# 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?

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

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 $z(ct).$

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

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?

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

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

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

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

$A\;3$-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

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?

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

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

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

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

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__________

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.)

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