Direction Sense Test Questions and Answers

Answer: C

Correct answer: South-East

The whole compass has been turned. South-east becoming north is a turn of 135° anticlockwise, and north-east becoming west confirms it - 45° less 135° leaves 270°, which is west. Applying the same turn to west: \[ 270^\circ - 135^\circ = 135^\circ \] which is south-east.

Answer: D

The answer is M and S travel in the same direction.

Q travels East. Facing East, one's right is South, so T travels South. S travels opposite to T, so S travels North. M also travels North.

So M and S travel in the same direction. S does not travel West and T does not travel North, and M and S are not opposite.

Answer: A

The distance is 5.34 km.

Place O at the origin, with east as x and north as y. N is 1 km south-east of O, so N is at \((0.707, -0.707)\). M is 4 km north of N, at \((0.707, 3.293)\). P is 2 km south of O, at \((0, -2)\). Then:

\[ \begin{aligned} MP &= \sqrt{0.707^{2} + 5.293^{2}} \\ &= \sqrt{0.5 + 28.02} \\ &= \sqrt{28.52} \approx 5.34 \end{aligned} \]

28.5 is the value of \(MP^{2}\) before taking the square root.

Answer: D

Amit is 10 km, North-East of the start.

His northward movement totals \(3 + 5 = 8\) km and his eastward movement 6 km. The straight-line distance is the hypotenuse:

\[ \begin{aligned} d &= \sqrt{8^{2} + 6^{2}} \\ &= \sqrt{64 + 36} = \sqrt{100} \\ &= 10\ \text{km} \end{aligned} \]

Since he ends up both north and east of the start, he is to the North-East. 14 km adds the legs as if he walked straight (3 + 6 + 5), and 'North' ignores the 6 km he went East.

Answer: B

The doctor's house is to the north-west of the hospital.

Take X as the origin, with east and north positive. The doctor goes 600 m east to A (600, 0), 450 m south to B (600, -450), 120 m west to C (480, -450) and 90 m north to Y (480, -360).

So the hospital Y is 480 m east and 360 m south of the house. Seen from the hospital, the house lies 480 m west and 360 m north, that is, north-west. South-east is the direction of the hospital from the house, the reverse of what is asked.

Answer: B

The doctor's house X is to the North-East of the clinic Y.

Put X at the origin, with east and north positive.

\[ \begin{aligned} A &= (0, -250) \\ B &= (400, -250) \\ C &= (400, -375) \\ Y &= (400 - 650, -375) = (-250, -375) \end{aligned} \]

From Y, X lies 250 m to the east and 375 m to the north, so X is north-east of Y.

The common slip is to give the direction of Y from X, which is south-west, the opposite. Getting only one of the two components right gives north-west or south-east.

Answer: C

Punjab and Kerala lie North-west; South-west of Bihar.

Bihar is in the east of the Gangetic plain. Punjab is in the far north-west of India, so from Bihar it lies to the north-west. Kerala is at the south-western tip of the peninsula, so from Bihar it lies to the south-west.

Kerala is not south-east of Bihar (that direction points towards Odisha and the Bay of Bengal), Punjab is not north-east (that is Sikkim and the North-East), and Punjab is well west of due north.

Answer: A

Put A at the starting point E and take the directions as on a map. A walks 2 m north. Turning to the right from facing north means facing east, so A walks 3 m east. A turns right again, from east to south, and walks 2 m south. A has gone 2 m north and 2 m south, so the north south displacement is zero, and A is 3 m east of the start. The direction of A from the starting point is east, option A. North, west and south are not possible because the net movement is only to the east.

Answer: A

The shortest distance from X to his home is 39 km. Take west as the negative east-west direction. Sunny goes 9 km west, turns right (north) and goes 15 km, then turns right again (east) and goes 45 km. Net displacement: 45 - 9 = 36 km east and 15 km north. The straight-line distance is \[\sqrt{36^2 + 15^2} = \sqrt{1296 + 225} = \sqrt{1521} = 39\] The other options are not the length of this hypotenuse: 36 km is only the east-west part.

Answer: C

Place Ram's house at the origin. Ram goes 3 km north, 2 km west, 3 km south and 5 km east, ending 3 km east of his house. Rohan goes 5 km south, 1 km east, 5 km north and 5 km west, so he ends 4 km west of his own start.

\[ x_R - 4 = 3 \Rightarrow x_R = 7 \]

Rohan's house is on the same line as Ram's, at 7 km to the east. So the shortest distance between the houses is 7 km. The options 9, 6 and 5 km do not agree with this meeting point.