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}
Steady state error,
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
Power Systems   Load Flow Studies
Question 10 Explanation: 
Both Y_{BUS} and Z_{BUS} are unsymmetrical with transformer.
There are 10 questions to complete.
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