GATE EC||NETWORK THEORY||PYQS(2000-2025)

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Question 1

The differential equation for the current i(t) in the circuit of the figure is

[GATE EC || PYQ || 2003 MCQ || 2 mark ]

Question 2

Consider the network graph shown in the figure. Which one of the following is NOT a 'tree' of this graph?

(GATE EC || PYQ || 2004 MCQ || 1 mark)

Question 3

In the following graph, the number of trees (P) and the number of cut-sets (Q) are

(GATE EC|| 2008 MCQ || 1 MARK)

P = 2, Q = 2
P = 2, Q = 6
P = 4, Q = 6
P = 4, Q = 10

Question 4

The first and the last critical frequency of an RC-driving point impedance function must respectively be

(GATE EC|| 2005 MCQ || 2 MARK)

a zero and a pole
a zero and a zero
a pole and a pole
a pole and a zero

Question 5

The driving-point impedance Z(s) of a network has the pole-zero locations as shown in the figure. If Z(0) = 3, then Z(s) is

(GATE EC|| 2003 MCQ || 2 MARK)

[Tex]\frac{3(s+3)}{s^2+2s+3}[/Tex]
[Tex]\frac{2(s+3)}{s^2+2s+2}[/Tex]
[Tex]\frac{3(s+3)}{s^2-2s-2}[/Tex]
[Tex]\frac{3(s-3)}{s^2-2s-3}[/Tex]

Question 6

A negative resistance R_neg is connected to a passive network N having driving point impedance as shown below. For Z₂(s) to be positive real

(GATE EC|| 2006 MCQ || 2 MARK)

[Tex]|R_{\mathrm{neg}}|\leq \operatorname{Re} Z_1(j\omega),\quad \forall \omega[/Tex]
[Tex]|R_{\mathrm{neg}}|\leq |Z_1(j\omega)|,\quad \forall \omega[/Tex]
[Tex]|R_{\mathrm{neg}}|\leq \operatorname{Im} Z_1(j\omega),\quad \forall \omega[/Tex]
[Tex]|R_{\mathrm{neg}}|\leq \angle Z_1(j\omega),\quad \forall \omega[/Tex]

Question 7

The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by

(PYQ || 2006 MCQ || 2 marks)