# NTA NET Electrical Engineering GATE 2018 Higher Questions and Answers Part 3

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**(Topic: Control Systems)**

**(Subtopic:** **State space model)**

**(Sub-Subtopic:** **Zero input response)**

Consider a system governed by the following equations

The initial conditions are such that . Let and . Which one of the following is true?

(A)

(B)

(C)

(D)

**(Topic: Control Systems)**

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

**(Sub-Subtopic:** **Calculation of left half poles)**

The number of roots of the polynomial, , in the open left half of the complex plane is

(A) 3

(B) 4

(C) 5

(D) 6

**(Topic: Engineering Mathematics)**

**(Subtopic:** **Complex Variables)**

**(Sub-Subtopic:** **Cauchy integral formula)**

If C is a circle and , then is

(A) 1

(B) 0

(C) -1

(D) -2

**(Topic: Analog and Digital Electronics)**

**(Subtopic:** **Combinational and Sequential logic circuits)**

**(Sub-Subtopic:** **Counters)**

Which one of the following statements is true about the digital circuit shown in the figure?

(A) It can be used for dividing the input frequency by 3.

(B) It can be used for dividing the input frequency by 5.

(C) It can be used for dividing the input frequency by 7.

(D) It cannot be reliably used as a frequency divider due to disjoint internal cycles.

**(Topic: Analog and Digital Electronics)**

**(Subtopic:** **Combinational and Sequential logic circuits)**

**(Sub-Subtopic:** **K-map)**

Digital input signals 𝐴, 𝐵, 𝐶 with 𝐴 as the MSB and 𝐶 as the LSB are used to realize the Boolean function , where denotes the 𝑖𝑡ℎ minterm. In addition, 𝐹 has a do not care for . The simplified expression for 𝐹 is given by

**(Topic: Signals and Systems)**

**(Subtopic:** **Representation of continuous and discrete‐time signals)**

**(Sub-Subtopic:** **Energy calculation)**

Consider the two continuous-time signals defined below:

These signals are sampled with a sampling period of T = 0.25 seconds to obtain discrete time signals and , respectively. Which one of the following statements is true?

(A) The energy of is greater than the energy of .

(B) The energy of is greater than the energy of .

(C) and have equal energies.

(D) Neither nor is a finite-energy signal.

**(Topic: Signals and Systems)**

**(Subtopic:** **Representation of continuous and discrete‐time signals)**

**(Sub-Subtopic:** **Energy calculation)**

The signal energy of the continuous-time signal

x(t) =[(t -1) u(t -1)]-[(t -2)u(t -2)]-[(t -3)u(t -3)]+[(t -4)u(t -4)] is

(A) 11/3

(B) 7/3

(C) 1/3

(D) 5/3

**(Topic: Signals and Systems)**

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

**(Sub-Subtopic:** **Fourier transform of continuous time signal)**

The Fourier transform of a continuous-time signal is given by , where and denotes frequency. Then the value of at t =1 is ___________ (up to 1 decimal place). ( denotes the logarithm to base e)

**(Topic: Engineering Mathematics)**

**(Subtopic:** **Calculus)**

**(Sub-Subtopic:** **Green’s theorem)**

**(Topic: Engineering Mathematics)**

**(Subtopic:** **Calculus)**

**(Sub-Subtopic:** **Maximum value)**

Let . The maximum value of f (x) over the interval [0, 2] is _______ (up to 1 decimal place).

**(Topic: Engineering Mathematics)**

**(Subtopic:** **Linear Algebra)**

**(Sub-Subtopic:** **Cayley Hamilton theorem)**

Let and , where I is the 3x3 identity matrix. The determinant of B is ________ (up to 1 decimal place).