GATE 2026 Question Paper Electronics and Communication Engineering (EC)

FOR GATE EXAM PREPARATION

GATE 2026
Question Paper ·
Electronics
Communication
Engineering (EC)
EXAM YEAR TYPE

GATE 2026 Question Paper
SUBJECT

Electronics Communication Engineering (EC)

Notes · Sample Papers · Previous Year Papers · Mock Tests

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Electronics & Communication Engineering (EC)

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 Among the following options, the antonym of the word ‘nocturnal’ is _________.

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normal m
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(A)
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(B) agdiurnal

(C) abnormal

(D) exceptional

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Electronics & Communication Engineering (EC)

Q.2 The statements (S1), (S2), and (S3) pertain to the scores obtained by students in
an exam. The maximum possible marks in the exam is 150.

(S1) The highest score is 100.

(S2) The fourth highest score is 76.

(S3) There are at least four students whose scores are within 25 of each other.

Which one of the following options is necessarily correct?

(A) (S1) and (S2) together imply (S3)

(B) (S1) and (S3) together imply (S2)

(C) (S2) and (S3) together imply (S1)

(D) (S1) implies (S3)

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Electronics & Communication Engineering (EC)

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Q.3 The figure below has exactly three intersecting line segments with a rectangular
portion WXYZ missing. Which one of the following options P, Q, R, and S is the
missing portion WXYZ?

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a

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P
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a

R S

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a
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(C) R

(D) S

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Electronics & Communication Engineering (EC)

Q.4 Real numbers 𝑦, 𝑝, and 𝑛 (all greater than 1) satisfy

(log 𝑝1/𝑛 𝑦)(log 𝑦 1/𝑛 𝑝) = 16,

where the logarithms are taken to the bases 𝑝1/𝑛 and 𝑦1/𝑛 .

The value of 𝑛 is ________

(A) 2

(B) 4

(C) 8

(D) 16

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Electronics & Communication Engineering (EC)

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Q.5 The following observation is made about the scores obtained by 100 students in an
exam:

‘For each student, there exists another student in the class such that their scores are
at most ten marks away.’

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If the above statement is false, which one of the following statements is necessarily
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true?
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aFor each student, the scores of all the other students are more than 10 marks away.
(A)

(B) There exists at least one student in the class for whom the scores of all the other
students are more than 10 marks away.

(C) There is exactly one student in the class for whom the scores of some students are
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more than 10 marks away.

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(D)
s
For each student, the score of exactly one other student is more than 10 marks
la
away.
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Electronics & Communication Engineering (EC)

Q.6 – Q.10 Carry TWO marks Each

Q.6 Each one of the following clues contains a keyword that is partially filled.

Clue 1: Synonym of recognize (8 letters): _ D _ NT_ FY

Clue 2: A story long enough to fill a book (5 letters): _ _ _ EL

Clue 3: Two of something (6 letters): _ _ _ PLE

Clue 4: A fraction of something, split equally into two parts (4 letters): _ _ _ F

The first letter of each of the keywords can be rearranged to form a four-letter
word.

Which one of the options below is a possible choice for the four-letter word?

(A) CHIN

(B) COIN

(C) ITCH

(D) NOSE

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Electronics & Communication Engineering (EC)

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Q.7 Three children P, Q, R and two grown-ups X, Y play a badminton doubles
tournament. X and Y are parents to two of the children playing. The child of X is
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not the same as the child of Y. Exactly one of the children does not have a parent
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a s
playing in the tournament. The following rules are followed:
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a (ii) A parent and his/her child cannot be on the same team.
A match can feature at most one parent and his/her child, that is, a
maximum of one parent-child pair can play in a match.

The following matches were played:

TEAM 1 TEAM 2

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P and X Q and R

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MATCH 2
g la P and R X and Y
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MATCH 3 R and X Q and Y

Which one of the following options is correct?

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P does not have any parent playing

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las (B) Q does not have any parent playing
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(C) R does not have any parent playing

(D) X does not have a child playing

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Q.8 Let 𝑃𝑘 represent the perimeter of a square with sides of length 𝑘. The value of the
expression 𝑃1 + 𝑃2 + 𝑃3 + ⋯ + 𝑃10 is __________

(A) 55

(B) 110

(C) 220

(D) 440

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Q.9 The city of Atlantis was crafted by the God of the seas, Poseidon. It was made
of alternating concentric circular rings of land (shaded) and water (not shaded)
as represented in the figure (not to scale). The radius of Inner Island was
2.5 stades (a unit of length used in ancient Greece). The water surrounding
Inner Island was one stade wide (length AB). This was surrounded by two pairs
of alternating rings of land and water. The first pair of land and water was two
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stades wide each (lengths BC and CD), and the outer pair is three stades wide
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each (lengths DE and EF).
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The ratio
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surface area of the land to that of the water in the city of Atlantis
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is _________ off to two decimal places).
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(A) 0.45
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(D) 0.90

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Q.10 If

Then

P Q

R S

(A) P

(B) Q

(C) R

(D) S

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Q.11 – Q.35 Carry ONE mark Each

1
⃗⃗ ̇ = 𝐴𝑤
Q.11
Consider the differential equation 𝑤 ⃗⃗ (𝑡 = 0) = [ ].
⃗⃗ , with 𝑤
1

⃗⃗ (𝑡) = 𝑒 𝑡 𝑢
If 𝑤 ⃗ 𝑥 + 𝑒 −2𝑡 𝑢
⃗ 𝑦 be the solution to the equation where 𝑢
⃗ 𝑥 and 𝑢
⃗ 𝑦 are
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unit vectors along the positive x and y axes respectively, then which of the

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following options is the correct matrix representing A?
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(A) 1 0
[ ]
0 −2

(B) −1 0
[ ]
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0 2

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(C)
[
0 −2
]
las
1 0
ag
(D) 0 2
[ ]
−1 0

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Q.12 A surface is given by 𝑧 2 = 2𝑥 2 − 𝑦 2 and 𝑛
⃗ and −𝑛⃗ are unit normal vectors to

̂.
⃗ = 𝒊̂ + √2 𝒌
the surface at the point 𝑃

Which of the following vectors can be 𝑛 ̂ are the unit vectors
⃗ , where 𝒊̂, 𝒋̂ and 𝒌

along x, y and z axes, respectively?

(A) ̂
𝒊̂ − √2 𝒌

(B) 2 1
𝒊̂ − 𝒌̂
3 3

(C) ̂
√2𝒊̂ − √3 𝒌

(D) ̂
√2𝒊̂ − 𝒌
√3

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Q.13 The Laplace Transform of the signal 𝑥(𝑡) = 𝑢(𝑡 − 2) ∗ (𝑡𝑢(𝑡)) is given by

which of the following expressions?

[“∗” represents convolution operator]
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(A) a 𝑒 −2𝑠
𝑠 2 (𝑠 − 2)

(B) 𝑒 −2(𝑠−2)
𝑠3
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(C) 𝑠𝑒 −2𝑠
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(𝑠 − 2)2
s e
g la
(D) 𝑒 −2𝑠 a
𝑠3

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Q.14 Consider carrier transport in a Zener diode in the breakdown region.

Which is the dominant transport mechanism for current flow in this case?

(A) Drift

(B) Diffusion

(C) Tunneling

(D) Ballistic transport

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Two analog signals 𝑥1 (𝑡) and 𝑥2 (𝑡) (t in second), are sampled at a rate
Q.15
𝐹𝑠 = 40 Hz, where

𝑥1 (𝑡) = 𝑐𝑜𝑠(20𝜋𝑡), 𝑡 ≥ 0, and 𝑥2 (𝑡) = 𝑐𝑜𝑠(100𝜋𝑡), 𝑡 ≥ 0.

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The first ten samples (starting from t = 0) are considered for the analysis.
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Which of the following statements is TRUE?
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(A) All of the first three samples of 𝑥1 (𝑡) are greater than the corresponding samples
of 𝑥2 (𝑡).

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All of the last three samples of 𝑥1 (𝑡) are greater than the corresponding samples
of 𝑥2 (𝑡).
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g la
(C) All of the samples of 𝑥2 (𝑡)aare greater than the corresponding samples of 𝑥1 (𝑡).

(D) All of the fourth to seventh samples of 𝑥1 (𝑡) are equal to the corresponding
samples of 𝑥2 (𝑡).

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Q.16 The response of a discrete time system y[n] obeys the following relation:

5 1
𝑦[𝑛] = 𝑦[𝑛 − 1] − 𝑦[𝑛 − 2] + 𝑥[𝑛].
6 6

1
The input to the system is 𝑥[𝑛] = 𝛿[𝑛] − 𝛿[𝑛 − 1].
3

Which of the following options is TRUE for 𝑦[𝑛]?

(A) Stable and causal response

(B) Stable and non-causal response

(C) Unstable and causal response

(D) Unstable and non-causal response

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Q.17 The ideal OP-AMP circuit shown in the Figure produces output voltage 𝑉𝑜 = 𝑥

when the Switch, S, is open.

Which of the options represents the output voltage when S is closed?
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1 kΩ 1 kΩ
-
Vo
+
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Vi = 1 V
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(A) 𝑥

(B) 2
𝑥
3

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(C) 3
𝑥
m 4

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s e (D) 1
𝑥
g l a
g la 2
a
a

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Q.18 Consider the circuit shown in the Figure with 𝑉𝑖 = 3 V and 𝑉𝐶𝐶 = 12 V.

Assume 𝑉𝐵𝐸 = 0.7 V and 𝛽𝑑𝑐 = 99 for the BJT.

Which of the following options is the correct value of the current 𝑰𝒐 ?

(A) 60 μA

(B) 6 μA

(C) 3 μA

(D) 30 μA

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Q.19 A control system is shown in the Figure.

Which option represents the correct transfer function of the system?

m
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+
( ) m ∑ ( )

m .co −
s e m
s e +
l a
g l a −
∑ ag
a

(A) 1
m
(𝑠+4)2
m .co
s e
(B) 1
g la
(𝑠+4) a
(C) 2
(𝑠+4)

(D) 1
(𝑠2 +8𝑠+17)
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Q.20 In the circuit shown in the Figure, A and B are logic inputs and Y is the logic

output.

Which of the following logic operations is realized by the circuit?

+VDD

A

B

Y

(A) NOR

(B) OR

(C) XOR

(D) AND

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Q.21 Consider the Friis’ transmission equation 𝑃𝑅 = (𝑃𝑇 𝐺𝑇 𝐺𝑅 𝜆2 )⁄(4𝜋𝐷)2 , where

𝑃𝑅 and 𝑃𝑇 are the received and the transmitted powers, respectively.

𝐺𝑇 and 𝐺𝑅 are the gain of transmitting and receiving antennas, respectively, 𝐷 is
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the distance between the transmitting and receiving antennas, and 𝜆 is the
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wavelength in free space.

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a Given: 𝐺 = 𝐺 = 1.0, 𝜆 = 0.30 m and P = +10 dBm.
𝑇 𝑅 T

Choose the distance (D), in km, from the following options at which the received

power, PR = −90 dBm?

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s e
g la
(A) 15 a
4𝜋

(B) 15
2𝜋

(C) 75
2𝜋
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c. o(D) m.co
m
3
s e
s e 4𝜋
g l a
g la a
a

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Q.22 Consider a discrete memoryless source with an alphabet of four source symbols.

s(t) is a multi-level (-1, 0, +1, +2) signal representing a long sequence of random

symbols from the above source which is generating 104 symbols per second.

Which of the following options is the correct value of equivalent Nyquist

bandwidth of s(t)?

(A) 10 kHz

(B) 64 kHz

(C) 5 kHz

(D) 20 kHz

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The relation between the input current (I) and the output voltage (V) of a circuit is
Q.23
𝑑𝑉
governed by the equation: 𝐶 = 𝐼(𝑡) − 𝑚(𝑡). The circuit is excited by
𝑑𝑡

I(t) = q(t), where q is a real valued constant. V at 𝑡 = 0− is V0.
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Which of the following is an equivalent representation of the above case?
m s e m
s e l a
g l a ag
a
(A) 𝑑𝑉
𝐶 = −𝑚(𝑡), with V(t = 0− ) = V0 + q/C
𝑑𝑡

(B) 𝑑𝑉
𝐶 = −𝑚(𝑡), with V(t = 0− ) = V0 + q/C + m(t = 0− )
𝑑𝑡

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(C) 𝑑𝑉
𝐶 = −𝑚(𝑡), with V(t = 0− ) = V0 - q/C + m(t = 0− )
em
𝑑𝑡

a s
=l0− ) = q/C
𝐶 = −𝑚(𝑡), with V(t g
𝑑𝑉
a
(D)
𝑑𝑡

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The electric field of a monochromatic plane wave travelling in a lossless isotropic
Q.24
and homogenous medium is given by

𝐸⃗ (𝑧, 𝑡) = 𝐸0 [𝑥̂𝑐𝑜𝑠(𝜔𝑡 − 𝑘𝑧) + 𝑦̂𝑠𝑖𝑛(𝜔𝑡 − 𝑘𝑧)]

in a right-handed orthogonal co-ordinate system.

Which of the following is the correct polarization of the electromagnetic wave?

(A) Right-handed circularly polarized

(B) Left-handed circularly polarized

(C) Linearly polarized

(D) Linearly polarized with −45o angle to 𝑥̂

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Q.25 Consider a p-n junction diode when it is forward biased with 2 V.

Which of the following is/are the correct magnitude(s) of the energy difference

between quasi Fermi-levels, Efn in the n-side and Efp in the p-side?
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(A) a 2 eV

(B) 1 eV

(C) 2V

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(D) 1V

e m
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ag

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Q.26 2 1 1
Consider the matrix M = [ 1 3 0].
−1 𝑎 𝑏
Which of the following options is/ are TRUE if det(M) ≠ 0?

(A) 1 1
𝑎=− and 𝑏 = −
2 2

(B) 1 1
𝑎= and 𝑏 =
2 2

(C) 𝑎 = −3 and 𝑏 = 0

(D) 1
𝑎= and 𝑏 = −3
2

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Q.27 A binary ripple counter is designed to count (0)10 to (64)10.

Which of the following is/are the number of flip-flops required to design the

counter?
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(A) a 6

(B) 7

(C) 4

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(D) 5

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Q.28 Which option(s) represents/ represent the dielectric loss tangent of a substrate?

(A) Ratio of the real to imaginary parts of the total displacement current

(B) (𝜔𝜖 ′′ + 𝜎)⁄(𝜔𝜖′)

(C) Ratio of the electric susceptibility to permittivity

(D) ⃗ to the displacement vector 𝐷
Ratio of the polarization vector 𝑃 ⃗

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Q.29 Figure shows the output characteristics of two different Bipolar Junction

Transistors (BJT), BJT 1 with magnitude of Early voltage |VA1|, and BJT 2 with

magnitude of Early voltage |VA2|.
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m .co
.co
Which of the following options is/are correct regarding the Early voltages?
m s e m
s e l a
g l a ag
a BJT 1
IC
BJT 2

IB = constant
m
.co
s em
VCE
l a
ag

(A) |VA1| > |VA2|

(B) |VA1| is infinitely large
m
m
c. o(C) |VA1| < |VA2|
m.co
m s e
s e g l a
g la (D) |VA2| is finite a
a

m .
.co s e m
s em l a
la
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Q.30 The output voltage Vo (in Volt) for the network given in the Figure is __.

(rounded off to two decimal places)

1 kΩ 1 kΩ +

Vo
6V
1 mA
1 kΩ 1 kΩ -

Q.31 Consider the circuit shown in the Figure, where the input vi (t) is in Volt.

The average power (in mW) dissipated in the load resistance of 1 kΩ at the

resonant frequency is __.

(rounded off to two decimal places)

vi (t)

1 μF 2.2 mH 1 kΩ

vi (t) = 12 sin(ωt)

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a
Q.32 A wireless digital transmission scheme is using 16-QAM over an additive white

Gaussian noise channel and a maximum-likelihood receiver. Consider the

information bit rate from source to be 4 × 106 bits per second.

m
.co
The minimum transmission bandwidth (in MHz) of the modulated signal
m
.co
necessary for optimum recovery of information at the receiver is __.
m s e m
s e l a
l a
(rounded off to two decimal places)
ag
ag
Q.33 The cutoff frequency (in GHz) for the dominant TE10 mode of an air-filled

rectangular waveguide of inner dimension 0.28 inch × 0.14 inch is __.

(rounded off to two decimal places).

m
.co
Q.34 For a lossless passive two-port network, |S11| and |S21| intersect at –3 dB.

s em
For a lossy passive two-port network, |S11| and |S21| intersect at – 4 dB..

g la in the lossy network at the intersection
a
The percentage of power dissipated

frequency is __.

(rounded off to two decimal places)

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.35 The negative edge triggered JK flip-flop in the Figure has J and K inputs tied to

Logic High and a square wave of 10 cycles/second is applied to its clock (C)

input.

The frequency of the output Q (in cycles/second) is __.

(rounded off to two decimal places)

C
K

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Q.36 – Q.65 Carry TWO mark Each

Q.36 Consider the two series, SA and SB, where

𝑛2
𝑆𝐴 = ∑∞
m
.co
𝑛=1 𝑛 2
m
c. 1o 1 s e m
em 2 8 16 + 64 + 128 + 512 + ⋯ a
1 1 1 1
𝑆𝐵 = 1 + + +
s l
g la ag
a Which of the following statements is correct for the two given series?

(A) Both SA and SB converge.
m
.co
(B) Neither SA nor SB converges.
s em
g la
(C) A a
S converges but S does not
B converge.

(D) SB converges but SA does not converge.

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.37 The continuous time signal x(t) is real, periodic with period T and satisfies the

Dirichlet conditions.

2𝜋𝑛𝑡
𝑗( )
The Fourier series representation of 𝑥(𝑡) = ∑∞
−∞ 𝑎𝑛 𝑒 𝑇 and x(t) satisfies

𝑇
the following: 𝑥 (𝑡 − ) = −𝑥(𝑡).
2

For any integer m, which of the following options is correct?

(A) a2m = 0

(B) a2m = 1

(C) a2m = a2m+1

(D) a2m = -1

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Q.38 Let X, N, Y and Z be random variables. The variables X and N are independent of

each other. X is uniformly distributed between -1 and 1; N follows Normal

distribution with zero mean and unity variance.

m
m .co
.co
Y and Z are defined as, 𝑌 = 𝑋 + 𝑁 and 𝑍 = 𝑋 2 + 𝑁.
e m
e m l as
l as
Which of the following pairs represents the values of correlation between X and Yg
a
g
a and that between X and Z?

(A) 1/3 and 0
m
(B) 1/3 and 1/9
m .co
s e
g la
(C) 1/3 and 1/3
a
(D) 1 and 0

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.39 In the given circuit, L = 1 μH and C = 1 μF. The phasor diagram for IC and IL is

also shown. Assume that the phase (θ1 + θ2) is 90o at a frequency of 159.15 kHz.

Among the following options, what is the nearest integer value of RC × RL?

IC IL IC
+
RC RL θ1
V V
θ2
- C L
IL

(A) 0

(B) 1

(C) 2

(D) 10

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Q.40 For the control system shown in the Figure, the transfer function of a plant,

1
𝐺(𝑠) = (𝑠+1)(𝑠+2) is connected in cascade with a compensator

𝐶(𝑠) = 𝐾 (𝑠 + 𝛼), where 𝐾 and 𝛼 are positive real valued constants.
m
c o m m .co
. s e
em
following pairs (𝐾, 𝛼) represent the correct values for the closed
a
Which of the

as g l
l a
ag
loop system to have poles at (−3 ± 𝑗√5)?

∑

m
m .co
s e
la
(A) 2, 3

ag
(B) 3, 4

(C) 2, 4

(D) 3, 3

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.41 The state and output equations for a control system are:

−4 −1.5 2
𝑥̇ = [ ]𝑥 + [ ]𝑢
4 0 0

𝑦 = [1.5 0.625] 𝑥

𝑌(𝑠)
Which of the following expressions correctly represents the transfer function
𝑈(𝑠)

of the system with zero initial conditions?

(A) 3𝑠
𝑠 2 +4𝑠−6

(B) 3𝑠+5
𝑠 2 +4𝑠−6

(C) 3𝑠+5
𝑠 2 +4𝑠+6

(D) 3𝑠
𝑠 2 +4𝑠+6

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Q.42 The address of the first location of a 256 kilo byte (KB) memory is (2500)H.

Choose the correct address of the last location of the memory.

m
m .co
.co s e m
s em l a
ag
(A) (2FFF)H

g la
(B) a (124FF) H

(C) (424FF)H

(D) (324FF)H

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.43 Consider a real signal x(t), -∞ < t < ∞, such that

x(t) = 0 for t <0, x(t) = 2 for 0 ≤ t < 1 and x(t) = 0 for t ≥ 1.

∞
Let 𝐸[𝑥(𝑡)] = ∫−∞[𝑥(𝑡)]2 𝑑𝑡.

Which of the following options correctly represents the ratio,

𝐸[𝑥(𝑡)]⁄𝐸[3 𝑥(−3𝑡 + 5)]?

(A) 3

(B) 1

(C) 1/3

(D) 1/9

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Q.44 A QPSK modulated signal from an additive white Gaussian noise (AWGN)

channel is received with an Eb/No = 8.4 dB at the input of a coherent QPSK

demodulator. A maximum-likelihood reception method is used in the

m
.co
demodulator.
o m m
Assumem
. c s e
s e the complimentary error function
l a
g l a ag
a 𝑒𝑟𝑓𝑐(𝑢) ≅ [1⁄(𝑢√𝜋)]𝑒𝑥𝑝(−𝑢2 ).

Which is the nearest bit error rate (BER) at the output of the demodulator?

m
m .co
10-3
e
(A)

las
(B) 10-4 ag

(C) 10-5

(D) 10-6

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.45 What is the 10′𝑠 complement of (47)10?

(A) 52

(B) 53

(C) 54

(D) 55

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Q.46 Consider a real baseband signal 𝑥(𝑡) = 𝑒 −2𝑡 , for t (in seconds) ≥ 0.

If 99% of energy of x(t) lies within B Hz, then which of the following options is

m
.co
TRUE for the value of B?
m
.co s e m
s em l a
g la ag
(A) a B > 1 kHz

(B) 63/π Hz < B < 64/π Hz

(C) 126/π Hz < B < 128/π Hz

m
.co
(D) B < 1 Hz

e m
las
ag

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.47 Consider the discrete time system (S) with input x[n] and output y[n] as shown in

the Figure. The two sub-systems represented by their impulse responses ℎ1 [𝑛]

and ℎ2 [𝑛] are linear and time invariant.

Which of the following statements is necessarily TRUE?

n] ∑

∑ n]

(A) S is causal.

(B) S is linear and time invariant.

(C) S is linear and time varying.

(D) S is non-linear.

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Q.48 A Boolean function, f(x,y,z) with x as MSB and z as LSB is realized by 4:1

multiplexer (MUX) with select lines, S1 and S0 ( S1 is MSB, S0 is LSB) and inputs,

I0, I1, I2, I3 as shown in the Figure.

m
m .co
.co m
Which of the following options is the correct expression of f(x,y,z)?

m s e
s e l a
g a
l1 ag
a I0
0 I1 4:1 f(x,y,z)
I2 MUX
y I3
S1 S0
m
.co
x
e m
z
las
ag

(A) 𝑥𝑧 + 𝑦

(B) 𝑥𝑦̅ + 𝑧
m
m
c. o(C) 𝑥𝑦 + 𝑧̅ m.co
m s e
s e g l a
g la (D) 𝑥̅ 𝑦 + 𝑧̅ a
a

m .
.co s e m
s em l a
la
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Q.49 A shift-left Shift Register (SR) and a D flip-flop are connected to a synchronized

clock as shown in the Figure. Assume that the SR and D flip-flops are initially

cleared and the XOR gate has no propagation delay.

Which of the following options gives the correct binary representation

(b7b6b5b4b3b2b1b0) of the content of the shift register immediately after the

5th clock transition (positive edge)?

SR (Shift Left)

b7 b6 b5 b4 b3 b2 b1 b0

D Q

C ̅ 1

Clock pulse

(A) 00011111

(B) 10111111

(C) 00111111

(D) 11000011

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Q.50 A small signal source, 𝑉𝑖 (𝑡) = 𝐴 cos(105 𝑡) + 𝐵 sin(107 𝑡) is applied to a
BJT circuit as shown in the Figure.

Assume zero source resistance, VBE = 0.7 V, βdc = 99, Early voltage = 100 V and

Thermal voltage = 25 mV. Effect of internal parasitic capacitances of the BJT
m
.co
may be neglected.
m
.co
Which expression is the best approximation of the output voltage 𝑉𝑜 (𝑡)?
m s e m
s e l a
g l a ag
a

m
m .co
s e
g la
a

(A) −9.1[𝐴 cos(105 𝑡) + 𝐵 sin(107 𝑡)] m
m
c. o(B) m.co
m 9.1[𝐴 cos(105 𝑡) − 𝐵 sin(107 𝑡)] s e
s e g l a
g la a
a (C) −190.4[𝐴 cos(105 𝑡) + 𝐵 sin(107 𝑡)]

(D) 190.4[𝐴 cos(105 𝑡) − 𝐵 sin(107 𝑡)]

m .
.co s e m
s em l a
la
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Q.51 Consider the two-port network as shown in the Figure.

Which of the following options provides the correct set of values of

A, B, C and D parameters?

1 kΩ 1 kΩ

P1 P2
1 kΩ

(A) A = 1/2, B = 3×103 Ω, C = 10-3 Ω-1, D = 1/2

(B) A = 2, B = 3 Ω, C = 1 Ω-1, D = 2

(C) A = 2, B = 6×103 Ω, C = 2×10-3 Ω-1, D = 2

(D) A = 2, B = 3×103 Ω, C = 10-3 Ω-1, D = 2

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Q.52 A complex load (in Ω) is represented as Γ𝐿 = 0.5∠30𝑜 on the Smith chart.

A co-axial cable with a characteristic impedance of 50 Ω is connected to the load.

The new input impedance of the load now moves to a diametrically opposite point

m
.co
on the same Γ circle on the Smith chart.
m
.co e m
em is the nearest input impedance of the cable connected load (in Ω)? glas
Which option
s
g la a
a

(A) 20.7 − 𝑗5.1

(B) 17.7 − 𝑗11.8

m
(C) 97.5 − 𝑗65.0
m .co
s e
(D) 97.5 + 𝑗65.0
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.53 A circuit using an ideal OP-AMP is shown in the Figure.

Which of the following options gives the correct value of the current 𝐼𝑋 ?

(A) 2.0 mA

(B) 1.5 mA

(C) 3.0 mA

(D) 0 mA

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Q.54 Consider an LED based on a direct bandgap semiconductor material with energy

bandgap 1.3 eV.

Given: Plank’s constant, ℎ = 6.63 × 10−34 J s and speed of light in free space is
m
m .co
.co
3 × 108 m s −1.
e m
e m l as
as
In which of the following wavelength ranges the LED will NOT emit?
l ag
ag

(A) 1410 ± 20 nm

(B) 1090 ± 20 nm
m
m .co
(C) 950 ± 20 nm
s e
g la
(D) 510 ± 20 nm a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.55 Let the relevant bandwidth (B) of a digital communication system be 1 MHz and

kT = −174 dBm/Hz, where k is Boltzmann’s constant and ‘T’ is equivalent noise

temperature of the receiver. The power (S) of signal received through an additive

Gaussian channel is −80 dBm.

Which of the following options is/are TRUE about Shannon capacity (C) of the

channel?

(A) C=B

(B) C = 2B

(C) C > 3B

(D) C<B

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Q.56 Consider the four-variable Boolean function,

𝑓(𝑤, 𝑥, 𝑦, 𝑧) = ∑ 𝑚(0,2,5,7,8,10,13,14,15) with ‘w’ as MSB and ‘z’ as LSB.

m
.co
Which of the following expressions is/are the valid form(s) of 𝑓(𝑤, 𝑥, 𝑦, 𝑧)?
m
.co s e m
s em l a
g la ag
(A)
a 𝑥̅ 𝑧̅ + 𝑥𝑧 + 𝑤𝑥𝑦

(B) 𝑥𝑧 + 𝑤𝑥𝑦 + 𝑤𝑥̅ 𝑧̅ + 𝑤𝑥𝑦𝑧̅

(C) 𝑥̅ 𝑧̅ + 𝑤𝑥𝑦 + 𝑤𝑥̅ 𝑧̅ + 𝑤 𝑥𝑦𝑧̅
m
(D) 𝑥̅ 𝑧̅ + 𝑥𝑧 + 𝑤𝑦𝑧̅
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.57 Consider a real, narrowband signal 𝑥(𝑡) = 𝐴(𝑡)cos[2𝜋𝑓𝑐 𝑡 + 𝜃(𝑡)] where the

maximum frequency components of A(t) and θ(t) are fM and fc (= 1000 fM),

respectively.

Which of the following statements is/are correct for −∞ < 𝑡 < ∞?

(A) x(t) represents a PSK modulated signal for suitable choices of A(t) and θ(t).

(B) x(t) represents an amplitude modulated signal for suitable choices of A(t) and θ(t).

(C) x(t) represents a band-limited Gaussian noise process.

(D) x(t) never represents a narrowband FM signal.

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Q.58 Let 𝑥1 (𝑡) = cos(2𝜋𝑛𝑡) and 𝑥2 (𝑡) = 2sin(4𝜋𝑛𝑡) represent two sinusoids

for a positive integer n and −∞ < 𝑡 < ∞ .

Which of the following statements about 𝑥1 (𝑡) and 𝑥2 (𝑡) is/are valid? m
m .co
m .co s e m
s e l a
g l a ag
a (𝑡)
(A) 𝑥1 and 𝑥2 (𝑡) are orthogonal to each other over 0 ≤ t < 1/n .

(B) 𝑥1 (𝑡) and 𝑥2 (𝑡) are orthonormal to each other over 0 ≤ t < 1/n .

(C) 𝑥2 (𝑡) is a harmonic of 𝑥1 (𝑡) .

o m
c
𝑥1 (𝑡) and 𝑥2 (𝑡) are non-orthogonal to.each other over 0 ≤ t < 1/(2n) .
em
(D)

las
a g

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
la
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Q.59 Consider the unity negative feedback control system shown in the Figure.

The value of gain K (>0) at which the given system will remain marginally stable

is __.

(Answer in integer)

∑

Q.60 An n-channel MOSFET is connected as shown in the Figure.

𝑊
Assume 𝑉𝑇𝐻 = 1 V, 𝑉𝐷𝐷 = 5 V, and 𝜇𝐶𝑜𝑥 ( ) = 2 mA V −2 and neglect
𝐿

channel length modulation effects.

The gate voltage (𝑉𝐺 ) of the n-channel MOSFET (in Volt) is __.

(rounded off to two decimal places)

+VDD

1 kΩ
VG

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a
Q.61 Consider the square region R in the X-Y plane as shown with the dark shading in

the Figure. The value of ∬𝑅 (𝑥 2 + 𝑦 2 − 1)𝑑𝑥𝑑𝑦 is ____.

m
.co
(rounded off to two decimal places)
m
.co s e m
s eym l a
g la ag
a
R
x
0,0 1 2

o m
c
. in the Figure.
m
Q.62 Consider an ideal OP-AMP circuit as shown

The resistances R = R = R = Ras
e
l = 50 kΩ.
ag
1 2 3 4

The magnitude of the closed loop gain is ___.

(rounded off to two decimal places)

R2 R3

m
m R4
.co
m .co R1
s e m
s e vi
l a
v g
-

g la ao

a +

m .
.co s e m
s em l a
la
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g
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ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 57 of 58

Electronics and Communication Engineering (EC)

Q.63 The average bit error rate at the input of a (7, 4, 1) Hamming decoder is 0.10.

The probability that the decoder will fail to decode a received word correctly is
__.

(rounded off to two decimal places)

Q.64 Consider that the concentration of electrons in a semiconductor bar varies linearly
from 2 × 1017 cm−3 at x = 1 m to 1× 1016 cm−3 at x = 4 m along the
x-direction. Assume that the concentration of electrons is not varying along other
directions (that is along y- and z-directions).

[Given: the mobility of electron is 1400 cm2 V −1 s−1 , thermal voltage is 25 mV
and electronic charge is 1.6× 10−19 Coulomb.]

The density of electron diffusion current (in A/mm2) is __.

(rounded off to two decimal places)

Q.65 Consider the ideal diodes D1 and D2 as shown in the Figure with cut-in voltage
Vγ = 0 Volt and vi(t) is in Volt.

The maximum voltage (Volt) of the output vo(t) is __.

(rounded off to two decimal places)

10 kΩ

+
10 kΩ
vi (t) vo (t)
D1 D2
2V 4V -

vi (t) = 6 sin(ωt)

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