GATE EE 2016: Electrical Engineering Session 1
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GATE 2016 General Aptitude - GA Set-6
Q. 1 – Q. 5 carry one mark each.
Q.1 The man who is now Municipal Commissioner worked as ____________________.
(A) the security guard at a university
(B) a security guard at the university
(C) a security guard at university
(D) the security guard at the university
Q.2 Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly
wickets in Australia.
Choose the option which is closest in meaning to the underlined phrase in the above sentence.
(A) put up with (B) put in with (C) put down to (D) put up against
Q.3 Find the odd one in the following group of words.
mock, deride, praise, jeer
(A) mock (B) deride (C) praise (D) jeer
Q.4 Pick the odd one from the following options.
(A) CADBE (B) JHKIL (C) XVYWZ (D) ONPMQ
Q.5 In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of
αα nn + ββ nn
αα −nn + ββ −nn
4 n 2n-1 n-1
(A) n (B) 4 (C) 2 (D) 4
Q. 6 – Q. 10 carry two marks each.
Q.6 Among 150 faculty members in an institute, 55 are connected with each other through Facebook®
and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook® or
WhatsApp® accounts. The number of faculty members connected only through Facebook® accounts
is ______________.
(A) 35 (B) 45 (C) 65 (D) 90
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GATE 2016 General Aptitude - GA Set-6
Q.7 Computers were invented for performing only high-end useful computations. However, it is no
understatement that they have taken over our world today. The internet, for example, is ubiquitous.
Many believe that the internet itself is an unintended consequence of the original invention. With
the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left
wondering if all these developments are good or, more importantly, required.
Which of the statement(s) below is/are logically valid and can be inferred from the above
paragraph?
(i) The author believes that computers are not good for us.
(ii) Mobile computers and the internet are both intended inventions
(A) (i) only (B) (ii) only (C) both (i) and (ii) (D) neither (i) nor (ii)
Q.8 All hill-stations have a lake. Ooty has two lakes.
Which of the statement(s) below is/are logically valid and can be inferred from the above
sentences?
(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake.
(A) (i) only (B) (ii) only
(C) both (i) and (ii) (D) neither (i) nor (ii)
Q.9 In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be
observed in the grid?
(A) 21 (B) 27 (C) 30 (D) 36
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GATE 2016 General Aptitude - GA Set-6
Q.10
f(x)
x
Choose the correct expression for f(x) given in the graph.
(A) ff(xx) = 1 − |xx − 1| (B) ff(xx) = 1 + |xx − 1|
(C) ff(xx) = 2 − |xx − 1| (D) ff(xx) = 2 + |xx − 1|
END OF THE QUESTION PAPER
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q. 1 – Q. 25 carry one mark each.
Q.1 The maximum value attained by the function ( ) = ( − 1)( − 2) in the interval [1, 2] is
_____.
Q.2 Consider a 3 × 3 matrix with every element being equal to 1. Its only non-zero eigenvalue is ____.
Q.3 The Laplace Transform of ( )= sin(5 ) ( ) is
(A) (B) (C) (D)
Q.4 A function ( ), such that (0) = 1 and (1) = 3 , is a solution of the differential equation
+ 2 + = 0. Then (2) is
(A) 5 (B) 5 (C) 7 (D) 7
Q.5 The value of the integral
2 +5
− ( − 4 + 5)
over the contour | | = 1, taken in the anti-clockwise direction, would be
(A) (B) (C) (D)
Q.6
( )
The transfer function of a system is = . The steady state output y(t) is (2 + ) for
( )
the input (2 ). The values of A and , respectively are
(A) , −45 (B) , +45 (C) √2, −45 (D) √2,+45
√ √
Q.7
The phase cross-over frequency of the transfer function ( )= in rad/s is
( )
(A) √3 (C) 3 (D) 3√3
(B)
√
EE 1/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.8 Consider a continuous-time system with input ( ) and output ( ) given by
( ) = ( ) cos( )
This system is
(A) linear and time-invariant
(B) non-linear and time-invariant
(C) linear and time-varying
(D) non-linear and time-varying
Q.9
The value of ∫ (2 − 2) d , where ( ) is the Dirac delta function, is
(A) (B) (C) (D)
Q.10 A temperature in the range of −40˚ C to 55˚ C is to be measured with a resolution of 0.1˚ C. The
minimum number of ADC bits required to get a matching dynamic range of the temperature sensor
is
(A) 8 (B) 10 (C) 12 (D) 14
Q.11 Consider the following circuit which uses a 2-to-1 multiplexer as shown in the figure below. The
Boolean expression for output F in terms of A and B is
0
Y F
S
1
A
B
(A) A ⊕ (B) + (C) + (D) ⊕
EE 2/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.12 A transistor circuit is given below. The Zener diode breakdown voltage is 5.3 V as shown. Take
base to emitter voltage drop to be 0.6 V. The value of the current gain β is _________.
10 V
4.7 k 220
0.5 mA
5.3 V
470
Q.13 In cylindrical coordinate system, the potential produced by a uniform ring charge is given by
= ( , ), where f is a continuous function of r and z. Let ⃗ be the resulting electric field. Then
the magnitude of ∇ × ⃗
(A) increases with . (B) is 0. (C) is 3. (D) decreases with .
Q.14 A soft-iron toroid is concentric with a long straight conductor carrying a direct current I. If the
relative permeability µr of soft-iron is 100, the ratio of the magnetic flux densities at two adjacent
points located just inside and just outside the toroid, is _______.
Q.15 RA and RB are the input resistances of circuits as shown below. The circuits extend infinitely in the
direction shown. Which one of the following statements is TRUE?
2 2 2
RA
1 1 1
2 2 2
RB
1 1 1 1
(A) RA=RB (B) RA=RB=0 (C) RA< RB (D) RB= RA /(1+RA)
EE 3/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.16 In a constant V/f induction motor drive, the slip at the maximum torque
(A) is directly proportional to the synchronous speed.
(B) remains constant with respect to the synchronous speed.
(C) has an inverse relation with the synchronous speed.
(D) has no relation with the synchronous speed.
Q.17 In the portion of a circuit shown, if the heat generated in 5 Ω resistance is 10 calories per second,
then heat generated by the 4 Ω resistance, in calories per second, is _______.
4 6
5
Q.18 In the given circuit, the current supplied by the battery, in ampere, is _______.
I1 1 1 I2
1V 1
I2
Q.19 In a 100 bus power system, there are 10 generators. In a particular iteration of Newton Raphson
load flow technique (in polar coordinates), two of the PV buses are converted to PQ type. In this
iteration,
(A) the number of unknown voltage angles increases by two and the number of unknown voltage
magnitudes increases by two.
(B) the number of unknown voltage angles remains unchanged and the number of unknown voltage
magnitudes increases by two.
(C) the number of unknown voltage angles increases by two and the number of unknown voltage
magnitudes decreases by two.
(D) the number of unknown voltage angles remains unchanged and the number of unknown
voltage magnitudes decreases by two.
Q.20 The magnitude of three-phase fault currents at buses A and B of a power system are 10 pu and 8 pu,
respectively. Neglect all resistances in the system and consider the pre-fault system to be unloaded.
The pre-fault voltage at all buses in the system is 1.0 pu. The voltage magnitude at bus B during a
three-phase fault at bus A is 0.8 pu. The voltage magnitude at bus A during a three-phase fault at
bus B, in pu, is ________.
EE 4/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.21 Consider a system consisting of a synchronous generator working at a lagging power factor, a
synchronous motor working at an overexcited condition and a directly grid-connected induction
generator. Consider capacitive VAr to be a source and inductive VAr to be a sink of reactive power.
Which one of the following statements is TRUE?
(A) Synchronous motor and synchronous generator are sources and induction generator is a sink of
reactive power.
(B) Synchronous motor and induction generator are sources and synchronous generator is a sink of
reactive power.
(C) Synchronous motor is a source and induction generator and synchronous generator are sinks of
reactive power.
(D) All are sources of reactive power.
Q.22 A buck converter, as shown in Figure (a) below, is working in steady state. The output voltage and
the inductor current can be assumed to be ripple free. Figure (b) shows the inductor voltage v
during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck
converter is ________.
vL
M
30V
+ vL - +
+
C R TON TOFF
Vg D Vo
- 0
t
-
20V
TS
(a) (b)
EE 5/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.23 A steady dc current of 100 A is flowing through a power module (S, D) as shown in Figure (a). The
V-I characteristics of the IGBT (S) and the diode (D) are shown in Figures (b) and (c), respectively.
The conduction power loss in the power module (S, D), in watts, is ________.
IS(A) ID (A)
S dV/dI=0.02 V o=0.7V dV/dI=0.01
D
V o=1V
VS(Volt) V D (Volt)
100 A
V-I characteristic of IGBT V-I characteristic of diode
(a) (b) (c)
Q.24 A 4-pole, lap-connected, separately excited dc motor is drawing a steady current of 40 A while
running at 600 rpm. A good approximation for the waveshape of the current in an armature
conductor of the motor is given by
40A
I
10A I
t t
(A) (B)
I 10A
I
10A
T=25ms T=25ms
t
t T=25ms
T=25ms -10A
-10A
(C) (D)
EE 6/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.25 If an ideal transformer has an inductive load element at port 2 as shown in the figure below, the
equivalent inductance at port 1 is
n:1
L
Port 1 Port 2
(A) (B) (C) (D)
Q. 26 – Q. 55 carry two marks each.
Q.26 Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were
the permitted pen colours that the candidate could bring. The probability that a candidate comes
with all 3 pens having the same colour is _____.
Q.27
n
Let S n where | | < 1. The value of
n 0
in the range 0 < < 1, such that =2
is _______.
Q.28 Let the eigenvalues of a 2 x 2 matrix A be 1, -2 with eigenvectors x1 and x2 respectively. Then the
eigenvalues and eigenvectors of the matrix − 3 + 4 would, respectively, be
(A) 2, 14; x1, x2 (B) 2, 14; x1+ x2, x1 - x2
(C) 2, 0; x1, x2 (D) 2, 0; x1+ x2, x1- x2
Q.29 Let A be a 4 × 3 real matrix with rank 2. Which one of the following statement is TRUE?
(A) Rank of is less than 2.
(B) Rank of is equal to 2.
(C) Rank of is greater than 2.
(D) Rank of can be any number between 1 and 3.
EE 7/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.30 Consider the following asymptotic Bode magnitude plot (ω is in rad/s).
magnitude (dB)
12 dB
20 dB/dec
- 40 dB/dec
0 dB
8
0.5
Which one of the following transfer functions is best represented by the above Bode magnitude
plot?
(A)
( . )( . )
( . )
(B)
( . )
(C)
( )( )
(D)
( )( )
Q.31 Consider the following state-space representation of a linear time-invariant system.
1 0 1 (0) = 1
̇( ) = ( ), ( )= ( ), = and
0 2 1 1
The value of ( ) for = log 2 is __________.
Q.32 s3
Loop transfer function of a feedback system is G( s) H ( s) 2 . Take the Nyquist contour in
s ( s 3)
the clockwise direction. Then, the Nyquist plot of G ( s ) H ( s ) encircles 1 j 0
(A) once in clockwise direction (B) twice in clockwise direction
(C) once in anticlockwise direction (D) twice in anticlockwise direction
EE 8/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.33 Given the following polynomial equation
+ 5.5 + 8.5 + 3 = 0,
the number of roots of the polynomial, which have real parts strictly less than −1, is ________ .
Q.34 Suppose ( ) and ( ) have the Fourier transforms as shown below.
X 1(j) X2(j)
1 1
0.5 0.5
0.3 0.3
1 0 1 2 2 1 0 1
Which one of the following statements is TRUE?
(A) ( ) and ( ) are complex and ( ) ( ) is also complex with nonzero imaginary part
(B) ( ) and ( ) are real and ( ) ( ) is also real
(C) ( ) and ( ) are complex but ( ) ( ) is real
(D) ( ) and ( ) are imaginary but ( ) ( ) is real
Q.35 The output of a continuous-time, linear time-invariant system is denoted by { ( )} where ( ) is
the input signal. A signal ( ) is called eigen-signal of the system T , when { ( )} = ( ),
where is a complex number, in general, and is called an eigenvalue of T. Suppose the impulse
response of the system T is real and even. Which of the following statements is TRUE?
(A) cos( ) is an eigen-signal but sin( ) is not
(B) cos( ) and sin( ) are both eigen-signals but with different eigenvalues
(C) sin( ) is an eigen-signal but cos( ) is not
(D) cos( ) and sin( ) are both eigen-signals with identical eigenvalues
Q.36 The current state QA QB of a two JK flip-flop system is 00. Assume that the clock rise-time is much
smaller than the delay of the JK flip-flop. The next state of the system is
5V
QA QB
J J
QA
K K
CLK
(A) 00 (B) 01 (C) 11 (D) 10
EE 9/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.37 A 2-bit flash Analog to Digital Converter (ADC) is given below. The input is 0 ≤ VIN ≤ 3 Volts.
The expression for the LSB of the output B0 as a Boolean function of X2, X1, and X0 is
3V
100
X2
200 B1
Digital
X1 Circuit B0
200
100 X0
VIN
(A) [ ⊕ ] (B) [ ⊕ ] (C) [ ⊕ ] (D) [ ⊕ ]
Q.38 Two electric charges and −2 are placed at (0,0) and (6,0) on the x-y plane. The equation of the
zero equipotential curve in the x-y plane is
(A) = −2 (B) =2 (C) + =2 (D) ( + 2) + = 16
Q.39 In the circuit shown, switch S2 has been closed for a long time. At time = 0 switch S1 is closed.
At = 0 , the rate of change of current through the inductor, in amperes per second, is _____.
S1 1 S2
2
3V 1H
3V
Q.40 A three-phase cable is supplying 800 kW and 600 kVAr to an inductive load. It is intended to
supply an additional resistive load of 100 kW through the same cable without increasing the heat
dissipation in the cable, by providing a three-phase bank of capacitors connected in star across the
load. Given the line voltage is 3.3 kV, 50 Hz, the capacitance per phase of the bank, expressed in
microfarads, is ________.
EE 10/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.41 A 30 MVA, 3-phase, 50 Hz, 13.8 kV, star-connected synchronous generator has positive, negative
and zero sequence reactances, 15%, 15% and 5% respectively. A reactance (Xn) is connected
between the neutral of the generator and ground. A double line to ground fault takes place
involving phases ‘b’ and ‘c’, with a fault impedance of j0.1 p.u. The value of Xn (in p.u.) that will
limit the positive sequence generator current to 4270 A is _________.
Q.42 If the star side of the star-delta transformer shown in the figure is excited by a negative sequence
voltage, then
(A) VAB leads Vab by 60º
(B) VAB lags Vab by 60º
(C) VAB leads Vab by 30º
(D) VAB lags Vab by 30º
Q.43 A single-phase thyristor-bridge rectifier is fed from a 230 V, 50 Hz, single-phase AC mains. If it is
delivering a constant DC current of 10 A, at firing angle of 30o, then value of the power factor at
AC mains is
(A) 0.87 (B) 0.9 (C) 0.78 (D) 0.45
EE 11/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.44 The switches T1 and T2 in Figure (a) are switched in a complementary fashion with sinusoidal
pulse width modulation technique. The modulating voltage ( ) = 0.8 sin (200 ) V and the
triangular carrier voltage ( ) are as shown in Figure (b). The carrier frequency is 5 kHz. The peak
value of the 100 Hz component of the load current (iL), in ampere, is ________ .
+ vc
T1
Vdc/2=250V
iL
1
0.8
t
XL=16 at
100 Hz R=12 T2
+
vm
Vdc/2=250V
(b)
-
(a)
Q.45 The voltage ( ) across and the current ( ) through a semiconductor switch during a turn-ON
transition are shown in figure. The energy dissipated during the turn-ON transition, in mJ, is
_______.
vs 600 V
0
t
50 A
is
100 A
0
t
T1=1s T2=1s
EE 12/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.46 A single-phase 400 V, 50 Hz transformer has an iron loss of 5000 W at the rated condition. When
operated at 200 V, 25 Hz, the iron loss is 2000 W. When operated at 416 V, 52 Hz, the value of the
hysteresis loss divided by the eddy current loss is ______.
Q.47 A DC shunt generator delivers 45 A at a terminal voltage of 220 V. The armature and the shunt
field resistances are 0.01 Ω and 44 Ω respectively. The stray losses are 375 W. The percentage
efficiency of the DC generator is ____________.
Q.48 A three-phase, 50 Hz salient-pole synchronous motor has a per-phase direct-axis reactance (Xd) of
0.8 pu and a per-phase quadrature-axis reactance (Xq) of 0.6 pu. Resistance of the machine is
negligible. It is drawing full-load current at 0.8 pf (leading). When the terminal voltage is 1 pu,
per-phase induced voltage, in pu, is _________.
Q.49 A single-phase, 22 kVA, 2200 V/ 220 V, 50 Hz, distribution transformer is to be connected as an
auto-transformer to get an output voltage of 2420 V. Its maximum kVA rating as an auto-
transformer is
(A) 22 (B) 24.2 (C) 242 (D) 2420
Q.50 A single-phase full-bridge voltage source inverter (VSI) is fed from a 300 V battery. A pulse of
120o duration is used to trigger the appropriate devices in each half-cycle. The rms value of the
fundamental component of the output voltage, in volts, is
(A) 234 (B) 245 (C) 300 (D) 331
Q.51 A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a
center-to-center distance of 1 m in a horizontal plane. This is now converted to a three-phase
transmission line by introducing a third conductor of the same radius. This conductor is fixed at an
equal distance D from the two single-phase conductors. The three-phase line is fully transposed.
The positive sequence inductance per phase of the three-phase system is to be 5% more than that of
the inductance per conductor of the single-phase system. The distance D, in meters, is _______.
EE 13/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
Q.52 In the circuit shown below, the supply voltage is 10 sin(1000 ) volts. The peak value of the steady
state current through the 1 Ω resistor, in amperes, is ______.
4
2F
250F 500mH
1
5
4mH
10sin(1000t)
Q.53 A dc voltage with ripple is given by ( ) = [100 + 10 sin( ) − 5 sin (3 )] volts.
Measurements of this voltage ( ), made by moving-coil and moving-iron voltmeters, show
readings of V1 and V2 respectively. The value of V2 − V1 , in volts, is _________.
Q.54 The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the admittance
of the circuit becomes a pure conductance at all frequencies is _____________.
100F R
0.02H R
Q.55 In the circuit shown below, the node voltage VA is ___________ V.
EE 14/15
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GATE 2016 EE paper Electrical Engineering Set 1 (2nd Stage)
END OF THE QUESTION PAPER
EE 15/15
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Q. No Type Section Key Marks 1 MCQ GA B 1 2 MCQ GA A 1 3 MCQ GA C 1 4 MCQ GA D 1 5 MCQ GA B 1 6 MCQ GA A 2 7 MCQ GA D 2 8 MCQ GA D 2 9 MCQ GA C 2 10 MCQ GA C 2 1 NAT EE-1 0.0 : 0.0 1 2 NAT EE-1 3.0 : 3.0 1 3 MCQ EE-1 A 1 4 MCQ EE-1 B 1 5 MCQ EE-1 B 1 6 MCQ EE-1 B 1 7 MCQ EE-1 A 1 8 MCQ EE-1 C 1 9 MCQ EE-1 A 1 10 MCQ EE-1 B 1 11 MCQ EE-1 D 1 12 NAT EE-1 18.0 : 20.0 1 13 MCQ EE-1 B 1 14 NAT EE-1 99.0 : 101.0 1 15 MCQ EE-1 D 1 16 MCQ EE-1 C 1 17 NAT EE-1 1.9 : 2.1 1 18 NAT EE-1 0.5 : 0.5 1 19 MCQ EE-1 B 1 20 NAT EE-1 0.83 : 0.85 1 21 MCQ EE-1 A 1 22 NAT EE-1 0.39 : 0.41 1 23 NAT EE-1 169.0 : 171.0 1 24 MCQ EE-1 C 1 25 MCQ EE-1 B 1 26 NAT EE-1 0.2 : 0.2 2 27 NAT EE-1 0.28 : 0.31 2 28 MCQ EE-1 A 2 29 MCQ EE-1 B 2 30 MCQ EE-1 A 2 31 NAT EE-1 5.9 : 6.1 2 32 MCQ EE-1 A 2 33 NAT EE-1 2.0 : 2.0 2 34 MCQ EE-1 C 2 35 MCQ EE-1 D 2 36 MCQ EE-1 C 2 37 MCQ EE-1 A 2 38 MCQ EE-1 D 2 39 NAT EE-1 1.9 : 2.1 2
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40 NAT EE-1 47.0 : 49.0 2 41 NAT EE-1 1.05 : 1.15 2 42 MCQ EE-1 D 2 43 MCQ EE-1 C 2 44 NAT EE-1 9.9 : 10.1 2 45 NAT EE-1 74.0 : 76.0 2 46 NAT EE-1 1.4 : 1.5 2 47 NAT EE-1 86.0 : 88.0 2 48 NAT EE-1 1.58 : 1.62 2 49 MCQ EE-1 C 2 50 MCQ EE-1 A 2 51 NAT EE-1 1.41 : 1.47 2 52 NAT EE-1 1.0 : 1.0 2 53 NAT EE-1 0.30 : 0.33 2 54 NAT EE-1 14.0 : 14.2 2 55 NAT EE-1 11.25 : 11.50 2
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GATE 2016 General Aptitude – GA Set-8
Q. 1 – Q. 5 carry one mark each.
Q.1 The chairman requested the aggrieved shareholders to _________________ him.
(A) bare with (B) bore with (C) bear with (D) bare
Q.2 Identify the correct spelling out of the given options:
(A) Managable (B) Manageable (C) Mangaeble (D) Managible
Q.3 Pick the odd one out in the following:
13, 23, 33, 43, 53
(A) 23 (B) 33 (C) 43 (D) 53
Q.4 R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes.
Which of the following can be logically inferred from the above statements?
(A) R2D2 is a robot which can only repair aeroplanes.
(B) R2D2 is the only robot which can repair aeroplanes.
(C) R2D2 is a robot which can repair only aeroplanes.
(D) Only R2D2 is a robot.
Q.5 If |9y−6| =3, then y2 −4y/3 is .
(A) 0 (B) +1/3 (C) −1/3 (D) undefined
1/3
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GATE 2016 General Aptitude – GA Set-8
Q. 6 – Q. 10 carry two marks each.
Q.6 The following graph represents the installed capacity for cement production (in tonnes) and the
actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a
plant is defined as ratio of actual production of cement to installed capacity. A plant with installed
capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a
small plant. The difference between total production of large plants and small plants, in tonnes is
____.
Q.7 A poll of students appearing for masters in engineering indicated that 60 % of the students believed
that mechanical engineering is a profession unsuitable for women. A research study on women with
masters or higher degrees in mechanical engineering found that 99 % of such women were
successful in their professions.
Which of the following can be logically inferred from the above paragraph?
(A) Many students have misconceptions regarding various engineering disciplines.
(B) Men with advanced degrees in mechanical engineering believe women are well suited to be
mechanical engineers.
(C) Mechanical engineering is a profession well suited for women with masters or higher degrees
in mechanical engineering.
(D) The number of women pursuing higher degrees in mechanical engineering is small.
2/3
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GATE 2016 General Aptitude – GA Set-8
Q.8 Sourya committee had proposed the establishment of Sourya Institutes of Technology (SITs) in line
with Indian Institutes of Technology (IITs) to cater to the technological and industrial needs of a
developing country.
Which of the following can be logically inferred from the above sentence?
Based on the proposal,
(i) In the initial years, SIT students will get degrees from IIT.
(ii) SITs will have a distinct national objective.
(iii) SIT like institutions can only be established in consultation with IIT.
(iv) SITs will serve technological needs of a developing country.
(A) (iii) and (iv) only. (B) (i) and (iv) only.
(C) (ii) and (iv) only. (D) (ii) and (iii) only.
Q.9 Shaquille O’ Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free
throws out of 100 attempts on average. What is the probability that he will successfully
make exactly 6 free throws in 10 attempts?
(A) 0.2508 (B) 0.2816 (C) 0.2934 (D) 0.6000
Q.10 The numeral in the units position of 211870 + 146127 × 3424 is _____.
END OF THE QUESTION PAPER
3/3
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q. 1 – Q. 25 carry one mark each.
Q.1 The output expression for the Karnaugh map shown below is
(A) + (B) + ̅ (C) ̅ + ̅ (D) ̅ +
Q.2 The circuit shown below is an example of a
(A) low pass filter. (B) band pass filter.
(C) high pass filter. (D) notch filter.
Q.3 The following figure shows the connection of an ideal transformer with primary to secondary turns
ratio of 1:100. The applied primary voltage is 100 V (rms), 50 Hz, AC. The rms value of the current
I, in ampere, is __________.
Q.4 ( )
Consider a causal LTI system characterized by differential equation + ( ) = 3 ( ). The
response of the system to the input ( )=3 ( ), where u(t) denotes the unit step
function, is
(A) 9 ( ). (B) 9 ( ).
(C) 9 ( )−6 ( ). (D) 54 ( ) − 54 ( ).
EE 1/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.5 Suppose the maximum frequency in a band-limited signal ( ) is 5 kHz. Then, the maximum
frequency in ( ) cos (2000π ), in kHz, is ________.
Q.6 Consider the function ( ) = + ∗ where is a complex variable and ∗
denotes its complex
conjugate. Which one of the following is TRUE?
(A) ( ) is both continuous and analytic
(B) ( ) is continuous but not analytic
(C) ( ) is not continuous but is analytic
(D) ( ) is neither continuous nor analytic
Q.7 A 3 × 3 matrix is such that, = . Then the eigenvalues of are
(A) 1, 1, −1
(B) 1, 0.5 + 0.866, 0.5 − 0.866
(C) 1, −0.5 + 0.866, −0.5 − 0.866
(D) 0, 1, −1
Q.8 The solution of the differential equation, for > 0, ( ) + 2 ( ) + ( ) = 0 with initial
conditions (0) = 0 and (0) = 1, is (u(t) denotes the unit step function),
(A) ( ) (B) ( − ) ( )
(C) (− + ) ( ) (D) ( )
Q.9 The value of the line integral
(2 +2 + )
along a path joining the origin (0, 0, 0) and the point (1, 1, 1) is
(A) 0 (B) 2 (C) 4 (D) 6
Q.10 Let f(x) be a real, periodic function satisfying (− ) = − ( ). The general form of its Fourier
series representation would be
(A) ( ) = +∑ cos ( )
(B) ( ) = ∑ sin ( )
(C) ( ) = +∑ cos( )
(D) ( ) = ∑ sin (2 + 1)
EE 2/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.11 A resistance and a coil are connected in series and supplied from a single phase, 100 V, 50 Hz ac
source as shown in the figure below. The rms values of plausible voltages across the resistance (VR)
and coil (VC) respectively, in volts, are
(A) 65, 35 (B) 50, 50
(C) 60, 90 (D) 60, 80
Q.12 The voltage (V) and current (A) across a load are as follows.
( ) = 100 sin( ),
( ) = 10 sin( − 60°) + 2 sin(3 ) + 5 sin(5 ).
The average power consumed by the load, in W, is___________.
Q.13 A power system with two generators is shown in the figure below. The system (generators, buses
and transmission lines) is protected by six overcurrent relays R1 to R6. Assuming a mix of
directional and nondirectional relays at appropriate locations, the remote backup relays for R4 are
(A) R1, R2 (B) R2, R6 (C) R2, R5 (D) R1, R6
Q.14 A power system has 100 buses including 10 generator buses. For the load flow analysis using
Newton-Raphson method in polar coordinates, the size of the Jacobian is
(A) 189 x 189 (B) 100 x 100 (C) 90 x 90 (D) 180 x 180
Q.15 The inductance and capacitance of a 400 kV, three-phase, 50 Hz lossless transmission line are 1.6
mH/km/phase and 10 nF/km/phase respectively. The sending end voltage is maintained at 400 kV.
To maintain a voltage of 400 kV at the receiving end, when the line is delivering 300 MW load, the
shunt compensation required is
(A) capacitive
(B) inductive
(C) resistive
(D) zero
EE 3/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.16 A parallel plate capacitor filled with two dielectrics is shown in the figure below. If the electric
field in the region A is 4 kV/cm, the electric field in the region B, in kV/cm, is
(A) 1 (B) 2 (C) 4 (D) 16
Q.17 A 50 MVA, 10 kV, 50 Hz, star-connected, unloaded three-phase alternator has a synchronous
reactance of 1 p.u. and a sub-transient reactance of 0.2 p.u. If a 3-phase short circuit occurs close to
the generator terminals, the ratio of initial and final values of the sinusoidal component of the short
circuit current is ________.
Q.18 Consider a linear time-invariant system with transfer function
1
( )=
( + 1)
If the input is cos( ) and the steady state output is cos( + ), then the value of is _________.
Q.19 A three-phase diode bridge rectifier is feeding a constant DC current of 100 A to a highly inductive
load. If three-phase, 415 V, 50 Hz AC source is supplying to this bridge rectifier then the rms value
of the current in each diode, in ampere, is _____________.
Q.20 A buck-boost DC-DC converter, shown in the figure below, is used to convert 24 V battery voltage
to 36 V DC voltage to feed a load of 72 W. It is operated at 20 kHz with an inductor of 2 mH and
output capacitor of 1000 µF. All devices are considered to be ideal. The peak voltage across the
solid-state switch (S), in volt, is ____________.
EE 4/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.21 For the network shown in the figure below, the frequency (in rad/s) at which the maximum phase
lag occurs is, ___________.
9
1
vin vo
1F
Q.22 The direction of rotation of a single-phase capacitor run induction motor is reversed by
(A) interchanging the terminals of the AC supply.
(B) interchanging the terminals of the capacitor.
(C) interchanging the terminals of the auxiliary winding.
(D) interchanging the terminals of both the windings.
Q.23 In the circuit shown below, the voltage and current sources are ideal. The voltage (Vout) across the
current source, in volts, is
(A) 0 (B) 5 (C) 10 (D) 20
Q.24 The graph associated with an electrical network has 7 branches and 5 nodes. The number of
independent KCL equations and the number of independent KVL equations, respectively, are
(A) 2 and 5 (B) 5 and 2 (C) 3 and 4 (D) 4 and 3
Q.25 Two electrodes, whose cross-sectional view is shown in the figure below, are at the same potential.
The maximum electric field will be at the point
(A) A (B) B (C) C (D) D
EE 5/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q. 26 – Q. 55 carry two marks each.
Q.26 The Boolean expression + + + ̅ + ( + ̅) simplifies to
(A) 1 (B) . (C) . (D) 0
Q.27 For the circuit shown below, taking the opamp as ideal, the output voltage Vout in terms of the input
voltages V1 , V2 and V3 is
(A)1.8V1 + 7.2V2 -V3 (B) 2V1 + 8V2 - 9V3 (C) 7.2V1 + 1.8V2 -V3 (D) 8V1 + 2V2 - 9V3
Q.28 Let ( ) ( ) and ( ) ( ) be two signals whose Fourier Transforms are as shown in
| |
the figure below. In the figure, ℎ( ) = denotes the impulse response.
For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be
uniquely reconstructed from its samples, is
(A) 2B1 (B) 2(B1+B2) (C) 4(B1 +B2) (D) ∞
Q.29 The value of the integral 2 ∫ is equal to
(A) 0 (B) 0.5 (C) 1 (D) 2
EE 6/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.30
Let ( ) be the solution of the differential equation −4 + 4 = 0 with initial
conditions (0) = 0 and = 1. Then the value of (1) is _________.
Q.31 The line integral of the vector field = 5 ̂ + (3 +2 ) ̂+ along a path from (0,0,0)
to (1,1,1) parametrized by ( , , ) is _____.
Q.32 3 1
Let = . Consider the set of all vectors such that + = 1 where = .
1 3
Then is
(A) a circle of radius √10
(B) a circle of radius
√
1
(C) an ellipse with major axis along
1
1
(D) an ellipse with minor axis along
1
Q.33 Let the probability density function of a random variable, , be given as:
3
( )= ( )+ (− )
2
where ( ) is the unit step function.
Then the value of 'a' and { ≤ 0}, respectively, are
(A) 2, (B) 4, (C) 2, (D) 4,
Q.34 The driving point input impedance seen from the source Vs of the circuit shown below, in Ω, is
______.
EE 7/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.35 The z-parameters of the two port network shown in the figure are z11 40 , z12 60 ,
z 21 80 and z 22 100 . . The average power delivered to RL 20 , in watts, is _______.
10 I1 I2
20V V1 Z V2 RL
Q.36 In the balanced 3-phase, 50 Hz, circuit shown below, the value of inductance (L) is 10 mH. The
value of the capacitance (C) for which all the line currents are zero, in millifarads, is ___________.
L C L
C C
L
Q.37 In the circuit shown below, the initial capacitor voltage is 4 V. Switch S1 is closed at = 0. The
charge (in µC) lost by the capacitor from = 25 μ to = 100 μ is ____________.
S1
4V
5
5F
EE 8/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.38 The single line diagram of a balanced power system is shown in the figure. The voltage magnitude
at the generator internal bus is constant and 1.0 p.u. The p.u. reactances of different components in
the system are also shown in the figure. The infinite bus voltage magnitude is 1.0 p.u. A three phase
fault occurs at the middle of line 2.
The ratio of the maximum real power that can be transferred during the pre-fault condition to the
maximum real power that can be transferred under the faulted condition is _________.
Q.39 The open loop transfer function of a unity feedback control system is given by
( + 1)
( )= , > 0, >0.
(1 + )(1 + 2 )
The closed loop system will be stable if,
( ) ( )
(A) 0 < < (B) 0 < <
( )
(C) 0 < < (D) 0 < <
Q.40 At no load condition, a 3-phase, 50 Hz, lossless power transmission line has sending-end and
receiving-end voltages of 400 kV and 420 kV respectively. Assuming the velocity of traveling
wave to be the velocity of light, the length of the line, in km, is ____________.
Q.41 The power consumption of an industry is 500 kVA, at 0.8 p.f. lagging. A synchronous motor is
added to raise the power factor of the industry to unity. If the power intake of the motor is 100 kW,
the p.f. of the motor is _____________
Q.42 The flux linkage (λ) and current (i) relation for an electromagnetic system is = (√ )/ . When i =
2A and (air-gap length) = 10 cm, the magnitude of mechanical force on the moving part, in N, is
________.
EE 9/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.43 The starting line current of a 415 V, 3-phase, delta connected induction motor is 120 A, when the
rated voltage is applied to its stator winding. The starting line current at a reduced voltage of 110 V,
in ampere, is _________.
Q.44 A single-phase, 2 kVA, 100/200 V transformer is reconnected as an auto-transformer such that its
kVA rating is maximum. The new rating, in kVA, is ______.
Q.45 A full-bridge converter supplying an RLE load is shown in figure. The firing angle of the bridge
converter is 120º. The supply voltage ( ) = 200 sin (100 ) V, R=20 Ω, E=800 V. The
inductor L is large enough to make the output current IL a smooth dc current. Switches are lossless.
The real power fed back to the source, in kW, is __________.
Load
IL
L
T1 T3
R=20
Bridge
vm
T2 -
T4
E=800V
+
Q.46 A three-phase Voltage Source Inverter (VSI) as shown in the figure is feeding a delta connected
resistive load of 30 Ω/phase. If it is fed from a 600 V battery, with 180o conduction of solid-state
devices, the power consumed by the load, in kW, is __________.
EE 10/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.47 A DC-DC boost converter, as shown in the figure below, is used to boost 360V to 400 V, at a
power of 4 kW. All devices are ideal. Considering continuous inductor current, the rms current in
the solid state switch (S), in ampere, is _________.
Q.48 A single-phase bi-directional voltage source converter (VSC) is shown in the figure below. All
devices are ideal. It is used to charge a battery at 400 V with power of 5 kW from a source Vs = 220
V (rms), 50 Hz sinusoidal AC mains at unity p.f. If its AC side interfacing inductor is 5 mH and the
switches are operated at 20 kHz, then the phase shift (δ) between AC mains voltage (Vs ) and
fundamental AC rms VSC voltage (VC1), in degree, is _________.
Q.49 Consider a linear time invariant system ̇ = , with initial condition (0) at = 0. Suppose and
are eigenvectors of (2 x 2) matrix A corresponding to distinct eigenvalues and respectively.
Then the response ( ) of the system due to initial condition (0) = is
(A) (B) (C) (D) +
Q.50 A second-order real system has the following properties:
a) the damping ratio = 0.5 and undamped natural frequency =10 rad/s,
b) the steady state value of the output, to a unit step input, is 1.02.
The transfer function of the system is
.
(A) (B)
(C) (D)
EE 11/12
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GATE 2016 Electrical Engineering Set 2 (2nd stage)
Q.51 Three single-phase transformers are connected to form a delta-star three-phase transformer of
110 kV/ 11 kV. The transformer supplies at 11 kV a load of 8 MW at 0.8 p.f. lagging to a nearby
plant. Neglect the transformer losses. The ratio of phase currents in delta side to star side is
(A) 1 : 10√3 (B) 10√3 : 1 (C) 1 : 10 (D) √3 : 10
Q.52 The gain at the breakaway point of the root locus of a unity feedback system with open loop
Ks
transfer function G (s ) is
(s 1)(s 4)
(A) 1 (B) 2 (C) 5 (D) 9
Q.53 Two identical unloaded generators are connected in parallel as shown in the figure. Both the
generators are having positive, negative and zero sequence impedances of j0.4 p.u., j0.3 p.u. and
j0.15 p.u., respectively. If the pre-fault voltage is 1 p.u., for a line-to-ground (L-G) fault at the
terminals of the generators, the fault current, in p.u., is ___________.
Q.54 An energy meter, having meter constant of 1200 revolutions/kWh, makes 20 revolutions in 30
seconds for a constant load. The load, in kW, is _____________.
Q.55 A rotating conductor of 1 m length is placed in a radially outward (about the z-axis) magnetic flux
density (B) of 1 Tesla as shown in figure below. Conductor is parallel to and at 1 m distance from
the z-axis. The speed of the conductor in r.p.m. required to induce a voltage of 1 V across it, should
be __________.
END OF THE QUESTION PAPER
EE 12/12
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Q. No Type Section Key Marks 1 MCQ GA C 1 2 MCQ GA B 1 3 MCQ GA B 1 4 MCQ GA B 1 5 MCQ GA C 1 6 NAT GA 120.0 : 120.0 2 7 MCQ GA C 2 8 MCQ GA C 2 9 MCQ GA A 2 10 NAT GA 7.0 : 7.0 2 1 MCQ EE-2 B 1 2 MCQ EE-2 A 1 3 NAT EE-2 9.5 : 10.5 1 4 MCQ EE-2 D 1 5 NAT EE-2 6.0 : 6.0 1 6 MCQ EE-2 B 1 7 MCQ EE-2 A;D 1 8 MCQ EE-2 A 1 9 MCQ EE-2 B 1 10 MCQ EE-2 B 1 11 MCQ EE-2 MTA 1 12 NAT EE-2 249.0 : 251.0 1 13 MCQ EE-2 D 1 14 MCQ EE-2 A 1 15 MCQ EE-2 B 1 16 MCQ EE-2 C 1 17 NAT EE-2 4.9 : 5.1 1 18 NAT EE-2 0.69 : 0.72 1 19 NAT EE-2 57.0 : 58.0 1 20 NAT EE-2 59.5 : 60.5 1 21 NAT EE-2 0.30 : 0.33 1 22 MCQ EE-2 C 1 23 MCQ EE-2 D 1 24 MCQ EE-2 D 1 25 MCQ EE-2 A 1 26 MCQ EE-2 D 2 27 MCQ EE-2 D 2 28 MCQ EE-2 B 2 29 MCQ EE-2 D 2 30 NAT EE-2 7.0 : 7.5 2 31 NAT EE-2 4.40 : 4.45 2 32 MCQ EE-2 D 2 33 MCQ EE-2 A 2 34 NAT EE-2 19.5 : 20.5 2 35 NAT EE-2 34.0 : 36.0 2 36 NAT EE-2 2.9 : 3.1 2 37 NAT EE-2 6.8 : 7.2 2 38 NAT EE-2 2.20 : 2.35 2 39 MCQ EE-2 C 2
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40 NAT EE-2 294.0 : 298.0 2 41 NAT EE-2 0.31 : 0.33 2 42 NAT EE-2 186.0 : 190.0 2 43 NAT EE-2 31.0 : 33.0 2 44 NAT EE-2 5.9 : 6.1 2 45 NAT EE-2 5.9 : 6.1 2 46 NAT EE-2 23.0 : 25.0 2 47 NAT EE-2 3.0 : 4.0 2 48 NAT EE-2 9.1 : 9.3 2 49 MCQ EE-2 A 2 50 MCQ EE-2 B 2 51 MCQ EE-2 A 2 52 MCQ EE-2 A 2 53 NAT EE-2 5.5 : 6.5 2 54 NAT EE-2 1.9 : 2.1 2 55 NAT EE-2 9.4 : 9.7 2
Official key not published for this paper.
Page 1 of 37
Source: GATE. Question paper published by GATE.