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Test: Routes & Networks - UPSC MCQ


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10 Questions MCQ Test - Test: Routes & Networks

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Test: Routes & Networks - Question 1
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Punit lives in village A and want to visit nearby villages B, C, D, E and F. All villages are connected by two–way routes. The length of the route from A to B is 15 km, from B to F is 20 km, from F to A is 24 km, from F to E is 21 km, from C to F is 17 km, from B to C is 22 km, from C to E is 19 km, from E to D is 28 km, from D to C is 25 km. Select the maximum distance, in km, that Punit require to cover to visit all villages and return to A. 

Detailed Solution for Test: Routes & Networks - Question 1

The possible routes are as follows:

 

A - B  - C - D - E - F - A = 15 + 22 + 25 + 28 + 21 + 24 = 135 km.

Since there is only one route which covers all villages and pass through a village only once. 

Hence, 135 km is the correct answer.

Test: Routes & Networks - Question 2
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A road map connecting to the colonies P, Q, R, S and T is shown in the figure below. Design the route starting from any colony of your choice so that you will have to walk on each of the seven routes once and only once. The starting point and the end point may not be the same. From how many points can such route be started?

Detailed Solution for Test: Routes & Networks - Question 2

The possible routes are as follows:

TQSRP

TPRSQ

TQPRS

TPQSR

Here, four such routes are possible.

Hence, four is the correct answer.

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Test: Routes & Networks - Question 3
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In the following question, select the related figure from the given alternatives.

Detailed Solution for Test: Routes & Networks - Question 3

The movement of symbols is as follows:

The symbol at position 1 will duplicate and move at position 9 and 6. The symbol at position 9 will duplicate and place at 4 and 3. The symbol at position 3 will move at position 5. The symbol at position 5 will move at position 7. The symbol at position 7 will move at position 1. The final figure will be as follows: 

Test: Routes & Networks - Question 4
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Five boys A1, A2, A3, A4 and A5 stand at various points in a field. A person B has to supply them with manure. B can directly go to A1 and then A2 or A3. B can go directly to A3 and then to A5. B can go directly to A2 and then to A4. Which of the following is definitely True?
Detailed Solution for Test: Routes & Networks - Question 4

1. B can directly go to A1 and then A2 or A3

2. B can directly go to A3 and then to A5

3. B can go directly to A2 and then to A4

Now, taking options:

a) B cannot supply manure to all of them without touching at least one person twice. → True →

To provide manure to A4 and A5 B have to touch A2 and A3. So, to provide manure to all of them B must touch A2 and A1 twice.

b) B must touch A1­ to go to A4 → False → B can directly go to A2 and then A4. It is not necessary for B to touch A1.

c) B must touch A1 to go to A3 → False → B can directly go to A3 also.

d) B must touch A2 to go to A5 → False → B must touch A3 to go to A5 not A2.

Hence, statement “B cannot supply manure to A4 of them without touching at-least one person twice” is True.

Test: Routes & Networks - Question 5
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There are six towns P, Q, R, S, T and U. They are connected as follows:

There are two one-way roads between P and Q. There are three one-way roads between Q and R. There is only one two-way road between R and T. S and T are connected by two way. Similarly, S and U are connected by two one-way road. Starting from Q if a person has to visit town S, how many ways are available?
Detailed Solution for Test: Routes & Networks - Question 5

1. There are two one-way roads between P and Q.

2. There are three one-way roads between Q and R.

3. There is only one two-way road between R and T.

4. S and T are connected by two two-way roads.

5. S and U are connected by two one-way road.

If a person has to visit town S, starting from two Q. There are six possible ways.

Hence, the correct answer is 6.

Test: Routes & Networks - Question 6
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In an office, two phones P1 and P2 are connected to LAN. L1 and L2 respectively. If the LAN is not in operation, then both the phones can be used for tele communication. There are three computers C1, C2 and C3 with which LAN L1 & L2 are directly connected L1 can be used for C1 and C2. L2 can be sued for C1 and C3. If L1 is not in operation which of the following operations will not be performed.
Detailed Solution for Test: Routes & Networks - Question 6

In an office, two phones P1 and P2 are connected to LAN L1 & L2 respectively. If LAN is not in operation, the both the phones can be used for telecommunication.

→ L1 can be used for computer C1 and C2 only

→ L2 can be used for computer C1 and C3 only

If L1 is not in operation, then P1 (telecom) will work and C1­ will work with network of L2. So, only network of C2 will not network.

Test: Routes & Networks - Question 7
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A road map connecting to the colonies A, B, C, D and E is shown in the figure below. Design the route starting from any colony of your choice so that you will have to walk on each of the seven routes once and only once. The starting point and the end point may not be the same. From how many points, can such route be started?
Detailed Solution for Test: Routes & Networks - Question 7

For this question, we can take all points one by one.

Such route started from Point A: Yes it exists, route ACDEBDAB, etc.

Such route started from Point B: Yes it exist , route BADEBDCA, etc.

Such route started from Point C: No it does not exist.

Such route started from Point D: No it does not exist.

Such route started from Point E: No it does not exist.

So, such route is started only from two points i.e., A and B.

Hence, the correct answer is option (c) i.e. Two.

Test: Routes & Networks - Question 8
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I live in a village Pali and I want to visit my therapy clients living in nearby villages Neli, Teli and Seli. All villages are connected by two-way routes. The length of the route from Pali to Neli is 31 km, from Teli to Pali is 20 km, from Seli to Pali is 22 km, from Neli to Teli is 16 km, from Teli to Seli 18 km, and from Seli to Neli is 26 km long. Select. the minimum distance, in km, that I require to cover to visit my clients and return to Pali.
Detailed Solution for Test: Routes & Networks - Question 8

There are six possibilities to visit clients and return to pali.

(1) Pali - Neli - Seli - Teli - Pali

Distance = 31 Km + 26 Km + 18 Km + 20 Km = 95 Km

(2) Pali - Neli - Teli - Seli - Pali

Distance = 31 Km + 16 Km + 18 Km + 22 Km = 87 Km

(3) Pali - Teli - Neli - Seli - Pali

Distance = 20 Km + 16 Km + 26 Km + 22 Km = 84 Km

(4) Pali - Teli - Seli - Neli - Pali

Distance = 20 Km + 18 Km + 26 Km + 31 Km = 95 Km

(5) Pali - Seli - Neli - Teli - Pali

Distance = 22 Km + 26 Km + 16 Km + 20 Km = 84 Km

(6) Pali - Seli - Teli - Neli - Pali

Distance = 22 Km + 18 Km + 16 Km + 31 Km = 87 Km

So, the minimum distance to visit clients and return to pali is 84 Km.

Hence, the correct answer is option(a) i.e., 84 Km.

Test: Routes & Networks - Question 9
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Sateja took her four grandchildren for a car ride and they visited six junctions. When she asked each of them to draw road maps that they used during their ride, they produced the following maps though all did not show exact relative positions of road connections. If only three maps are correct, then select the map with incorrect connections.
Detailed Solution for Test: Routes & Networks - Question 9

Except for option(a), every map shows four 3-road junctions and two 2-road junctions while option(a) shows all junctions have 3-road junctions.

Hence the correct answer is an option(a) i.e., 

Test: Routes & Networks - Question 10
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Rohit live in city T and want to visit branch offices of his company in nearby cities P, Q, R and S. All cities are connected by two – way routes. The length of the route from T to P is 22 km, from P to R is 15 km, from R to Q is 26 km, from Q to P is 24 km, from Q to S is 19 km, from R to S is 17 km, from T to R is 25 km, and from T to S is 20 km. Select the maximum distance, in km, that Rohit require to cover to visit all branch offices and return to T. 
Detailed Solution for Test: Routes & Networks - Question 10

The possible routes are as follows:

T - P - R - Q - S - T = 22 + 15 + 26 + 19 + 20 = 102 km

T - P - Q - R - S - T = 22 + 24 + 26 + 17 + 20 =  109 km

T - S - Q - R - P - T = 20 + 19 + 26 +15 + 22 = 102 km

T - S - R - Q - P - T =  20 + 17 + 26 + 24 + 22 =  109 km

Hence, 109 km is the correct answer.

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