GATE 2020: Network Theory Quiz 1 (App update required to attempt this test)

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Question 1

The complete graph of electrical network has 5 nodes. The number of possible trees is

• A243
• B25
• C125
• D216

Question 2

The graph of an electrical network has N nodes and B branches. The number of independent KVL equations

• Ab-N-1
• Bb-N+1
• Cb-N
• Db+N+1

Question 3

Consider the following statements for a network graph, if is its fundamental cut set matrix and and are its sub matrices corresponding to links and twigs respectively
1) is a unit matrix
2) is a rectangular matrix
3)
Where S is the identity matrix and and are its sub matrices corresponding to twigs and links respectively.
and are the sub matrices of fundamental tie set matrix corresponding to twigs and links respectively.
Which of the above statements are correct?

• A1 and 2 only
• B3 only
• C1, 2 and 3
• DNone of these

Question 4

For a given connected network and for the fixed tree, fundamental loop matrix is given by
[B] =
The fundamental cut set matrix Q corresponding to the same tree is given by

• A
• B
• C
• D

Question 5

Consider the following relations
1) [A].[B]^t=0
2) [B].[Q]^t=0
3) [A].[B]^t=I
4) [B].[Q]^t=I
Where [A] = incidence matrix
[B] = tie set matrix
[Q] = cut set matrix
I = identity matrix
Which of the above relations are correct?

• A1 only
• B3 and 4 only
• C1 and 2 only
• D1 and 4 only

Question 6

The incidence matrix of a graph is as given below

A=

The number of possible trees is_______

Answer

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