# GATE EE 2017 SET 2

 Question 1
In the circuit shown, the diodes are ideal, the inductance is small, and $I_o \neq 0$. Which one of the following statements is true?
 A $D_1$ conducts for greater than 180$^\circ$ and $D_2$ conducts for greater than 180$^\circ$ B $D_2$ conducts for more than 180$^\circ$ and $D_1$ conducts for 180$^\circ$ C $D_1$ conducts for 180$^\circ$ and $D_2$ conducts for 180$^\circ$ D $D_1$ conducts for more than 180$^\circ$ and $D_2$ conducts for 180$^\circ$
Power Electronics   Phase Controlled Rectifiers
Question 1 Explanation:

Both diodes will conduct for more than $180^{\circ}$.
 Question 2
For a 3-input logic circuit shown below, the output Z can be expressed as
 A $Q+\bar{R}$ B $P\bar{Q}+R$ C $\bar{Q}+R$ D $P+\bar{Q}+R$
Digital Electronics   Logic Gates
Question 2 Explanation:

$Z=\overline{\overline{P\bar{Q}}\cdot Q\cdot \overline{Q\cdot R} }$
$\;\;=P\bar{Q}+\bar{Q}+Q R$
$\;\;=\bar{Q}(P+1)+QR$
$\;\;=\bar{Q}+QR$
$\;\;=(\bar{Q}+Q)(\bar{Q}+R)$
$\;\;=\bar{Q}+R$
 Question 3
An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the second draw is
 A $\frac{1}{2}$ B $\frac{4}{9}$ C $\frac{5}{9}$ D $\frac{6}{9}$
Engineering Mathematics   Probability and Statistics
Question 3 Explanation:

$P(red)=\frac{5}{10}\frac{4}{9}+\frac{5}{10}\frac{5}{9}=\frac{45}{90}=\frac{1}{2}$
 Question 4
When a unit ramp input is applied to the unity feedback system having closed loop transfer function
$\frac{C(s)}{R(s)}=\frac{Ks+b}{s^{2}+as+b}(a \gt 0,b \gt 0,K\gt 0)$,
the steady state error will be
 A 0 B $\frac{a}{b}$ C $\frac{a+K}{b}$ D $\frac{a-K}{b}$
Control Systems   Time Response Analysis
Question 4 Explanation:
Closed loop transfer function $=\frac{Ks+b}{s^2+as+b}$
Open loop transfer function $= G(s)=\frac{Ks+b}{s^2+as+b-Ks-b}$
$G(s)=\frac{Ks+b}{s^2+as-Ks} =\frac{Ks+b}{s(s+a-K)}$
Steady state error for ramp input given to type-1 system $=1/K_V$
where, velocity error coefficient,
$K_V=\lim_{s \to 0}s\cdot \frac{Ks+b}{s(s+a-K)} =\frac{b}{a-K}$
$e_{ss}=\frac{a-K}{b}$
 Question 5
A three-phase voltage source inverter with ideal devices operating in 180$^{\circ}$ conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is $V_{dc}$. The peak of the fundamental component of the phase voltage is
 A $\frac{V_{dc}}{\pi}$ B $\frac{2V_{dc}}{\pi}$ C $\frac{3V_{dc}}{\pi}$ D $\frac{4V_{dc}}{\pi}$
Power Electronics   Inverters
Question 5 Explanation:
$3-\phi \;\text{ VSI }180^{\circ} \text{ mode:}$

\begin{aligned} V_{Rn}&=\frac{6 V_{dc}/3}{n \pi} \sin n\omega t\\ &= \frac{2 \times V_{dc}}{n \pi} \sin n\omega t \\ V_{Rn} &= \frac{2 V_{dc}}{ \pi} \sin \omega t \end{aligned}
 Question 6
The figures show diagrammatic representations of vector fields $\vec{X},\vec{Y}$ and $\vec{Z}$ respectively. Which one of the following choices is true?
 A $\bigtriangledown \cdot \vec{X}=0$, $\bigtriangledown \times \vec{Y}\neq 0,\bigtriangledown \times \vec{Z}=0$ B $\bigtriangledown \cdot \vec{X} \neq 0$, $\bigtriangledown \times \vec{Y}=0$, $\bigtriangledown \times \vec{Z} \neq 0$ C $\bigtriangledown \cdot \vec{X}\neq 0$, $\bigtriangledown \times \vec{Y}\neq 0$, $\bigtriangledown \times \vec{Z}\neq 0$ D $\bigtriangledown \cdot \vec{X}=0$, $\bigtriangledown \times \vec{Y}= 0$, $\bigtriangledown \times \vec{Z}=0$
Electromagnetic Fields   Coordinate Systems and Vector Calculus
Question 6 Explanation:
$\vec{X}$ is going away so $\vec{\triangledown } \cdot \vec{X}\neq 0$
$\vec{Y}$ is moving circulator direction so $\vec{\triangledown } \cdot \vec{Y}\neq 0$
$\vec{Z}$ has circular rotation so $\vec{\triangledown } \cdot \vec{Z}\neq 0$
 Question 7
Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ________.
 A 0.4 B 0.9 C 1.5 D 2.6
Engineering Mathematics   Probability and Statistics
Question 7 Explanation:
$t$ be arrival time of vehicles of the junction is uniformaly distributed in [0,5].
Let y be the waiting time of the junction.

\begin{aligned} \text{Then }y&=\left\{\begin{matrix} 0 & t \lt 2 \\ 5-t & 2\leq t \lt 5 \end{matrix}\right.\\ y\rightarrow &[0,5]\\ f(y)&=\frac{1}{5-0}=\frac{1}{5}\\ E(y)&=\int_{-\infty }^{0}y(y)dy=\int_{0}^{5}yf(y)dy\\ &=\int_{2}^{5}y\left ( \frac{1}{5} \right )dy=\frac{1}{5}\int_{2}^{5}(5-t)dt\\ &=\frac{1}{5}\left ( 5t-\frac{t^2}{2} \right )|_2^5\\ &=\frac{1}{5}\left [ \left ( 25-\frac{25}{2} \right )-\left ( 10-\frac{4}{2} \right ) \right ]\\ &=\frac{1}{5}\left ( \frac{25}{2}-8 \right )=\frac{1}{5}\frac{9}{2}=0.9 \end{aligned}
 Question 8
Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed.
 A uniformly over the entire volume of the sphere B uniformly over the outer surface of the sphere C concentrated around the centre of the sphere D along a straight line passing through the centre of the sphere
Electromagnetic Fields   Electrostatic Fields
Question 8 Explanation:
Added charge (one million electrons) to be solid spherical conductor is uniformly distributed over the outer surface of the sphere.
 Question 9
The transfer function C(s) of a compensator is given below.
$C(s)=\frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$
The frequency range in which the phase (lead) introduced by the compensator reaches the maximum is
 A $0.1 \lt \omega \lt 1$ B $1 \lt \omega \lt 10$ C $10 \lt \omega \lt 100$ D $\omega \gt 100$
Control Systems   Design of Control Systems
Question 9 Explanation:
Pole zero diagram of compensator transfer function is shown below.

Maximum phase lead is between 0.1 and 1.
$0.1 \lt \omega \lt 1$
 Question 10
The figure show the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where $\alpha$ is a complex number with non-zero real and imaginary parts.

For the given circuit, $Y_{bus}\; and \; Z_{bus}$ are bus admittance matrix and bus impedance matrix, respectively, each of size 2x2. Which one of the following statements is true?
 A Both $Y_{bus}\; and \; Z_{bus}$ are symmetric B $Y_{bus}$ is symmetric and bus $Z_{bus}$ is unsymmetric C $Y_{bus}$ is unsymmetric and $Z_{bus}$ is symmetric D Both $Y_{bus}\; and \; Z_{bus}$ are unsymmetric
Both $Y_{BUS}$ and $Z_{BUS}$ are unsymmetrical with transformer.