Direction Sense Test Questions and Answers

Answer: C

Both 1 and 2 are correct.

Statement 1: the South and East legs are perpendicular, so the distance is

\[ \sqrt{5^2 + 12^2} = \sqrt{169} = 13 \text{ km} \]

Statement 2: measure directions clockwise from North. North-West is 315°; turning 225° clockwise gives \(315 + 225 = 540\), and \(540 - 360 = 180\)°, which is South. Turning 180° from North-West would give South-East, and the extra 45° clockwise brings it to South.

Answer: C

Statement I is true but Statement II is false.

Clockwise from North the directions run North, East, South, West. A 90° clockwise turn from North therefore faces East, so Statement I is true.

Anti-clockwise from North the order is North, West, South, East, so a 90° anti-clockwise turn faces West, not East. Statement II is false.

The options treating both as true miss that the two turns go in opposite senses and so must end in opposite directions.

Answer: B

I am now facing North-east.

Measure directions clockwise from North, so East is 90°.

\[ \begin{aligned} 90 + 100 &= 190^\circ \\ 190 - 145 &= 45^\circ \end{aligned} \]

45° from North is North-east. In net terms the two turns amount to 45° anticlockwise from East. South-west is the exact opposite direction, a 180° error, and North would need a net turn of 90° anticlockwise from East.

Answer: D

Suresh was facing South.

In the morning the sun is in the east, so shadows fall towards the west. Mahesh's shadow falls to his left, so his left is west, which means he is facing north. Suresh sits back to back with him, so Suresh faces the opposite way: south.

North is Mahesh's direction, not Suresh's. East and west would put the shadow in front of or behind them, not to the side.

Answer: D

The office is 50 m to the South East.

Mohan goes 20 m south, turns left (east when facing south) for 30 m, then turns right (south again) for 20 m. In all he is 40 m south and 30 m east of his house.

\[ \begin{aligned} d &= \sqrt{40^2 + 30^2} \\ &= \sqrt{2500} = 50\ \text{m} \end{aligned} \]

70 m is the total distance walked along the path, not the straight-line distance, and South West is wrong because the left turn while facing south takes him east.

Answer: D

Ram now faces South-West.

Facing East, a 45° clockwise turn brings him to South-East. Turning 270° anticlockwise is the same as turning 90° clockwise, which takes him from South-East to South-West.

North-East is what you get by making the 270° turn clockwise instead, and North-West by reversing both turns.

Measuring directions clockwise from North in degrees: East is 90, the 45° clockwise turn gives 135 (South-East), and turning 270° anticlockwise gives 135 - 270 = -135, the same as 225, which is South-West. North would need a net turn of 90° anticlockwise from East.

Answer: C

The trace is the five-pointed star of option (C).

After its first turn the ant heads 72° north of east. It then repeats 'move 10 cm, turn 144° clockwise' five times. Each turn changes its heading by 144°, so after five turns it has turned through 5 × 144° = 720°, exactly two full revolutions, and it is back at P facing its first direction.

A closed path of five equal strokes that turns through two full revolutions is a regular star pentagon. The angle between consecutive strokes at each point is 180° - 144° = 36°, which is the point angle of a five-pointed star.

A regular pentagon (A) would need turns of 72° each, giving one revolution in five steps. A hexagon (B) needs six strokes with 60° turns. The seven-pointed star (D) needs seven strokes, but the ant makes only five.

Answer: C

Akash is 10 km from the starting point.

Walking south and then turning left means turning to face east. After 6 km east he turns right, which faces south again, and walks 4 km. So in total he is 4 + 4 = 8 km south and 6 km east of the start.

\[ d = \sqrt{8^{2} + 6^{2}} = \sqrt{100} = 10\ \text{km} \]

18 km is the total distance walked, not the straight-line distance. 8 km counts only the southward part, and 12 km fits no combination of the legs; the displacement combines 8 km south with 6 km east.

Answer: B

Ravi was facing North.

At sunrise the sun is in the east, so a pole casts its shadow towards the west. If the shadow falls on Ravi's left side, west is on his left. A person with west on the left faces north (east is then on the right and south behind).

Facing south would put west on his right; facing east would put the shadow behind him; facing west would put it in front of him. Only north places the morning shadow on the left.

Answer: C

He is 5 km from his house.

Track the net movement. North 4 km and then south 8 km leaves him 4 km south of the start; the 3 km west is the only east-west movement. The two displacements are at right angles:

\[ d = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5\ \text{km} \]

8 km takes only the southward walk, 7 km adds the 4 km and 3 km legs, and 6 km does not correspond to any combination of the moves. The straight-line distance is the hypotenuse.