# Electrical Engineering - GATE 2017 Paper Solution

The matrix $A=\left[\begin{array}{ccc}\frac{3}{2}& 0& \frac{1}{2}\\ 0& -1& 0\\ \frac{1}{2}& 0& \frac{3}{2}\end{array}\right]$ has three distinct eigenvalues and one of its eigenvectors is $\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]$.

Which one of the following can be another eigenvector of A?

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For a complex number z, $\begin{array}{c}\lim\\z\rightarrow i\end{array}\frac{z^2+1}{z^3+2z-i(z^2+2)}$ is

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Let $z(t)=x(t)\ast y(t),$ where $"\ast"$ denotes convolution. Let $c$ be a positive real-valued constant. Choose the correct expression for $z(ct).$

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A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines inside the cylinder will

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Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and proton. At t=0, the particles are release but are constrained to move along the same straight line. Which of these will collide first?

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The transfer function of a system is given by,

$\frac{V_0(s)}{V_i(s)}=\frac{1-s}{1+s}$

Let the output of the system be ${v}_{o}\left(t\right)={V}_{m}\mathrm{sin}\left(\omega t+\phi \right)$ for the input, $v_i(t)=V_m\;\sin\left(wt\right).$ Then the minimum and maximum values of $\varphi$ (in radius) are respectively

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Consider the system with following input-output relation

$y\lbrack n\rbrack=(1+(-1)^n)x\lbrack n\rbrack$

where, $x\lbrack n\rbrack$ is the input and $y\lbrack n\rbrack$ is the output. The system is

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A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in RPM is

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A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $V_{an}=220\;\sin\left(100\;\mathrm{πt}\right)\;V$ and $i_a=10\;\sin\left(100\;\mathrm{πt}\right)\;A,$ respectively. Similarly for phase-b, the instantaneous voltage and current are $V_{bn}=220\;\cos\left(100\;\mathrm{πt}\right)\;V$ and $i_b=10\;\cos\left(100\;\mathrm{πt}\right)\;A,$, respectively.

The total instantaneous power flowing from the source to the load is

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$A\;3$-bus power system is shown in the figure below, where the diagonal elements of $Y$-bus matrix are: $Y_{11}=-j12\;pu,\;Y_{22}=-j15\;pu$ and $Y_{33}=-j7\;pu.$

The per unit values of the lines reactances $p,q$ and $r$ shown in the figure are

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A closed loop system has the characteristic equation given by ${s}^{3}+K{s}^{3}+\left(K+2\right)s+3=0$. For this system to be stable, which one of the following conditions should be statisfied?

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The slope and level detector circuit in a CRO has delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of

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The Boolean expression $AB+A\overline{)C}+BC$ simplifies to

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For the circuit shown in the figure below, assume that diodes D1, D2 and D3 are ideal.

The DC components of voltages v1 and v2, respectively are

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For the power semiconductor device IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE?

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Consider $g(t)=\left\{\begin{array}{lc}t-\left\lfloor t\right\rfloor,&t\geq0\\t-\left\lceil t\right\rceil,&otherwise\end{array}\right.$, where $t\in\mathbb{R}.$

Here, $\left\lfloor t\right\rfloor$ represent the largest integer less than or equal to t and $\left\lfloor t\right\rfloor$ denotes the smallest integer greater than or equal to t.  The coefficient of the second harmonic of the Fourier series represent g(t) is__________

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Let $I=\;c\iint_R\;xy^2\;dxdy$, where R is the region shown in the figure and c = 6 × 10-4. The value of I equals _________. (Give the answer up to two decimal places.)

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The power supplied by the 25 V source in the figure shown below is _________ W.

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The equivalent resistance between the terminal A and B is__________$\Omega$.

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A three-phase, 50 Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draw current at unity power factor (UPF). The synchronous reactance of the motor is 30 $\Omega$ per phase. The load angle is 30°. The power delivered to the motor in kW is________. (Give the answer up to two decimal phase).