GATE 2027 Sample Paper (Electrical - EE)

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

GATE 2027 (Electrical - EE)
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME

65 100 180 Min

GENERAL INSTRUCTIONS

1. This paper contains 65 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 1 or 2 marks (varies by question); for a multiple-choice question, one-third (1-mark
question) or two-thirds (2-mark question) of the allotted marks is deducted for a wrong answer; numerical-answer-type
questions carry no negative marking.

4. Total time allowed is 180 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

GATE 2027 (Electrical - EE)
SAMPLE QUESTION PAPER

Questions 65 Max Marks 100 Time 180 Min

Attempt all questions. Choose the one correct option for each.

GENERAL APTITUDE

1. The CEO's decision to quit was as shocking to the 2. Under a certain legal system, prisoners are allowed to
Board as it was to ________ . make one statement. If their the statement turns out to
be true then they are hanged. If the statement turns out
(A) I
to be false then they are shot. One prisoner made a
(B) me
statement and the judge had no option but to set him
(C) my free. Which one Of the following could be that statement?
(D) myself
(A) I did not commit the crime

(B) I committed the crime

(C) 1 will be shot

(D) You committed the crime

3. "A recent High Court judgement has sought to dispel the idea Of begging as a disease — which leads to its
stigmatization and criminalization — and to regard it as a symptom. The underlying disease is the failure Of the State
to protect citizens who fall through the social security net." Which one Of the following statements can be inferred
from the given passage?

(A) Beggars are lazy people who beg because they are unwilling to work

(B) Beggars are created because Of the lack Of social welfare schemes

(C) Begging is an offence that has to be dealt with firmly

(D) Begging has to be banned because it adversely affects the welfare of the state

4. The roots of ax2 + bx + c = 0 are real and positive. a, b 5. The smallest angle of a triangle is equal to two thirds
and c are real. Then ax2 + b|x| + c = 0 has of the smallest angle of a quadrilateral. The ratio
between the angles of the quadrilateral is 3:4:5:6. The
(A) no roots
largest angle of the triangle is twice its smallest angle.
(B) 2 real roots
What is the sum, in degrees, of the second largest angle
(C) 3 real roots of the triangle and the largest angle of the quadrilateral?
(D) 4 real roots
(A) 89°

(B) 180°

(C) 85°

(D) 50°

6. The expenditure on the project __________ lakhs, and 7. One percent of the people of country X are taller than
contingency Rs.3 lakhs. as follows: equipment Rs.20 6 ft. Two percent of the people of country Y are taller
lakhs, salaries Rs.12 than 6 ft. There are thrice as many people in country X as
in country Y. Taking both countries together, what is the
(A) break down
percentage of people taller than 6 ft?
(B) break
(A) 3.0
(C) breaks down
(B) 2.5
(D) breaks
(C) 1.5

(D) 1.25

8. The growth rate of ABC Motors in 2017 was the same 9. "l read somewhere that in ancient times the prestige
___________ XYZ Motors in 2016. Of a kingdom depended upon the number Of taxes that it
was able to levy on its people. It was very much like the
(A) as off
prestige Of a head-hunter in his own community." Based
(B) as those of
on the paragraph above, the prestige Of a head-hunter
(C) as that off depended upon
(D) as that of
(A) the prestige of the kingdom

(B) the prestige of the heads

(C) the number of taxes he could levy

(D) the number of heads he could gather

10. Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank Of India, banking
institutions have been making a demand to reduce interest rates on small saving schemes. Finally, the government
announced yesterday a reduction in interest rates on small saving schemes to bring them on par with fixed deposit
interest rates. Which one Of the following statements can be inferred from the given passage?

(A) Whenever the Reserve Bank of India reduces the repo rate, the interest rates on small saving schemes are also reduced

(B) Interest rates on small saving schemes are always maintained on par with fixed deposit interest rates

(C) The government sometimes takes into consideration the demands Of banking institutions before reducing the interest rates
on small saving schemes

(D) A reduction in interest rates on small saving schemes follow only after a reduction in repo rate by the Reserve Bank of India.

ELECTRICAL ENGINEERING

11. In the system whose signal flow graph is shown in 12. A sequence detector is designed to detect precisely 3
the figure, U1(s) and U2(s) are inputs. The transfer digital inputs, with overlapping sequences detectable.
function Y(s)/U1(s) is For the sequence (1,0,1) and input data what is the
output of this detector? (1,1,0,1,0,0,1,1,0,1,1,0), what is
(A) k J L s2+J R s+k k
1 1 2
the output of this detector?
(B) k J L s2-J R s-k k
1 1 2
2
(A) 1,1,0,0,0,0,1,1,0,1,0,0
(C) k -U (R+s L)J L s +(J R-U L) s+k k -U R
1 2 2 1 2 2
(B) 0,1,0,0,0,0,0,1,01,0,0
(D) k -U (s L-R)J L s2-(J R+U L) s-k k +U R
1 2 2 1 2 2
(C) 0,1,0,0,0,0,0,1,0,1,1,0

(D) 0,1,0,0,0,0,0,0,1,0,0,0

13. Consider the diode circuit shown below. The diode, D, obeys the current-voltage characteristic I = I ( (V n V )-
D S D T
1) , where n > 1, V > 0, V is the voltage across the diode and I is the current through it. The circuit is biased so
T D D
that voltage, V > O and current, I O. If you had to design this circuit to transfer maximum power from the current
source (I ) to a resistive load (not shown) at the output, what values of R and R would you choose?
1 I 2

(A) Large R and large R
1 2

(B) Small R and small R
1 2
(C) Large R and small R
1 2
(D) Small R and large R
1 2

14. It takes two hours for a person X to mow the lawn. Y 15. The function shown in the figure can be represented
can mow the same lawn in four hours. How long (in
minutes) will it take X and Y, if they work together to
mow the lawn?

(A) 60

(B) 80
as
(C) 90

(D) 120

(A)

(B)

(C)

(D)

16. A non-ideal diode is biased with a voltage of —0.03 V,
and a diode current of I is measured. The thermal
1
voltage is 26 mV and the ideality factor for the diode is
15/13. The voltage, in V, at which the measured current
increases to 1.5I is closest to:
1

(A) -0.02 17.

(B) -0.09

(C) -1.50 (A) 0.4 to 0.5

(D) -4.50 (B) 0.9 to 2.0

(C) 0.8 to 0.9

(D) 0.7 to 0.8

18. Which of the options is an equivalent representation 19. Two wattmeter method is used for measurement of
of the signal flow graph shown here? power in a balanced three-phase load supplied from a
balanced three-phase system. If one of the wattmeters
(A)
reads half of the other (both positive), then the power
(B)
factor of the load is
(C)
(A) 0.532
(D)
(B) 0.632

(C) 0.707

(D) 0.866

20. The value of the following complex integral, with C 21. In the figure, the voltages are ��(��) = 100cos⁡(����),
(��) =
��
1 2
representing the unit circle centered at origin in the 100cos⁡(���� + ��/18) and
(��) =
�� 100cos⁡(���� + ��/36). The circuit is in
3
counterclockwise sense, is: ∫ z2+1z2-2 z d z sinusoidal steady state, and �� ����.
, ��and
�� ��are the average
C 1 2 3
power outputs. Which one of the following statements is
(A) 8πi
true?
(B) -8πi
(A) ⁡��= ��= ��= 0
(C) -πi 1 2 3
(B) ⁡ ��0, ��> 0, ��> 0
(D) πi 1 2 3
(C) ⁡ ��0, ��> 0, ��0
1 2 3
(D) ⁡ ��> 0, ��0, ��> 0
1 2 3

22. A 250 V dc shunt motor has an armature resistance of 0.2 Ω and a field resistance of 100 Q. When the motor is
operated on no-load at rated voltage, it draws an armature current of 5 A and runs at 1200 rpm. When a load is
coupled to the motor, it draws total line current of 50 A at rated voltage, with a 5 % reduction in the air-gap flux due
to armature reaction. Voltage drop across the brushes can be taken as 1 V per brush under all operating conditions.
The speed of the motor, in rpm, under this loaded condition, is closest to:

(A) 1200

(B) 1000

(C) 1220

(D) 900

24. The reading of the voltmeter (rms) in volts, for the
circuit shown in the figure is __________

23.

(A) g(t) would always be proportional to f(t)

(B) g(t) would be proportional to f(t) if f(t) is an even
function.

(C) g(t) would be proportional to f(t) only if f(t) is a
sinusoidal function. (A) 140 to 142

(D) g(t) would never be proportional to f(t) (B) 139 to 141

(C) 142 to 144

(D) 145 to 147

25. A DC-DC buck converter operates in continuous 26. Consider a signal x[n] = (½)n 1[n], where 1[n] = 0 if n
conduction mode. It has 48 V input voltage, and it feeds a 0, and 1[n] = 1 if n ≥ 0. The z-transform of x[n— k], k > 0
resistive load of 24Ω. The switching frequency of the is z-k1-(1)/(2) z-1 with region of convergence being
converter is 250 Hz. If switch-on duration is 1 ms, the
(A) |z| 2
load power is
(B) |z| > 2
(A) 6 W
(C) |z| ½
(B) 12 W
(D) |z| > ½
(C) 24 W

(D) 48 W

27. A moving coil instrument having a resistance of 10 Ω, 28. For a specified input voltage and frequency, if the
gives a full-scale deflection when the current is 10 mA. equivalent radius of the core of a transformer is reduced
What should be the value of the series resistance, so that by half, the factor by which the number of turns in the
it can be used as a voltmeter for measuring potential primary should change to maintain the same no load
difference up to 100 V? current is

(A) 9 Ω (A) 1/4

(B) 99 Ω (B) 1/2

(C) 990 Ω (C) 2

(D) 9990 Ω (D) 4

29. The logical gate implemented using the circuit shown 30. A benchtop dc power supply acts as an ideal 4 A
below where, V1 and V2 are inputs (with 0 V as digital O current source as long as its terminal voltage is below 10
and 5 V as digital 1) and Vout is the output, is V. Beyond this point, it begins to behave as an ideal 10 V
voltage source for all load currents going down to 0 A.
(A) NOT
When connected to an ideal rheostat, find the load
(B) NOR
resistance value at which maximum power is transferred,
(C) NAND and the corresponding load voltage and current.
(D) XOR
(A) Short, ∞ A, 10 V

(B) open, 4 A, 0 V

(C) 2.5 Ω, 4 A, 10 V

(D) 2.5 Ω, 4 A, 5 V

31. Consider a permanent magnet dc (PMDC) motor 32. A person decides to toss a fair coin repeatedly until
which is initially at rest. At t = 0, a dc voltage of 5 V is he gets a head. He will make at most 3 tosses. Let the
applied to the motor. Its speed monotonically increases random variable Y denote the number of heads. The
from O rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 value ofvar{Y}, where var{•} denotes the variance,
rad/s. Assuming that the armature inductance of the equals
motor is negligible, the transfer function for the motor is
(A) 7/8
(A) (10)/(0.5 s+1) (B) 79/64
(B) (2)/(0.5 s+1) (C) 7/64
(C) (2)/( s+0.5) (D) 105/64
(D) (10)/(s +0.5)

33. Which of the following statements is true about the 34. A closed loop system has the characteristic equation
two sided Laplace transform? given by s3 + Ks2 + (K + 2)s + 3 = O. For this system to
be stable, which one of the following conditions should
(A) It exists for every signal that may or may not have a
be satisfied?
Fourier transform.

(B) It has no poles for any bounded signal that is non-zero (A) 0 K 0.5

only inside a finite time interval. (B) 0.5 K 1

(C) The number of finite poles and finite zeroes must be (C) 0 K 1
equal. (D) K > 1
(D) If a signal can be expressed as a weighted sum of
shifted one sided exponentials, then its Laplace Transform
will have no poles.

35. A 220 V, 10 kW. 900 rpm separately excited DC motor 36. The output expression for the Karnaugh map shown
has an armature resistance Rₐ = 0.02 ᘯ. WIIen the motor below is
operates at rated speed and with rated tenninal voltage,
(A) ���� ̅ + ��
the electromagnetic torque developed by the motor is 70
(B) ���� ̅ + �� ̅
Nm. Neglecting the rotational losses of the machine, the
cunent draml by the motor from the 220 V supply is (C) ���� + ��

(D) ���� + �� ̅
(A) 34.2 A

(B) 30 A

(C) 22 A

(D) 4.84 A

37. The enhancement type MOSFET in the circuit below 38. x(t) is nonzero only for T t T' , and similarly, y(t) is
x x
operates according to the square law. �� = 100 μA/V2, the nonzero only for T t T' , Let z(t) be convolution of x(t)
��
ox y y
threshold voltage (V ) is 500 mV. Ignore channel length and y(t). Which one of the following statements is TRUE?
T
modulation. The output voltage V is
out (A) z(t) can be nonzero over an unbounded interval
(A) 100 mV (B) z(t) is nonzero for t T + T .
x y
(B) 500 mV (C) z(t) is zero outside of T + T t T' + T'
x y x y
(C) 600 mV (D) z(t) is nonzero for t > T' + T' .
x y
(D) 2 V

39. The mean-square of a zero-mean random process is ����/��
40. Which one of the following statements is true about
, where �� is Boltzmann’s constant, �� is the absolute the digital circuit shown in the figure
temperature, and �� is a capacitance. The standard
(A) It can be used for dividing the input frequency by 3.
deviation of the random process is
(B) It can be used for dividing the input frequency by 5.
(A) ������
(C) It can be used for dividing the input frequency by 7.
(B) √((k T)/(c))
(D) It cannot be reliably used as a frequency divider due to
(C) ������ disjoint internal cycles.
(D) √����/��

41. How many integers are there between 100 and 1000 42. Let X(s) = 3s + 5 / s2 + 10 s + 21 be the Laplace
all of whose digits are even? Transform of a signal x(t). Then, x(0+) is

(A) 60 (A) 0

(B) 80 (B) 3

(C) 100 (C) 5

(D) 90 (D) 21

43. Which of the following is true for all possible non- 44. For the circuit shown in the figure below, assume
zero choices of integers m, n; m ≠ n, or all possible non- that diodes D1, D2 and D3 are ideal. The DC components
zero choices of real numbers p, q; p ≠q, as applicable? of voltages V1 and V2 are respectively
sin mo sin n0d9 = 0
(A) 0 V and 1V
(A) (1)/(π) ∫ π m θ n θ d θ=0 (B) -0.5 v 0.5 v
0
(B) (1)/(2 π) ∫ π / 2 p θ q θ d θ=0
-π / 2 (C) 1 V and 0.5 V
(C) (1)/(2 π) ∫ π p θ q θ d θ=0 (D) 1 V and 1V
-π
(D) (1)/(2 α) ∫ α p θ q θ d θ=0
α arrow ∞ -α

45. The Boolean expression AB + AC̅ + BC simplifies to: 46. Given, ��
is the gate-source voltage, ��
is the drain
���� ����
source voltage, and ��is the threshold voltage of an
(A) BC+AC̅ ��ℎ
enhancement type NMOS transistor, the conditions for
(B) AB + AC̅ + B
transistor to be biased in saturation are
(C) AB + AC̅
(A) ��
��; ��
≥ ��
− ��
����
��ℎ ����������ℎ
(D) AB +BC
(B) ��
> ��; ��
≥−�� ��
������ℎ ��������
��ℎ
(C) ��
> ��; ��
≤ ��
− ��
������ℎ ����������ℎ
(D) ��
����
; ��
≤ ��
− ��
����
��ℎ ����������ℎ

47. A periodic function ��(��), with a period of 2��, is 48. Consider the line integral I=∫ (x2+i y2) d z where z =
C
represented as its Fourier series, If f(t)=a +Σ ∞a n x + iy. The line C is shown in the figure below. The value
0 n=1 n
t+Σ ∞ b n t f(t)=\arrayll A t, & 0 ≤ t ≤ π \\ 0, & π2 π of I is
n=1 n
array. the Fourier series coefficients ��and ��of ��(��) are
1 1 (A) 1/2i
(A) ��= ��/��=; ��
0 (B) 2/3i
1 1
(B) ��= ��; ��= 0 (C) 3/4i
1 2 1
(C) ��= 0 ; ��= ��/�� (D) 4/5i
1 1
(D) ��1 = 0 ; =
�� ��/2
1

49. A stationmy closed Lissajous pattem on an 50. The output response of a system is denoted as y(t),
oscilloscope has 3 horizontal tangencies and 2 veltical and its Laplace transform is given by Y(s)=10s(s2+s+100
tangencies for a horizontal input with frequency 3 kHz. √(2)) The steady state value of y(t) is
The frequency of the vertical input is
(A) 1/10√2
(A) 1.5 kHz (B) 10√2
(B) 2 kHz (C) 1/100√2
(C) 3 kHz (D) 100√2
(D) 4.5 kHz

51. A DC voltage source is connected to a series L-C 52. The symbols, �� and ��, represent positive quantities,
circuit by turning on the switch S at time t=0 as shown in and ��(��) is the unit step function. Which one of the
the figure. Assume i(0) = 0, v(0) = 0. Which one of the following impulse responses is NOT the output of a causal
following circular loci represents the plot of i(t) versus linear time-invariant system?
v(t) ? +����
(A) ��
��(��)
(A) (B) −��(��+��)
�� ��(��)
(B) −����
(C) 1 + ��
��(��)
(C) −��(��−��)
(D) �� ��(��)
(D)

53. Let a , a and a be unit vectors along r, φ and z 54.  ax3 + bx2 + cx + d is a polynomial on real x over real
r φ z
directions, respectively in the cylindrical coordinate coefficients a, b, c, d wherein a ≠ 0. Which of the
system. For the electric flux density given by D = (a 15 + following statements is true?
r
aφ2r - a 3rz) Coulomb/m2, the total electric flux, in
z (A) d can be chosen to ensure that x = 0 is a root for any
Coulomb, emanating from the volume enclosed by a solid
given set a, b, c.
cylinder of radius 3 m and height 5 m oriented along the
(B) No choice of coefficients can make all roots identical.
z-axis with its base at the origin is:
(C) a, b, c, d can be chosen to ensure that all roots are
(A) 54 π
complex.
(B) 90 π
(D) c alone cannot ensure that all roots are real
(C) 108 π

(D) 180 π

55. A six-pulse thyristor bridge rectifier is connected to a 56. Consider a signal x[n] = (½)n 1[n], where 1[n] = 0 if n
balanced three-phase, 50 Hz AC source. Assuming that 0, and 1[n] = 1 if n ≥ 0. The z-transform of x[n— k], k > 0
the DC output current of the rectifier is constant, the is z-k1-(1)/(2) z-1 with region of convergence being
lowest harmonic component in the AC input current is
(A) |z| 2
(A) 100 Hz (B) |z| > 2
(B) 150 Hz (C) |z| ½
(C) 250 Hz (D) |z| > ½
(D) 300 Hz

57. A benchtop dc power supply acts as an ideal 4 A 58. The output expression for the Karnaugh map shown
current source as long as its terminal voltage is below 10 below is
V. Beyond this point, it begins to behave as an ideal 10 V
(A) ���� ̅ + ��
voltage source for all load currents going down to 0 A.
(B) ���� ̅ + �� ̅
When connected to an ideal rheostat, find the load
resistance value at which maximum power is transferred, (C) ���� + ��

and the corresponding load voltage and current. (D) ���� + �� ̅

(A) Short, ∞ A, 10 V

(B) open, 4 A, 0 V

(C) 2.5 Ω, 4 A, 10 V

(D) 2.5 Ω, 4 A, 5 V

59. A fair coin is tossed n times. The probability that the 60. A single-phase, full-bridge diode rectifier fed from a
difference between the number of heads and tails is (n-3) 230 V, 50 Hz sinusoidal source supplies a series
is combination of finite resistance, R, and a very large
inductance, L. The two most dominant frequency
(A) 2-n
components in the source current are:
(B) 0
(A) 50 Hz, 0 Hz
(C) nCn - 3 2-n
(B) 50 Hz, 100 Hz
(D) 2-n + 3
(C) 50 Hz, 150 Hz

(D) 150 Hz, 250 Hz

61. Four power semiconductor devices are shown in the 62. A non-ideal diode is biased with a voltage of —0.03 V,
figure along with their relevant terminals. The device( s) and a diode current of I is measured. The thermal
1
that can carry dc current continuously in the direction voltage is 26 mV and the ideality factor for the diode is
shown when gated appropriately is (are) 15/13. The voltage, in V, at which the measured current
increases to 1.5I is closest to:
(A) Triac only 1

(B) Triac and MOSFET (A) -0.02

(C) Triac and GTO (B) -0.09

(D) Thyristor and Triac (C) -1.50

(D) -4.50

63. Which of the options is an equivalent representation 64. A stable real linear time-invariant system with single
of the signal flow graph shown here? pole at p, has a transfer function H(s)=s2+100s-p with a
dc gain of 5. The smallest positive frequency, in rad/s, at
(A)
unity gain is closest to:
(B)
(A) 8.84
(C)
(B) 11.08
(D)
(C) 78.13

(D) 122.87

65. The characteristic equation of a linear time-invariant
4+
(LTI) system is given by ∆(��) = 3 + 3��
�� 3�� 2 + �� + �� = 0. The

system is BIBO stable if

(A) 0 �� 129

(B) �� > 3

(C) 0 �� 8/9

(D) �� > 6

ANSWER KEY

1. (B) 2. (C) 3. (B) 4. (D) 5. (B) 6. (C) 7. (D)

8. (D) 9. (D) 10. (C) 11. (A) 12. (B) 13. (D) 14. (B)

15. (A) 16. (B) 17. (D) 18. (C) 19. (B) 20. (C) 21. (C)

22. (C) 23. (B) 24. (A) 25. (A) 26. (D) 27. (D) 28. (C)

29. (B) 30. (C) 31. (B) 32. (C) 33. (B) 34. (D) 35. (B)

36. (A) 37. (C) 38. (C) 39. (B) 40. (B) 41. (C) 42. (B)

43. (D) 44. (B) 45. (A) 46. (B) 47. (D) 48. (B) 49. (D)

50. (A) 51. (B) 52. (C) 53. (D) 54. (C) 55. (C) 56. (D)

57. (C) 58. (A) 59. (B) 60. (C) 61. (B) 62. (B) 63. (C)

64. (A) 65. (C)