing West ⇒ right is North (≠ West).Facing North ⇒ right is East (≠ West).Final AnswerSouth

Question 4

Turn-by-turn path and final orientation: Determine Sundar's final facing direction.  Moves: 20 m East → right 10 m → right 9 m → right 5 m → left 12 m → right 6 m. All turns are 90° unless stated. Question: After completing all moves, in which direc…

Accepted Answer

Track headingsStart toward East.Right of East ⇒ South.Right of South ⇒ West.Right of West ⇒ North.Left of North ⇒ West.Right of West ⇒ North.Final orientationNorth

Question 5

Grid navigation back-to-home: Minimum straight distance to return.  Path: From home, Ravi cycles 10 km South → right 5 km → right 10 km → left 10 km. Question: How many kilometers must he cycle in a straight line to reach home? Choose the correct va…

Accepted Answer

Coordinate setupHome = (0,0)10 km South ⇒ (0, −10)Right (from South) = West 5 ⇒ (−5, −10)Right (from West) = North 10 ⇒ (−5, 0)Left (from North) = West 10 ⇒ (−15, 0)Straight-line back to homeDistance = |x| = 15 km.

Question 6

Direction after sequential turns: Identify X's final facing direction.  Path: Walk straight toward South for 5 m → turn left and walk 3 m → turn right and walk 5 m. Question: After the last move, which direction is X facing?

Accepted Answer

Track headingsInitial heading: South.Left of South ⇒ East.Right of East ⇒ South.Final AnswerSouth

Question 7

Distance from start after multiple orthogonal moves: Compute Shyam's displacement.  Moves: 5 km East → left 6 km (North) → right 9 km (East) → right 6 km (South). Question: What is his straight-line distance from the starting point?

Accepted Answer

CoordinatesStart (0,0) → (5,0) → (5,6) → (14,6) → (14,0)Distance from startΔx = 14, Δy = 0 ⇒ distance = √(14²) = 14 km.

Question 8

Cardinal relation composition: Determine P's direction from Y.  Relations: Y is East of X; X is North of Z; P is South of Z. Question: In which direction of Y is P located? Select the correct option.

Accepted Answer

Map placementLet Z = (0,0).X North of Z ⇒ X = (0, +1).Y East of X ⇒ Y = (+1, +1).P South of Z ⇒ P = (0, −1).Direction from Y to PVector = (−1, −2) ⇒ South-West, which is not among North/South/South-East.Hence: None of these.

Question 9

Shortest distance (Pythagoras): Golu's distance from home after two legs.  Path: From home, 8 km North, then 6 km West. Question: What is the straight-line (shortest) distance back to his house? Choose the correct value.

Accepted Answer

Right triangleLegs: 8 km (North) and 6 km (West).Distance = √(8² + 6²) = √(64 + 36) = √100 = 10 km.

Question 10

Direction after a 135° right turn: Determine the required compass direction.  Path: 25 m West → right 10 m (North) → right 15 m (East). Final instruction: Turn right by 135° and cover 30 m. Question: In which compass direction should P go for the la…

Accepted Answer

Heading before the last turnAfter the third leg, P is facing East.Apply the 135° right turnFrom East, a right (clockwise) 90° points South; an additional 45° points toward South-West.ConclusionThe final leg should be in the South-West direction.

Question 11

Direction sense with morning shadows: determine Udai’s facing direction at a crossing  One morning, Udai and Vishal are standing face to face at a road crossing. Vishal's shadow is exactly to the left side of Udai. Using the fact that in the morning…

Accepted Answer

Given data

Time: Morning ⇒ Sun in the East ⇒ Shadows fall toward the West. Udai and Vishal are face to face. Vishal's shadow is to Udai's left. Concept/Approach If shadows point West, then for Vishal's shadow to lie on Udai's left side, Udai's left must align with West. That happens when Udai is facing North (because when you face North, West is on your left). Verification Facing North ⇒ left = West. Shadow direction = West. Consistent. Final Answer North

Question 12

Path tracing with right/left turns: find final direction from the start  A man walks 5 km toward the South, then turns right and walks 3 km, then turns left and walks 5 km. From the starting place, identify his final direction. Choose the correct op…

Accepted Answer

Coordinate walk (East = +x, North = +y)
Start (0,0)
5 km South → (0, −5)
Right from South = West: 3 km → (−3, −5)
Left from West = South: 5 km → (−3, −10)

Direction from start Vector (−3, −10) lies in the South-West quadrant ⇒ South-West.

Question 13

Grid walk with four turns: determine the net direction from home  From his house, Lokesh goes 15 km North, then 10 km West, then 5 km South, and finally 10 km East. Relative to his house, in which direction is he now located? Choose the correct answ…

Accepted Answer

Compute net displacement
North: +15, then South: −5 ⇒ Net North = 10 km.
West: 10, then East: 10 ⇒ Net East/West = 0.

Conclusion He is 10 km due North of the start.

Question 14

Rectangular path with left/right turns: find Jayant’s final position from X  Starting at point X, Jayant walks: 15 m West → left 20 m (South) → left 15 m (East) → right 12 m (South). How far and in which direction is Jayant from X at the end? Choose…

Accepted Answer

Step-by-step coordinates
Start X = (0,0)
15 m West → (−15, 0)
Left from West ⇒ South 20 → (−15, −20)
Left from South ⇒ East 15 → (0, −20)
Right from East ⇒ South 12 → (0, −32)

Distance and direction From (0,0) to (0, −32) = 32 m, South.

Question 15

Perimeter plus diagonal: total distance run along room walls and a diagonal  A room measures length = 8 m and breadth = 6 m. A cat runs along all four walls (effectively the perimeter) and then along a room diagonal to catch a rat. Compute the total…

Accepted Answer

Given

Perimeter of rectangle = 2(L + B) = 2(8 + 6) = 28 m. Diagonal = √(8² + 6²) = √(64 + 36) = √100 = 10 m. Total distance 28 + 10 = 38 m.

Question 16

Multi-leg city walk: find straight-line distance from start after four moves  A child goes 90 m East, turns right and goes 20 m (South), turns right and goes 30 m (West) to uncle's house, then goes 100 m North to meet his father. How far from the st…

Accepted Answer

Coordinates
Start (0,0) → (90,0) → (90, −20) → (60, −20) → (60, 80)

Pythagoras Distance = √(60² + 80²) = √(3600 + 6400) = √10000 = 100 m.

Question 17

Four-turn square path: compute final distance from the start  Sachin walks 20 km North, turns left and walks 40 km West, turns left and walks 20 km South, then turns left and walks another 20 km. How far is he from his starting position? Choose the …

Accepted Answer

Trace the path
(0,0) → (0,20) → (−40,20) → (−40,0) → (−20,0)

Distance from origin |Δ| = √((−20)² + 0²) = 20 km.

Question 18

Direction Sense — Starting facing East, turn 100° clockwise and then 145° anti-clockwise. After these two turns, which compass direction will you finally face?

Accepted Answer

Introduction / Context:Direction-sense problems ask you to track orientation after a sequence of turns. We will convert each turn into an angle relative to the starting facing (East) and simplify carefully, keeping clockwise and anti-clockwise signs consistent.Given Data / Assumptions:Initial facing: East.First turn: 100° clockwise.Second turn: 145° anti-clockwise (i.e., opposite direction to clockwise).We treat clockwise as + and anti-clockwise as − relative to the current facing (or use a consistent angular system and subtract/ add appropriately).Concept / Approach:Normalize angles to one full circle. A helpful scheme is: East = 0°, South = 90°, West = 180°, North = 270° (or −90°). Clockwise moves increase the angle; anti-clockwise moves decrease it. Reduce the final angle modulo 360° and map back to a compass direction.Step-by-Step Solution:Start at East = 0°.Clockwise 100° → 0° + 100° = 100°. (Between South (90°) and West (180°) — i.e., South-West quadrant.)Anti-clockwise 145° → 100° − 145° = −45°.Normalize: −45° = 360° − 45° = 315°.315° lies between North (270°) and East (360°), i.e., North-East.Verification / Alternative check:Think in net rotation: +100° − 145° = −45°, which is a 45° turn anti-clockwise from East, landing in the North-East quadrant. Both methods agree.Why Other Options Are Wrong:East: would require net 0°.North: would require net 270° or −90°.South-West: corresponds to around 225°; that was only after the first turn, not the final state.None of these: unnecessary because a listed option matches.Common Pitfalls:Mixing sign conventions or forgetting to normalize negative angles. Always compute net rotation and then map to a compass point.Final Answer:North-East

Question 19

Facing West, you turn 45° clockwise, then 180° clockwise again, and finally 270° anti-clockwise. After all these turns, what direction are you facing?

Accepted Answer

Introduction / Context:This item checks cumulative turn tracking. You must add clockwise rotations and subtract anti-clockwise rotations, then map the resulting angle to a compass direction.Given Data / Assumptions:Initial facing: West.Turns: +45° clockwise, +180° clockwise, −270° anti-clockwise.Compass mapping (one convenient scheme): East = 0°, South = 90°, West = 180°, North = 270°.Concept / Approach:Convert the initial facing to an angle, accumulate signed turns, reduce modulo 360°, and interpret the quadrant.Step-by-Step Solution:West corresponds to 180°.After +45°: 180° + 45° = 225°.After +180°: 225° + 180° = 405° → 405° − 360° = 45°.After −270°: 45° − 270° = −225° → add 360° → 135°.135° lies between South (90°) and West (180°): that is South-West.Verification / Alternative check:Combine the turns first: total rotation = +45° + 180° − 270° = −45°. From West (180°), −45° gives 135°, i.e., South-West. Same result.Why Other Options Are Wrong:South: 90° exact; we have 135°.West: 180° exact; not our final bearing.North-West: 315° or around that quadrant; not matching 135°.None of these: incorrect since South-West fits.Common Pitfalls:Forgetting to wrap angles within 0°–360° or mixing the sign of anti-clockwise rotation.Final Answer:south-west

Question 20

Kunal walks 10 km North, then 6 km South, and then 3 km East. How far from the start is he now, and in which direction relative to the starting point?

Accepted Answer

Introduction / Context:Position-tracking problems reduce to adding vectors on the North–South and East–West axes, then computing the resultant distance and bearing quadrant.Given Data / Assumptions:North movement: +10 km; South movement: −6 km; net North = 4 km.East movement: +3 km; no West movement.Resultant from origin: (East 3 km, North 4 km).Concept / Approach:Compute Pythagorean distance and determine the quadrant. The pair (3, 4) is the classic 3-4-5 right triangle.Step-by-Step Solution:Net North = 10 − 6 = 4 km.Net East = 3 km.Distance = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5 km.Direction: East positive and North positive ⇒ North-East quadrant.Verification / Alternative check:Draw a quick coordinate sketch: starting at (0,0), you end at (3,4). The straight line back to origin is 5 km, heading South-West; hence from origin to the point is North-East 5 km.Why Other Options Are Wrong:5 km West / 7 km East / 7 km West: wrong magnitude or axis.None of these: unnecessary, as 5 km North-East is exact.Common Pitfalls:Subtracting incorrectly on the North–South axis or forgetting that bearing is from the start to the final point.Final Answer:5 kilometers North-east

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