# NTA NET Electrical Engineering GATE 2012 Higher Questions and Answers Part 4

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**(Topic: Signals and Systems)**

**(Subtopic: Laplace Transform and z-Transform)**

**(Sub-Subtopic: Differential equation with initial conditions)**

Consider the differential equation

with and

The numerical value of is

(A) -2

(B) -1

(C) 0

(D) 1

**(Topic: Electric Circuits)**

**(Subtopic: Maximum power transfer theorem)**

**(Sub-Subtopic: MPT across load)**

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

(A)

(B)

(C)

(D)

**(Topic: Control Systems)**

**(Subtopic: Controllability and Observability)**

**(Sub-Subtopic: Kalman’s teat)**

The state variable description of an LTI system is given by

where is the output and is the input? The system is controllable for

(A)

(B)

(C)

(D)

**(Topic: Signals and Systems)**

**(Subtopic: Applications of Fourier Transform)**

**(Sub-Subtopic: Sampling function)**

The Fourier transform of a signal is . The value of is

(A) 1/4

(B) 1/2

(C) 1

(D) 2

**(Topic: Control Systems)**

**(Subtopic: Routh-Hurwitz and Nyquist criteria)**

**(Sub-Subtopic: Oscillation frequency)**

The feedback system shown below oscillates at 2 rad/s when

(A)

(B)

(C)

(D)

**(Topic: Signals and Systems)**

**(Subtopic: Linear Time Invariant and Causal systems)**

**(Sub-Subtopic: TIV and stability)**

The input and output of a system are related as . The system is

(A) time-invariant and stable

(B) stable and not time-invariant

(C) time-invariant and not stable

(D) not time-invariant and not stable

**(Topic: Electric Circuits)**

**(Subtopic: Two‐port networks)**

**(Sub-Subtopic: Thevenin equivalent)**

For the same network, with 6 V dc connected at port A, connected at port B draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is

(A) 6 V

(B) 7 V

(C) 8 V

(D) 9 V

**(Topic: Electric Circuits)**

**(Subtopic: Two‐port networks)**

**(Sub-Subtopic: Thevenin equivalent)**

With 10 V dc connected at port A, the current drawn by connected at port B is

(A) 3/7 A

(B) 5/7 A

(C) 1 A

(D) 9/7 A

**(Topic: Electric Circuits)**

**(Subtopic: Power and power factor in AC circuits)**

**(Sub-Subtopic: Power factor)**

The power factor of the load is

(A) 0.45

(B) 0.50

(C) 0.55

(D) 0.60

**(Topic: Electric Circuits)**

**(Subtopic: Power and power factor in AC circuits)**

**(Sub-Subtopic: Average power)**

If , the approximate power consumption in the load is

(A) 700 W

(B) 750 W

(C) 800 W

(D) 850 W

**(Topic: Control Systems)**

**(Subtopic: Lead and Lead‐Lag compensators)**

**(Sub-Subtopic: Lead compensator)**

is a lead compensator if

(A)

(B)

(C)

(D)

**(Topic: Control Systems)**

**(Subtopic: Lead and Lead‐Lag compensators)**

**(Sub-Subtopic: Cut off frequency for Lead compensator)**

The phase of the above lead compensator is maximum at

(A)

(B)

(C)

(D)