GATE EC 2026: Electronics and Communication Engineering
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Electronics & Communication Engineering (EC) General Aptitude (GA) Q.1 – Q.5 Carry ONE mark Each Q.1 Among the following options, the antonym of the word ‘nocturnal’ is _________. (A) normal (B) diurnal (C) abnormal (D) exceptional Organizing Institute: IIT Guwahati Page 1 of 58
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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)
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?
P Q
R S
P
(A)
Q
(B)
(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)
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.’
If the above statement is false, which one of the following statements is necessarily
true?
(A) For each student, the scores of all the other students are more than 10 marks away.
(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
more than 10 marks away.
(D) For each student, the score of exactly one other student is more than 10 marks
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)
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
not the same as the child of Y. Exactly one of the children does not have a parent
playing in the tournament. The following rules are followed:
(i) A parent and his/her child cannot be on the same team.
(ii) 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
MATCH 1 P and X Q and R
MATCH 2 P and R X and Y
MATCH 3 R and X Q and Y
Which one of the following options is correct?
(A) P does not have any parent playing
(B) Q does not have any parent playing
(C) R does not have any parent playing
(D) X does not have a child playing
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Electronics & Communication Engineering (EC)
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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Electronics & Communication Engineering (EC)
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
stades wide each (lengths BC and CD), and the outer pair is three stades wide
each (lengths DE and EF).
The ratio of the surface area of the land to that of the water in the city of Atlantis
is _________ (round off to two decimal places).
(A) 0.45
(B) 0.60
(C) 0.75
(D) 0.90
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Electronics & Communication Engineering (EC)
Q.10 If
Then
P Q
R S
(A) P
(B) Q
(C) R
(D) S
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Electronics and Communication Engineering (EC)
Q.11 – Q.35 Carry ONE mark Each
Q.11 1
ẇ = Aw
Consider the differential equation ⃗⃗ ⃗⃗ , with ⃗⃗w(t = 0) = [ ].
1
w(t) = e t ⃗ux + e −2t ⃗uy be the solution to the equation where ⃗ux and ⃗uy are
If ⃗⃗
unit vectors along the positive x and y axes respectively, then which of the
following options is the correct matrix representing A?
(A) 1 0
[ ]
0 −2
(B) −1 0
[ ]
0 2
(C) 0 −2
[ ]
1 0
(D) 0 2
[ ]
−1 0
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Electronics and Communication Engineering (EC)
Q.12 A surface is given by z 2 = 2x 2 − y 2 and ⃗n and −n
⃗ are unit normal vectors to
̂.
⃗ = î + √2 k
the surface at the point P
̂ are the unit vectors
Which of the following vectors can be ⃗n, where î, ĵ and k
along x, y and z axes, respectively?
(A) ̂
î − √2 k
(B) 2 1
î − ̂k
3 3
(C) ̂
√2î − √3 k
(D) ̂
√2î − k
√3
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Electronics and Communication Engineering (EC)
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]
(A) e −2s
s 2 (s − 2)
(B) e −2(s−2)
s3
(C) se −2s
(s − 2)2
(D) e −2s
s3
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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.
The first ten samples (starting from t = 0) are considered for the analysis.
Which of the following statements is TRUE?
(A) All of the first three samples of x1 (t) are greater than the corresponding samples
of x2 (t).
(B) All of the last three samples of x1 (t) are greater than the corresponding samples
of x2 (t).
(C) All of the samples of x2 (t) are 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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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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?
S
2 kΩ
1 kΩ 1 kΩ
-
Vo
+
Vi = 1 V
(A) x
(B) 2
x
3
(C) 3
x
4
(D) 1
x
2
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
Q.19 A control system is shown in the Figure.
Which option represents the correct transfer function of the system?
+
( ) ∑ ( )
−
+
−
∑
(A) 1
(s+4)2
(B) 1
(s+4)
(C) 2
(s+4)
(D) 1
(s2 +8s+17)
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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
the distance between the transmitting and receiving antennas, and λ is the
wavelength in free space.
Given: GT = GR = 1.0, λ = 0.30 m and PT = +10 dBm.
Choose the distance (D), in km, from the following options at which the received
power, PR = −90 dBm?
(A) 15
4π
(B) 15
2π
(C) 75
2π
(D) 3
4π
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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.
Which of the following is an equivalent representation of the above case?
(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
(C) dV
C = −m(t), with V(t = 0− ) = V0 - q/C + m(t = 0− )
dt
(D) dV
C = −m(t), with V(t = 0− ) = q/C
dt
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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?
(A) 2 eV
(B) 1 eV
(C) 2V
(D) 1V
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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?
(A) 6
(B) 7
(C) 4
(D) 5
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Electronics and Communication Engineering (EC)
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) Ratio of the polarization vector ⃗
P to the displacement vector ⃗D
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Electronics and Communication Engineering (EC)
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|.
Which of the following options is/are correct regarding the Early voltages?
BJT 1
IC
BJT 2
IB = constant
VCE
(A) |VA1| > |VA2|
(B) |VA1| is infinitely large
(C) |VA1| < |VA2|
(D) |VA2| is finite
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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.
The minimum transmission bandwidth (in MHz) of the modulated signal
necessary for optimum recovery of information at the receiver is __.
(rounded off to two decimal places)
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).
Q.34 For a lossless passive two-port network, |S11| and |S21| intersect at –3 dB.
For a lossy passive two-port network, |S11| and |S21| intersect at – 4 dB..
The percentage of power dissipated in the lossy network at the intersection
frequency is __.
(rounded off to two decimal places)
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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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Electronics and Communication Engineering (EC)
Q.36 – Q.65 Carry TWO mark Each
Q.36 Consider the two series, SA and SB, where
n2
SA = ∑∞
n=1 n 2
1 1 1 1 1 1
SB = 1 + + + + + + +⋯
2 8 16 64 128 512
Which of the following statements is correct for the two given series?
(A) Both SA and SB converge.
(B) Neither SA nor SB converges.
(C) SA converges but SB does not converge.
(D) SB converges but SA does not converge.
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Electronics and Communication Engineering (EC)
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.
Y and Z are defined as, Y = X + N and Z = X 2 + N.
Which of the following pairs represents the values of correlation between X and Y
and that between X and Z?
(A) 1/3 and 0
(B) 1/3 and 1/9
(C) 1/3 and 1/3
(D) 1 and 0
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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.
Which of the following pairs (K, α) represent the correct values for the closed
loop system to have poles at (−3 ± j√5)?
∑
(A) 2, 3
(B) 3, 4
(C) 2, 4
(D) 3, 3
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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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Electronics and Communication Engineering (EC)
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.
(A) (2FFF)H
(B) (124FF)H
(C) (424FF)H
(D) (324FF)H
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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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Electronics and Communication Engineering (EC)
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
demodulator.
Assume the complimentary error function
erfc(u) ≅ [1⁄(u√π)]exp(−u2 ).
Which is the nearest bit error rate (BER) at the output of the demodulator?
(A) 10-3
(B) 10-4
(C) 10-5
(D) 10-6
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Electronics and Communication Engineering (EC) Q.45 What is the 10′s complement of (47)10? (A) 52 (B) 53 (C) 54 (D) 55 Organizing Institute: IIT Guwahati Page 42 of 58
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Electronics and Communication Engineering (EC)
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
TRUE for the value of B?
(A) B > 1 kHz
(B) 63/π Hz < B < 64/π Hz
(C) 126/π Hz < B < 128/π Hz
(D) B < 1 Hz
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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.
Which of the following options is the correct expression of f(x,y,z)?
1 I0
0 I1 4:1 f(x,y,z)
I2 MUX
y I3
S1 S0
x
z
(A) xz + y
(B) xy̅ + z
(C) xy + z̅
(D) x̅ y + z̅
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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
may be neglected.
Which expression is the best approximation of the output voltage Vo (t)?
(A) −9.1[A cos(105 t) + B sin(107 t)]
(B) 9.1[A cos(105 t) − B sin(107 t)]
(C) −190.4[A cos(105 t) + B sin(107 t)]
(D) 190.4[A cos(105 t) − B sin(107 t)]
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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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Electronics and Communication Engineering (EC)
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
on the same Γ circle on the Smith chart.
Which option is the nearest input impedance of the cable connected load (in Ω)?
(A) 20.7 − j5.1
(B) 17.7 − j11.8
(C) 97.5 − j65.0
(D) 97.5 + j65.0
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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
3 × 108 m s −1.
In which of the following wavelength ranges the LED will NOT emit?
(A) 1410 ± 20 nm
(B) 1090 ± 20 nm
(C) 950 ± 20 nm
(D) 510 ± 20 nm
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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.
Which of the following expressions is/are the valid form(s) of f(w, x, y, z)?
(A) x̅ z̅ + xz + wxy
(B) xz + wxy + wx̅ z̅ + wxyz̅
(C) x̅ z̅ + wxy + wx̅ z̅ + w xyz̅
(D) x̅ z̅ + xz + wyz̅
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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?
(A) x1 (t) 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) .
(D) x1 (t) and x2 (t) are non-orthogonal to each other over 0 ≤ t < 1/(2n) .
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Electronics and Communication Engineering (EC)
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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Electronics and Communication Engineering (EC)
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 ____.
(rounded off to two decimal places)
y
R
x
0,0 1 2
Q.62 Consider an ideal OP-AMP circuit as shown in the Figure.
The resistances R1 = R2 = R3 = R4 = 50 kΩ.
The magnitude of the closed loop gain is ___.
(rounded off to two decimal places)
R2 R3
R4
R1
vi -
vo
+
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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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Answer Key for Electronics & Communication Engineering (EC)
Q. No. Session Question Type Section Key/Range Marks
1 7 MCQ GA B 1
2 7 MCQ GA A 1
3 7 MCQ GA D 1
4 7 MCQ GA B 1
5 7 MCQ GA B 1
6 7 MCQ GA A 2
7 7 MCQ GA C 2
8 7 MCQ GA C 2
9 7 MCQ GA C 2
10 7 MCQ GA C 2
11 7 MCQ EC A 1
12 7 MCQ EC D 1
13 7 MCQ EC D 1
14 7 MCQ EC C 1
15 7 MCQ EC D 1
16 7 MCQ EC A 1
17 7 MCQ EC C 1
18 7 MCQ EC D 1
19 7 MCQ EC B 1
20 7 MCQ EC A 1
21 7 MCQ EC B 1
22 7 MCQ EC C 1
23 7 MCQ EC A 1
24 7 MCQ EC A 1
25 7 MSQ EC A 1
26 7 MSQ EC B;D 1
27 7 MSQ EC B 1
28 7 MSQ EC A;B 1
29 7 MSQ EC C;D 1
30 7 NAT EC 0.95 to 1.05 1
31 7 NAT EC 71.50 to 72.50 1
32 7 NAT EC 0.95 to 1.05 1
33 7 NAT EC 20.50 to 21.50 1
34 7 NAT EC 20.00 to 21.00 1
35 7 NAT EC 4.90 to 5.10 1
36 7 MCQ EC A 2
37 7 MCQ EC A 2
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Q. No. Session Question Type Section Key/Range Marks
38 7 MCQ EC A 2
39 7 MCQ EC B 2
40 7 MCQ EC B 2
41 7 MCQ EC C 2
42 7 MCQ EC C 2
43 7 MCQ EC C 2
44 7 MCQ EC B 2
45 7 MCQ EC B 2
46 7 MCQ EC B 2
47 7 MCQ EC B 2
48 7 MCQ EC C 2
49 7 MCQ EC A 2
50 7 MCQ EC A 2
51 7 MCQ EC D 2
52 7 MCQ EC B 2
53 7 MCQ EC C 2
54 7 MSQ EC A;B;D 2
55 7 MSQ EC C 2
56 7 MSQ EC A;D 2
57 7 MSQ EC A;B;C 2
58 7 MSQ EC A;C;D 2
59 7 NAT EC 1386 to 1386 2
60 7 NAT EC 2.50 to 2.60 2
61 7 NAT EC 0.60 to 0.70 2
62 7 NAT EC 2.90 to 3.10 2
63 7 NAT EC 0.10 to 0.20 2
64 7 NAT EC -36.50 to -34.50 OR 34.50 to 36.50 2
65 7 NAT EC 3.70 to 4.30 2
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Source: GATE. Question paper published by GATE.