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Test: Graph Theory


10 Questions MCQ Test GATE ECE (Electronics) 2022 Mock Test Series | Test: Graph Theory


Description
This mock test of Test: Graph Theory for Railways helps you for every Railways entrance exam. This contains 10 Multiple Choice Questions for Railways Test: Graph Theory (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Graph Theory quiz give you a good mix of easy questions and tough questions. Railways students definitely take this Test: Graph Theory exercise for a better result in the exam. You can find other Test: Graph Theory extra questions, long questions & short questions for Railways on EduRev as well by searching above.
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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