Direction Sense MCQ - 1 - Railways MCQ

Explanation:
Let's visualize Hemant's movements step by step:
1. Hemant started at point A and walked 40 meters North to point B.
2. Then, he turned left (towards West) and walked 50 meters to point C.
3. Finally, he turned left again (towards South) and walked 40 meters to point D.
Now, let's analyze his final position relative to the starting point:
- Hemant is 40 meters South of point B (his position after the first move), so he is at the same vertical level as point A (his starting point).
- Hemant is 50 meters West of point A (his starting point).
Hence, Hemant's final position relative to his starting point is:
- 50 meters West
Therefore, the correct answer is:
D: 10 m, West

To find the distance between Rohit's final position and his house, we can solve this problem using vector addition.
Step 1: Break down the directions and distances into components
- South-East: This direction can be broken down into two components, South and East.
- South: 7 * cos(45) = 7 * 0.707 = 4.95 km
- East: 7 * sin(45) = 7 * 0.707 = 4.95 km
- West: This direction has only one component, West.
- West: 14 km
- North-West: This direction can be broken down into two components, North and West.
- North: 7 * cos(45) = 7 * 0.707 = 4.95 km
- West: 7 * sin(45) = 7 * 0.707 = 4.95 km
- East: This direction has only one component, East.
- East: 9 km
Step 2: Add all the components
- Total South: 4.95 km
- Total East: 4.95 + 9 = 13.95 km
- Total North: 4.95 km
- Total West: 14 + 4.95 = 18.95 km
Step 3: Find the net displacement in North-South and East-West directions
- Net displacement in North-South direction: Total North - Total South = 4.95 - 4.95 = 0 km
- Net displacement in East-West direction: Total East - Total West = 13.95 - 18.95 = -5 km (negative sign indicates the direction is West)
Step 4: Calculate the distance
Since the net displacement in the North-South direction is 0 km, the total distance Rohit is from his house is the same as the net displacement in the East-West direction, which is 5 km (ignoring the negative sign as distance is always positive).
Answer: D. 5 km

Explanation:
Let's analyze Manisha's movements step by step:
1. Manisha goes 10 km towards the west from her office.
2. She turns left and goes 8 km. Since she was going west, a left turn will lead her to the south direction.
3. She turns left again and goes 4 km. Since she was going south, a left turn will lead her to the east direction.
Now, let's find out how far she is from her office:
- In the east-west direction: Manisha initially went 10 km towards west and then 4 km towards east. So, her net displacement in the east-west direction is (10 - 4) = 6 km towards west.
- In the north-south direction: Manisha went 8 km towards the south.
To find the shortest distance between Manisha and her office, we can use the Pythagorean theorem:
Distance = √[(east-west displacement)² + (north-south displacement)²]
Distance = √[(6 km)² + (8 km)²]
Distance = √(36 + 64)
Distance = √100
Distance = 10 km
So, the correct answer is:
E: None of these (10 km)

Let's analyze Manju's movements step by step:
Initial position:
- Manju is at a fixed point (let's call this point A).
First Movement:
- She goes 20 meters towards West.
- Let's call this point B.
Second Movement:
- From point B, she goes 10 meters towards North.
- Let's call this point C.
Third Movement:
- From point C, she goes 35 meters towards East.
- Let's call this point D.
Fourth Movement:
- From point D, she goes 5 meters towards South.
- Let's call this point E.
Fifth Movement:
- From point E, she goes 15 meters towards West.
- Let's call this point F.
Now, we need to find the distance between point A and point F.
- Since Manju initially moved 20 meters West and then moved an additional 15 meters West in her last movement, she is a total of 35 meters West from her starting point A.
- However, she also moved 35 meters East from point C to point D, which brings her back to the same vertical line as her starting point A.
- Considering her North and South movements, she moved a total of 10 meters North and 5 meters South, resulting in a net movement of 5 meters North from point A.
Now, we can use the Pythagorean theorem to find the distance between points A and F:
AF = √((Horizontal Distance)² + (Vertical Distance)²)
AF = √((0 meters)² + (5 meters)²)
AF = √(25)
AF = 5 meters
So, Manju is 5 meters away from her initial fixed point.
Answer: **A: 5 km** (Note: It should be "5 meters" instead of "5 km" in the options)

The answer is C.

Ramesh walks 15m towards South from a fixed point. From there he goes 12 m towards North and then 4 m towards West. This means that he is 3 meters south and 4 meters west of his starting point. To find the distance between Ramesh and his starting point, we can use the Pythagorean theorem:

d2=32+42=9+16=25

d=25​=5

Therefore, Ramesh is 5 meters from his starting point. To find the direction, we can use the tangent function:

tan(θ)=34​

θ=arctan(34​)≈53.13 degrees

Therefore, Ramesh is 5 meters from his starting point, in the south-west direction.

Explanation:
Let's break down Sam's movements step by step:

1. Sam walked 10 m towards West from his house.
2. He then turned to his left (which is South when facing West) and walked 5 m.
3. Next, he turned to his left again (which is East when facing South) and walked 10 m.
4. Finally, he turned to his left one more time (which is North when facing East) and walked 10 m.

At the end of these movements, Sam is facing North from his starting point. So, the correct answer is B: North.

To find the distance between the market and Raman's house, we need to follow the steps and directions given in the question.
1. Abhishek walks 100 m from his house towards North.
2. From there he goes 100 m towards West. Here is the house of Shyam.
3. From Shyam's house, they both go to the market which is in the South-West direction from Shyam's house.
4. The market is in the West of Raman's house.
Now, let's analyze the information:
- Since the market is in the South-West direction from Shyam's house, the distance from the market to Shyam's house can be represented as a diagonal in a right-angled triangle.
- Let's assume the market is x meters South and y meters West from Shyam's house.
- The market is in the West of Raman's house, so Raman's house is East of the market.
However, with the given information, we cannot determine the exact distance between the market and Raman's house. Therefore, the answer is:
E: None of these

Explanation:
Let's break down Sahil's movements step by step:
1. 5 km North: Sahil starts at a fixed point and goes 5 km towards the North.
2. 3 km East: Sahil turns to his right (which would be East) and goes 3 km.
3. 5 km South: Sahil turns to his right again (which would now be South) and goes 5 km.
4. 4 km West: Sahil turns to his left (which would be West) and goes 4 km.
Now, let's analyze his final position:
- Horizontal position: Sahil moved 3 km to the East and then 4 km to the West. So his net horizontal displacement is 3 - 4 = -1 km (1 km to the West).
- Vertical position: Sahil moved 5 km to the North and then 5 km to the South. So his net vertical displacement is 5 - 5 = 0 km.
Final position: Sahil is 1 km to the West of the starting point. Therefore, the answer is 1 km, West. However, this option is not available in the given choices, so the correct answer is E: None of these.