# NTA NET Electrical Engineering GATE 2019 Higher Questions and Answers Part 1

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**(Topic: Engineering Mathematics)**

**(Subtopic: Transform Theory)**

**(Sub-Subtopic: Laplace Transform)**

The inverse Laplace transform of for is

(A)

(B)

(C)

(D)

**(Topic: Engineering Mathematics)**

**(Subtopic: Linear Algebra)**

**(Sub-Subtopic: Eigen values)**

M is a 2x2 matrix with eigen values 4 and 9. The eigen values of are

(A) 4 and 9

(B) 2 and 3

(C) -2 and -3

(D) 16 and 81

**(Topic: Engineering Mathematics)**

**(Subtopic: Differential Equations)**

**(Sub-Subtopic: Partial differential equation)**

The partial differential equation

is known as

(A) Heat equation

(B) Wave equation

(C) Poisson’s equation

(D) Laplace equation

**(Topic: Engineering Mathematics)**

**(Subtopic: Complex Variables)**

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

Which one of the following functions is analytic in the region ?

(A)

(B)

(C)

(D)

**(Topic: Engineering Mathematics)**

**(Subtopic: Probability and Statistics)**

**(Sub-Subtopic: Mean and Variance)**

The mean-square of a zero-mean random process is kT/C, where k is Boltzmann’s constant. T is the absolute temperature, and C is a capacitance. The standard deviation of the random process is

(A)

(B)

(C)

(D)

**(Topic: Electric Circuits)**

**(Subtopic: Passive filters)**

**(Sub-Subtopic: Identification of filters)**

A system transfer function is . If , and all other coefficients are positive, the transfer function represents a

(A) band pass filter

(B) high pass filter

(C) low pass filter

(D) notch filter

**(Topic: Signals and Systems)**

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

**(Sub-Subtopic: Causal and Time invariant)**

The symbols, a, and T represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?

(A)

(B)

(C)

(D)

**(Topic: Electric Circuits)**

**(Subtopic: Sinusoidal steady‐state analysis)**

**(Sub-Subtopic: DC offset current)**

**(Topic: Control Systems)**

**(Subtopic: Transient and Steady‐state analysis of linear time invariant systems)**

**(Sub-Subtopic: Final value theorem)**

The output response of a system is denoted as y(t) and its Laplace transform is given by

The steady state value of y(t) is

(A)

(B)

(C)

(D)

**(Topic: Control Systems)**

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

**(Sub-Subtopic: Phase angle calculation)**

The open loop transfer function of a unity feedback system is given by

In plane, the Nyquist plot of passes through the negative real axis at the point

(A)

(B)

(C)

(D)