### Direction Sense Test Question 1: Mahender walked 30 meters towards east, took a right turn and walked another 40 meters. He again took a left turn and moved 30 meters. In which direction is he now from the starting point?

A. North-East

B. East

C. South-East

D. South

The path followed by Mahender looks like this:

Clearly, Mahender is to the south-east of the starting point. So, C is the correct option.

### Direction Sense Test Question 2: A clock is placed in such a manner that at 12 o’ clock, its minute-hand points towards north-east. In which direction does its hour hand point at 1:30 pm?

A. West

B. South

C. North

D. East

At 1:30 pm, the hour hand would make 45 degrees angle (clockwise) with the north-east direction. Hence, it will point to the east direction. So, D is the correct option.

### Direction Sense Test Question 3: Mr. Raghav went in his car to meet his friend John. He drove 30 kms towards the north and then 40 kms towards west. He then turned to the south and covered 8 kms. Further, he turned to the east and moved 26 kms. Finally, he turned right and drove 10 kms and then turned left to travel 19 kms. How far and in which direction is he from the starting point?

A. East of starting point, 5 kms

B. East of starting point, 13 kms

C. North-East of starting point, 13 kms

D. North-East of starting point, 5 kms

The path followed by Mr. Raghav would look like this:

Clearly, Mr. Raghav is 13 km north-east of the starting point. Therefore, C is the correct option.

### Direction Sense Test Question 4: Answer the questions based on the following information.

In a motor race competition, certain rules are given for the participants to follow. To control the direction and speed of the motorists, guards are placed at different signal points with caps of different colors. Guard with red cap indicates the direction of the participant’s movement and guards with green cap indicates the speed of the participant’s movement. At any signal point presence of three guards, two guards and one guard with red cap means the participant must stop, turn left and turn right respectively. Signal points with three guards, two guards and one guard with green cap means the participants must move at 10, 4 and 2 km/hour respectively.

Kartikay, one of the participants, starts at a point where his car was heading towards north and he encountered signals as follows: at start point one guard with green cap; after half an hour two guards with red cap and two guards with green cap at first signal; after fifteen minutes one guard with red cap at second signal; after half an hour one guard with red cap and three guards with green caps at third signal; after 24 minutes two guards with red cap and two guards with green cap at fourth signal; after 15 minutes three guards with red cap at fifth signal. (Time mentioned in each case is applicable after crossing the previous signal).

1. Total distance traveled by Kartikay from starting point till the last signal is:

A. 9 km

B. 10 km

C. 8 km

D. 12 km

2. What would be the final position of Kartikay if one guard with red cap and two guards with green caps were placed at the first signal point after the starting point?

A. 3.0 km to the west and 2.0 km to the south

B. 3.0 km to the west and 4.0 km to the north

C. 5.0 km to the east and 4.0 km to the north

D. 2.0 km to the west and 4.0 km to the south

3. If at the starting point Kartikay was heading towards south what would be his final position?

A. 3.0 km to the east and 4.0 km to the south

B. 5.0 km to the east and 4.0 km to the south

C. 3.0 km to the west and 4.0 km to the south

D. 5.0 km to the west and 2.0 km to the north

1. Signals encountered by Kartikay:

> At start point: 1 guard with green cap

He travels towards the north at 2 km/hour for half an hour.

Total distance traveled by him in the north direction = 2 km/hr × (1/2) hr = 1 km

> First signal: 2 guards with red cap and 2 guards with green cap

He turns left and travels at the speed of 4 km/hr for 15 minutes.

Total distance traveled by him between the first and the second signal = 4 km/hr × (1/4) hr = 1 km

> Second signal: 1 guard with red cap

He turns right and continues to travel at the same speed for half an hour.

Total distance traveled by him between the second and the third signal = 4 km/hr × (1/2) hr = 2 km

> Third signal: 1 guard with red cap and 3 guards with green cap

He turns right and travels at the speed of 10 km/hr for 24 minutes.

Total distance traveled by him between the third and the fourth signal = 10 km/hr × (24/60) hr = 4 km

> Fourth signal: 2 guards with red cap and 2 guards with green cap

He turns left and travels at the speed of 4 km/hr for 15 minutes.

Total distance traveled by him between the fourth and the fifth signal = 4 km/hr × (1/4) hr = 1 km

> Fifth signal: 3 guards with red cap

At fifth signals, he stops.

Therefore, the total distance traveled by him = (1 + 1 + 2 + 4 + 1) km = 9 km. So, A is the correct option.

2.

At first signal, he turns right and travels at the speed of 4 km/hr. So, instead of turning left, he turns right at the first signal.

The path followed by him looks like this:

In the above figure, we can see that the final position is 3 km to the west and 2 km to the south of the starting point. Therefore, A is the correct option.

3.

If Kartikay was heading towards south at the starting point, the path followed by him would look like this:

In the above figure, we can see that the final position is 3 km to the west and 4 km to the south of the starting point. Therefore, C is the correct option.

### Direction Sense Test Question 5: Study the following information and answer the questions given below:Point A is 3m east of point B. Point D is 4m north of point C. Point K is 7m west of point J. Point D is 4m south of point A. Point L is 4m south of point G which is 6m west of point F. Point E is 5m east of point C and point B is 5m north of point F. Point M is 5m south of point E which is 4m west of point N. Point K is 3m north of Q. Point I is 4m east of point A. Point J is 6m north of I.

1. What is the shortest distance between point N and point K?

A. $340m$

B. $\sqrt{340}m$

C. $75m$

D. $\sqrt{341}m$

E. None of the above

2. If Point W 3m east of point J and point V 4m north of point W. what is the shortest distance between point V and point L?

A. $\sqrt{145}m$

B. $\sqrt{581}m$

C. $\sqrt{617}m$

D. $24m$

E. $\sqrt[3]{145}m$

3. In which direction is point M with respect to point Q?

A. North

B. South

C. North-east

D. South-west

E. South-east

The points are arranged as shown in the figure below:

1.

In ΔONK, $ON = 12m$ and $OK = 14m$. Using Pythagoras theorem, we can write

$KN^2 = 12^2 + 14^2$

$KN = \sqrt{340}m$

Therefore, B is the correct option.

2.

$LV^2 = 19^2 + 16^2$

$LV = \sqrt{617}m$

Therefore, C is the correct option.

3.

Point M is to the south-east of point Q. Therefore, E is the correct option.