The least number of computers required to connect 10 computers to 5 routers to guarantee 5 computers can directly access 5 routers is _________.a)74b)104c)30d)67Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Solution:

To guarantee 5 computers can directly access 5 routers, we need to connect 5 computers to each router. Therefore, the total number of computers required to connect 10 computers to 5 routers is:

Total number of computers = Number of routers x Number of computers per router
Total number of computers = 5 x 5
Total number of computers = 25

However, we need to take into account that each computer can only be connected to one router. Therefore, we need to add the number of routers to the total number of computers required:

Total number of computers required = Number of routers + Total number of computers
Total number of computers required = 5 + 25
Total number of computers required = 30

Therefore, the least number of computers required to connect 10 computers to 5 routers to guarantee 5 computers can directly access 5 routers is 30 (option C).

Answer

It is given that, each 5 computer needs directly connected with each router.

Let c1 to c5 be the 5 computer needs directly connected with each router r1 to r5. Now,

c1 → r1, r2, r3, r4, r5

c2 → r1, r2, r3, r4, r5

c3 → r1, r2, r3, r4, r5

c4 → r1, r2, r3, r4, r5

c5 → 1, r2, r3,r 4, r5

c6 → 1

c7 → r2

c8 → r3

c9 → r4

c10 → r5

So, 25 connections + now remaining 5 computer, each connected to 5 different routers, so 5 connections =30 connections.

Now, any pick of 5 computers will have a direct connection to all the 5 routers.

Hence, the correct option is (C).

Similar Computer Science Engineering (CSE) Doubts

An OSPF router receives an LSA. The router checks its sequence number and finds thatthis number is higher than the sequence number it already has. Which two tasks doesthe router perform with the LSA?

To prevent Service Advertisements (SAPs) from flooding a network, Cisco routersdo not forward them. How are services advertised to other networks?

Top Courses for Computer Science Engineering (CSE)View all

GATE Computer Science Engineering(CSE) 2025 Mock Test Series

Question Bank for GATE Computer Science Engineering

General Aptitude for GATE

Computer Networks

Programming and Data Structures

Top Courses for Computer Science Engineering (CSE)

Top Courses for Computer Science Engineering (CSE)

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company