Test: Graph Theory


10 Questions MCQ Test GATE ECE (Electronics) 2023 Mock Test Series | Test: Graph Theory


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Attempt Test: Graph Theory | 10 questions in 30 minutes | Mock test for Railways preparation | Free important questions MCQ to study GATE ECE (Electronics) 2023 Mock Test Series for Railways Exam | Download free PDF with solutions
QUESTION: 1

Consider the following circuits :




The planner circuits are

Solution:

The circuit 1 and 2 are redrawn as below. 3 and 4 can not be redrawn on a plane without crossing other branch.

QUESTION: 2

Consider the following graphs




Non-planner graphs are

Solution:

Other three circuits can be drawn on plane without crossing


QUESTION: 3

A graph of an electrical network has 4 nodes and 7 branches. The number of links l, with respect to the chosen tree, would be

Solution:

l = b - (n - 1) = 4.

QUESTION: 4

For the graph shown in fig.correct set is

Solution:

There are 4 node and 6 branches.

t = n - 1 = 3, l = b - n + 1 = 3

QUESTION: 5

A tree of the graph shown in fig. is

Solution:

From fig. it can be seen that a f h g is a tree of given graph

QUESTION: 6

Branch current and loop current relation are expressed in matrix form as

where ij represent branch current and Ik loop current. The number of independent node equation are

Solution:

Number of branch = 8

Number of link = 4

Number of twigs = 8 - 4 = 4

Number of twigs = number of independent node equation.

QUESTION: 7

If the number of branch in a network is b, thenumber of nodes is n and the number of dependent loop is l, then the number of independent node equations will be

Solution:

The number of independent node equation are n - 1.

QUESTION: 8

Branch current and loop current relation are expressed in matrix form as

 .

where ij represent branch current and Ik loop current.

The rank of incidence matrix is

Solution:

Number of branch b = 8

Number of link l = 4

Number of twigs t = b - l = 4

rank of matrix = n - 1 = t = 4

QUESTION: 9

A network has 8 nodes and 5 independent loops. The number of branches in the network is

Solution:

Independent loops = link

l = b - (n - 1)

= 5 = b - 7

b = 12

QUESTION: 10

A branch has 6 node and 9 branch. The independent loops are

Solution:

Independent loop = link

l = b - (n-1) = 4

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