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Test: Distance And Direction- 1 - CUET Commerce MCQ


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20 Questions MCQ Test General Test Preparation for CUET - Test: Distance And Direction- 1

Test: Distance And Direction- 1 for CUET Commerce 2024 is part of General Test Preparation for CUET preparation. The Test: Distance And Direction- 1 questions and answers have been prepared according to the CUET Commerce exam syllabus.The Test: Distance And Direction- 1 MCQs are made for CUET Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Distance And Direction- 1 below.
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Test: Distance And Direction- 1 - Question 1

Salim started walking from point 'P' towards South. After walking 40 metres, he took a left turn and walked 30 metres and reached point Q. What is the straight line distance between P and Q, and Q is towards which direction of P?

Detailed Solution for Test: Distance And Direction- 1 - Question 1

As per the given information;

Point Q is in South East of Point P.

Distance between P and Q (PQ) = √(PO2 + OQ2)

PQ = √(402 + 302)

PQ = √(1600 + 900)

PQ = √2500

PQ = 50 m

Hence, "50 metres, Southeast" is the correct answer.

Test: Distance And Direction- 1 - Question 2

Sonu started from his house and walked 3 km Eastward, then he turned right and walked 2 km, then again he turned left and walked 1 km.  Again he turned left and walked 3 km, then turned right and walked 2 km. He turned right again and walked 1 km and reached his school. What is the shortest distance between Sonu's house and his school?

Detailed Solution for Test: Distance And Direction- 1 - Question 2

Sonu started from his house and walked 3 km Eastward, then he turned right and walked 2 km, then again he turned left and walked 1 km. Again he turned left and walked 3 km, then turned right and walked 2 km. He turned right again and walked 1 km and reached his school.

Shortest distance between Sonu's home and school is, Home to point A + AD + point D to school = 3 + 2 + 1 = 6 km.
Hence, the distance between Sonu's home and the school is 6 km.
Thus, this is the correct answer.

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Test: Distance And Direction- 1 - Question 3

If South East becomes North, North East becomes West and this trend is continued, what will be the original West become?

Detailed Solution for Test: Distance And Direction- 1 - Question 3
  • If South-east becomes North and North East becomes West, therefore, the whole figure moves through 135º. Hence, West will be South-East.
  • See, Actual figure is rotating 135º anticlockwise.
  • So, When West will be rotated by same degree anticlockwise. It will hold the place of south-East.
Test: Distance And Direction- 1 - Question 4

Gaurav walks 20 metres towards North. He then turns left and walks 40 metres. He again turns left and walks 20 metres. Further, he moves 20 metres after turning to the right. How far is he from his original position ?

Detailed Solution for Test: Distance And Direction- 1 - Question 4

Final distance from original position = AE = AD + DE = 60 metres

solution

Test: Distance And Direction- 1 - Question 5

Hemant started from his house and walked 3km eastward, then he turned right and walked 2km, then again he turned left and walked 1 km, then turned right and walked 2 km. He turned right again and walked 1 km and reached his school. What is the minimum distance between Hemant’s house and his school?

Detailed Solution for Test: Distance And Direction- 1 - Question 5

To solve this, let's break down Hemant's movements step by step and visualize his path:

  1. Hemant starts from his house and walks 3 km eastward.
  2. He turns right and walks 2 km south.
  3. He turns left and walks 1 km east.
  4. He turns right and walks 2 km south.
  5. He turns right and walks 1 km west and reaches his school.

Now, let's consider the overall east-west and north-south movement:

  • East-West: Hemant initially walked 3 km east, then 1 km east, and finally 1 km west. So, the net eastward distance is 3 + 1 − 1 = 3 km.
  • North-South: Hemant walked 2 km south, then another 2 km south, so he walked a total of 2 + 2 = 4 km south.

The minimum distance from Hemant’s house to the school can be found using the Pythagorean theorem (since he moved in perpendicular directions):

Thus, the minimum distance between Hemant’s house and his school is: D: 5 km

Test: Distance And Direction- 1 - Question 6

Sushant started from his house and walked 5km north of his house. Then he turned left and walked 3km, then he turned right and walked 5km. Again he turned right and walked 3km. Where is his final destination from his house?

Detailed Solution for Test: Distance And Direction- 1 - Question 6

To solve this question, let's analyze Sushant's path step-by-step based on the directions provided:

  1. Sushant starts at his house and walks 5 km north.
  2. He then turns left and walks 3 km west.
  3. Next, he turns right and walks 5 km north again.
  4. Finally, he turns right and walks 3 km east.

Now let’s assess Sushant's final position relative to his starting point:

  • North-South movement: He walked 5 km north, then another 5 km north, totaling 10 km north.
  • East-West movement: He walked 3 km west and then 3 km back east, which brings him back to the original east-west position he started from.

Given this analysis, Sushant's final destination is directly north of his house without any deviation east or west. Therefore, the correct answer is:

D: 10 km North

Test: Distance And Direction- 1 - Question 7

Rohan starts for morning walk towards west. He walks 1 km, then turns left and walks 600m, then turns left and walks 1.3km, again he turns right and walks 600m further.  In which direction is he moving now?

Detailed Solution for Test: Distance And Direction- 1 - Question 7

Rohan is walking in south now

Test: Distance And Direction- 1 - Question 8

If a man on the moped starts from a point and rides 4km south, then turns left and rides 2km, then turn again to the right to ride 4km more, towards which direction is he moving?

Detailed Solution for Test: Distance And Direction- 1 - Question 8


The man starts riding in south direction then he rides 2 km in the east (for him his left is the east direction)and then it rides 4km in the south (for him his right is in south direction).

Test: Distance And Direction- 1 - Question 9

Namratha walks 14 metres towards west, then turns to her right and walks 14 meters and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance (in metres) between her starting point and her present position?  

Detailed Solution for Test: Distance And Direction- 1 - Question 9

Let's break down Namratha's movements step by step:

  1. First Movement: She walks 14 meters west.
  2. Second Movement: She turns right and walks 14 meters north.
  3. Third Movement: She turns left and walks 10 meters west.
  4. Fourth Movement: She turns left again and walks 14 meters south.

Now, let's analyze her position.

  • After the first movement, she's 14 meters west of the starting point.
  • After the second movement, she's 14 meters west and 14 meters north of the starting point.
  • After the third movement, she's 24 meters west and 14 meters north of the starting point.
  • After the fourth movement, she moves 14 meters south, so she's now 24 meters west and at the same latitude as her starting point (because the south movement cancels out the north movement).

To find the shortest distance between her starting point and her present position, we just need to calculate the straight-line distance (which is the horizontal distance since her vertical displacement is zero).

Since she is 24 meters west of her starting point, the shortest distance is:

Distance = 24 meters

So the correct answer is 24 meters (Option 3).

Test: Distance And Direction- 1 - Question 10

Jenny walked 2.5 km towards North and turned towards West. After covering 2 km’s he turned to South and walked 1.5 km’s. He then turned to East and covered 2 km’s. How far is Jenny from original point?

Detailed Solution for Test: Distance And Direction- 1 - Question 10

To find out how far Jenny is from her original point, we will break down her journey step by step:

  1. North: Jenny walks 2.5 km north.
  2. West: She turns and walks 2 km west.
  3. South: She turns again and walks 1.5 km south.
  4. East: Finally, she turns and walks 2 km east.

Now, let's analyze her final position relative to the start:

  • North-South movement: Jenny initially walked 2.5 km north, then 1.5 km south, resulting in a net movement of 2.5 − 1.5 = 1.0 km north.
  • East-West movement: She walked 2 km west and then 2 km east. This means she ended up exactly where she started in terms of east-west movement, as these cancel each other out.

So, Jenny's final position is 1.0 km north of her starting point. Thus, she is: D: 1 km

Test: Distance And Direction- 1 - Question 11

If A is to the south of B, and C is to the east of B, in what direction is A with respect to C?

Detailed Solution for Test: Distance And Direction- 1 - Question 11

A diagram is made according to the directions given in the question. Clearly A will be South-West of C.

Test: Distance And Direction- 1 - Question 12

Lakshay starting walking towards west and goes 10km. Then he turns left and goes 8km. He again turns left and goes 18km. In which direction is he now from his starting point? 

Detailed Solution for Test: Distance And Direction- 1 - Question 12

From the figure given, clearly the direction is OC which is South-East.

Test: Distance And Direction- 1 - Question 13

Ayush starts from his house and moves towards South. He walks 100m, then turns left and walks 200m, turns right and walks 500m. How far is he from his house?

Detailed Solution for Test: Distance And Direction- 1 - Question 13

We can solve this problem using the Pythagorean theorem.
First, let's break down Ayush's movements:
1. He walks 100m south.
2. He turns left (which means he is now facing east) and walks 200m.
3. He turns right (which means he is now facing south again) and walks 500m.
Now, let's determine his horizontal (east-west) and vertical (north-south) displacements.
Horizontal displacement:
Ayush only moved horizontally during step 2, where he walked 200m east. Therefore, his total horizontal displacement is 200m.
Vertical displacement:
Ayush moved vertically during steps 1 and 3. In step 1, he walked 100m south, and in step 3, he walked 500m south. Therefore, his total vertical displacement is 100m + 500m = 600m.
Now we can use the Pythagorean theorem to calculate the distance between his starting point (his house) and his final position:
Distance = √(horizontal displacement2 + vertical displacement2)
Distance = √(200m2 + 600m2)
Distance = √(40,000m2 + 360,000m2)
Distance = √(400,000m2)
Distance = 200√10m
So the correct answer is 3 (200√10m).

Test: Distance And Direction- 1 - Question 14

Tanuj started walking from a point ‘P’ towards South. After walking 40 metres he took a left turn. He then walked 30 metres and reached a point Q.  What is the straight distance between P and Q and Q is towards in which direction with reference to point P?          

Detailed Solution for Test: Distance And Direction- 1 - Question 14

Step 1: Tanuj starts from point P and walks 40 metres south.
Step 2: He takes a left turn (facing east) and walks 30 metres to reach point Q.
Applying the Pythagorean Theorem:
The path forms a right-angled triangle with:
One side = 40 metres (southward movement)
Another side = 30 metres (eastward movement)
Using the Pythagorean theorem to find the distance from P to Q:
PQ = √(40² + 30²) = √(1600 + 900) = √2500 = 50 metres
Direction of Q from P:
Since Tanuj moved south first and then east, Q is located South-East of P.
Answer:
c) 50 metres, South-East

Test: Distance And Direction- 1 - Question 15

Starting from a point X Jayant walked 15 metres towards West, he turned to his left and walked 20 metres. He then turned to his left and walked 15 metres. He then further turned to his right and walked 12 metres. How far is Jayant from the point X and in which direction?

Detailed Solution for Test: Distance And Direction- 1 - Question 15

Required distance= 20 +12
= 32 m in south direction

Test: Distance And Direction- 1 - Question 16

A man walks 1 km to East and then he turns to South and walks 5 km. Again he turns to East and walks 2 km. After this he turns to North and walks 9 km. Now, how far is he from his starting point?

Detailed Solution for Test: Distance And Direction- 1 - Question 16

The last position of the man is P and OEP is a Right angled triangle in which
EP = 3 km and OE = 4 km
Thus,
OP = √(32 +42)
OP = √25
OP = 5 km.

Test: Distance And Direction- 1 - Question 17

A starts from his house and moves towards B’s house which is 4km North.  After walking for three-fourth of the distance he finds B coming towards him along with C, who is A’s enemy. Wanting to avoid him, A takes a left turn and runs for a distance of 2kms. Now, if from this point (say ‘P’) he decides to go to B’s house, how much distance would he need to cover?

Detailed Solution for Test: Distance And Direction- 1 - Question 17

Let's analyze the path taken by A and the distances involved:

  1. A moves towards B's house: A starts moving north towards B's house which is 4 km away.
  2. A covers three-fourth of the distance: He covers 4 × 3/4 = 3 km towards the north.
  3. A takes a left turn: At this point, A is 1 km away from B's house (since he has covered 3 km out of 4 km). He then takes a left turn, which would be towards the west and runs 2 km.

Now, A is 1 km south of B's house and 2 km west of a direct line north from B’s house. To find the distance from point P (A's new location) to B's house, we use the Pythagorean theorem:

Thus, A would need to cover a distance of: B: √5km  

Test: Distance And Direction- 1 - Question 18

A starts from his house and moves towards B’s house which is 4km North.  After walking for three-fourth of the distance he finds B coming towards him along with C, who is A’s enemy. Wanting to avoid him, A takes a left turn and runs for a distance of 2kms.Now, if from this point (say ‘P’) he decides to go to B’s house.

How far is A, from his own house?

Detailed Solution for Test: Distance And Direction- 1 - Question 18

1. A walks three-fourths of the distance towards B's house, which is:
(3/4) × 4 km = 3 km (north).
After walking 3 km north, A takes a left turn and runs 2 km west.

2. Now, we have a right-angled triangle, where:
- One leg (north) = 3 km,
- Another leg (west) = 2 km.

3. The distance from A’s current position (P) to his house is the hypotenuse of this right-angled triangle:
Distance = √(3² + 2²) = √(9 + 4) = √13 km.

Thus, the distance from A’s current position to his own house is √13 km.

Test: Distance And Direction- 1 - Question 19

Y is to the East of X, which is to the North-East of Z. If P is to the South of Z, then P is in which direction with respect to Y.

Detailed Solution for Test: Distance And Direction- 1 - Question 19

P is in South-West of Y.

Test: Distance And Direction- 1 - Question 20

A man walks 5 km toward south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place?

Detailed Solution for Test: Distance And Direction- 1 - Question 20

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