GATE Sample Paper for Electronics and Communication

Sample Paper aglase .co

EC: Electronics and Communication Engg.

Q.No. 1 For a narrow base PNP BJT, the excess minority carrier concentrations (Δn f orem itter, Δp , for base.
E B

Δn C
for collector) normalised to equilibrium minority carrier concentrations (n for emitter p f orbas e, n
E0 B0 C0

for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following
biasing modes is the transistor operating in?

(A) Forward active

(B) Saturation

(C) Inverse active

(D) Cutoff

Q.No. 2 Consider a wireless communication link between a transmitter and a receiver located in free space, with
finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas. and the
distance between them are all doubled. and everything else remains unchanged. The maximum capacity of the
wireless link

(A) increases by a factor of 2

(B) decreases by a factor of 2

(C) remains unchanged

(D) decreases by a factor of √2

Q.No. 3 The expression for an electric field in free space is E = E (x^ + y^ + j 2z^)e
0
−j (ωt−k x +k y)
where, x, y, z
represent the spatial coordinates. t represents time, and ω, k are constants. This electric field

(A) does not represent a plane wave.

(B) represents a circularly polarized plane wave propagating nonnal to the z-axis.

(C) represents an elliptically polarized plane wave propagating along the x-y plane.

(D) represents a linearly polarized plane wave.

t
Q.No. 4 The input x(t) and the output y(t) of a continuous-time system are related as y(t) = ∫ t−T
x (u)du The
system is

(A) linear and time-variant

(B) linear and time-invariant

(C) non-linear and time-variant

(D) non-linear and time-invariant

Answer: (B)

Q.No. 5 A programmable logic array (PLA) is shown in the figure.

The Boolean function F implemented
is

(A) P̄ Q̄R + P̄ QR + P Q̄R̄

(B) (P̄ + Q̄ + R)(P̄ + Q + R)(P + Q̄ + R̄)

(C) P̄ Q̄R + P̄ QR + P Q̄R

(D) (P̄ + Q̄ + R)(P̄ + Q + R)(P + Q̄ + R)

Q.No. 6 A single crystal intrinsic semiconductor is at a temperature of 300 K with an effective density of states for
holes twice that of electrons. The thermal voltage is 26 mV. The intrinsic Fermi level is shifted from mid-band gap
energy level by

(A) 18.02 meV.

(B) 9.01 mev

(C) 13.45 meV

(D) 290 mev.

Answer: (B)

Q.No. 7 The Nyquist plot of the transfer function G(s ) = 2
K

(s +2s +2)(s +2)
does not encircle the point (—1 + j0) for
K = 10 but does encircle the point (—1 + j0) for K = 100. Then the closed loop system (having unity gain
feedback) is

(A) stable for K = 10 and stable for K = 100

(B) stable for K = 10 and unstable for K = 100

(C) unstable for K = 10 and stable for K = 100

(D) unstable for K = 10 and unstable for K = 100

Answer: (B)

Q.No. 8 Which one of the following options contains two solutions of differential equation dy

dx
= (y − 1)x ?

(A) ln |y − 1| = 0.5x 2
+ C and y = 1

(B) ln |y − 1| = 2x 2
+ C and y = 1

(C) ln |y − 1| = 0.5x 2
+ C and y = −1

(D) ln |y − 1| = 2x 2
+ C and y = −1

Q.No. 9 In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are 20 V and 60
mA, respectively. The values of 𝑅1 and 𝑅𝐿 are 200 Ω and 1 kΩ, respectively. What is the range of Vi that will

maintain the Zener diode in the ‘on’ state?

(A) 22 V to 34 V

(B) 24 V to 36 V

(C) 18 V to 24 V

(D) 20 V to 28 V

Answer: (B)

Q.No. 10 Consider a causal second-order system with the transfer function 𝐺(𝑠) =1/1 + 2𝑠 + 𝑠2 with a unit-step
𝑅(𝑠) =1𝑠 as an input. Let 𝐶(𝑠) be the corresponding output. The time taken by the system output 𝑐(𝑡) to reach 94%
of its steady-state value lim𝑡→∞𝑐(𝑡), rounded off to two decimal places, is

(A) 5.25

(B) 4.50

(C) 3.89

(D) 2.81

Answer: (B)

Q.No. 11 The logic function f (X ,Y ) realized by the given circuit is

(A) NOR

(B) AND

(C) NAND

(D) XOR

Answer: (D)

Q.No. 12 An enhancement MOSFET of threshold voltage 3 V is being used in the sample and hold circuit given
below. Assume that the substrate of the MOS device is connected to -10 V. If the input voltage Vi lies between ±10
V, the minimum and the maximum values of VG Required for proper sampling and holding respectively, are

(A) 3V and -3V

(B) 10V and -10V

(C) 13V and -7V

(D) 10V and -13V

Q.No. 13 The partial derivative of the function f (x , y, z ) = e with respect to x at the point
2
1−x cos y −1/(1+y )
+ x ze

(1,0, e) is

(A) -1

(B) 0

(C) 1

(D) 1/e

Answer: (B)

Q.No. 14 A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of
products is given by F = A̅⋅ B̅ ⋅ C̅+ A̅⋅ B ⋅ C̅+ A ⋅ B̅ ⋅ C̅ where, A̅, B̅, and C̅are the complements of the respective
variables. The product of sums (POS) form of the function F is

(A) F = (A + B + C) ⋅ (A + B̅ + C) ⋅ (A̅+ B + C)

(B) F = (A̅+ B̅ + C̅) ⋅ (A̅+ B + C̅) ⋅ (A + B̅ + C̅)

(C) F = (A + B + C̅) ⋅ (A + B̅ + C̅) ⋅ (A̅+ B + C̅) ⋅ (A̅+ B̅ + C) ⋅ (A̅+ B̅ + C̅)

(D) F = (A̅+ B̅ + C) ⋅ (A̅+ B + C) ⋅ (A + B̅ + C) ⋅ (A + B + C̅) ⋅ (A + B + C)

2

Q.No. 15 The General Solution of d y

dx
2
− 6
dy

dx
+ 9y = 0

(A) y = C e1
3x
+ C2 e
−3x

(B) y = (C + C x )e
1 2
−3x

(C) y = (C + C x )e
1 2
3x

(D) y = C e1
3x

Q.No. 16 The impedances Z = jx, for all X in the range (-∞, ∞), map to the Smith chart as .

(A) a circle of radius 1 with centre at (0,0)

(B) a point at the centre of the chart

(C) a line passing through the centre of the chart.

(D) a circle of radius 0.5 with centre at (0.5, 0).

Q.No. 17 A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is
linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword
1100110, then the message 0010 is mapped to

(A) 0010011

(B) 1100001

(C) 1111000

(D) 1111111

Answer: (B)

Q.No. 18 Which of the following statements is incorrect?

(A) Lead compensator is used to reduce the settling time

(B) Lag compensator is used to reduce the steady state error.

(C) Lead compensator may increase the order of a system.

(D) Lag compensator always stabilizes an rmstable system.

Answer: (D)

Q.No. 19 The circuit shown in the figure is used to provide regulated voltage (5 V) across the 1kᘯ resistor.
Assume that the Zener diode has a constant reverse breakdown voltage for a current range, starting from a
minimum required Zener current, I = 2mA to its maximum allowable current. The input voltage Vₗ may vary
Z min

by 5% from its nominal value of 6 V. The resistance of the diode in the breakdown region is negligible.

The value of R and the minimum
required power dissipation rating of the diode, respectively, are

(A) 186ᘯ and 10 mW

(B) 100ᘯ and 40 mW

(C) 100ᘯ and 10 mW

(D) 186ᘯ and 40 mW

Answer: (B)

Q.No. 20 Consider the line integral ∫c(𝑥𝑑𝑦 − 𝑦𝑑𝑥) the integral being taken in a counterclockwise direction over the
closed curve 𝐶 that forms the boundary of the region 𝑅 shown in the figure below. The region 𝑅 is the area
enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to

(A) 6 + 𝜋/2

(B) 8 + 𝜋

(C) 12 + 𝜋

(D) 16 + 2𝜋

Q.No. 21 A standard CMOS inverter is designed with equal rise and fall times (β𝑛 = βp). If the width of the pMOS
transistor in the inverter is increased, what would be the effect on the LOW noise margin (𝑁𝑀𝐿) and the HIGH
noise margin 𝑁𝑀𝐻?

(A) (𝑁𝑀𝐿) increases and 𝑁𝑀𝐻 decreases.

(B) (𝑁𝑀𝐿) decreases and 𝑁𝑀𝐻 increases.

(C) Both (𝑁𝑀𝐿) and 𝑁𝑀𝐻 increase.

(D) No change in the noise margins.

Q.No. 22 An n-channel enhancement mode MOSFET is biased at VGS > VTH and VDS > (VGS - VTH), where
VGS the gate-to-source voltage, VDS is the drain-to-source voltage and VTH is the threshold voltage.
Considering channel length modulation effect to be significant, the MOSFET behaves as a

(A) voltage source with zero output impedance

(B) voltage source with non-zero output impedance

(C) current source with finite output impedance

(D) current source with infinite output impedance

Q.No. 23 The Miller effect in the context of a Common Emitter amplifier explains

(A) an increase in the low-frequency cutoff frequency

(B) an increase in the high-frequency cutoff frequency

(C) a decrease in the low-frequency cutoff frequency

(D) a decrease in the high-frequency cutoff frequency

Answer: (D)

Q.No. 24 In the circuit shown below, Thevenin voltage VTH is

(A) 2.4V

(B) 2.8V

(C) 3.6V

(D) 4.5V

Q.No. 25 The state diagram of a sequence detector is shown below. State So is the initial state of the sequence

detector. If the output is 1, then

(A) the sequence 01010 is detected

(B) the sequence 01011 is detected

(C) the sequence 01110 is detected

(D) the sequence 01001 is detected

Q.No. 26 An abrupt pn junction (located at x = 0) is uniformly doped on both p and n sides. The width of the
depletion region is W and the electric field variation in the x-direction is E(x). Which of the following figures
represents the electric field profile near the pn junction?

(A)

(B)

(C)

(D)

Q.No. 27 A finite duration discrete-time signal x[n] is obtained by sampling the continuous-time signal x(t) =
cos(200πt) at sampling instants t = n/400, n = 0,1,.,7. The 8-point discrete Fourier transform (DFT) of x[n] is
πk n

defined as X [k ] = ∑ k = 0, 1, ⋯ , 7Which one of the following statements is TRUE?
7 −j
x [n]e ,
4
n=0

(A) All X[k] are non-zero

(B) Only X[4] is non-zero.

(C) Only X [2] and X[6] are non-zero.

(D) Only X[3] and X[5] are non-zero.

Q.No. 28 The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure

represent:

(A) P: Open Circuit, Q: Short Circuit, R: Matched Load

(B) P: Open Circuit, Q: Matched Load, R: Short Circuit

(C) P: Short Circuit, Q: Matched Load, R: Open Circuit

(D) P: Short Circuit, Q: Open Circuit, R: Matched Load

Q.No. 29 For the BJT in the amplifier shown below, VBE = 0.7 V, KT/q = 26 mV. Assume that BJT output
resistance (ro) is very high and the base current is negligible. The capacitors are also assumed to be short circuited
at signal frequencies. The input Vi is direct coupled. The low frequency voltage gain V0/vi; of the amplifier is

(A) - 89.42

(B) - 128.21

(C) - 178.85

(D) - 256.42

Q.No. 30 Which one of the following pole-zero plots corresponds to the transfer function of an LTI system
characterized by the input-output difference equation given below? y[n] = ∑ (−1) x [n − k ]
3 k
k =0

(A)

(B)

(C)

(D)

1 1 1 1
Q.No. 31 The value of the integrals ∫ (∫ and ∫ (∫ are
x −y x −y
3
dy)dx 3
dx )dy
0 0 (x +y) 0 0 (x +y)

(A) same and equal to 0.5

(B) same and equal to - 0.5

(C) 0.5 and - 0.5, respectively

(D) - 0.5 and 0.5, respectively

Q.No. 32 The Output y[n] of a discrete-time system for an input x[n] is y[n] = max −∞≤k ≤n |x [k ]| The unit
impulse response of the system is

(A) 0 for all n

(B) 1 for all n

(C) unit step signal u[n]

(D) unit impulse signal δ[n].

Q.No. 33 The figure below shows a multiplexer where S1 and S0 are the select lines, I0 and I3 are input data lines,

EN is the enable line, and F(P,Q,R) is the output F is

(A) PQ+Q̅R

(B) P+QR̅

(C) PQ̅R+P̅Q

(D) Q̅+PR

Q.No. 34 In the latch circuit shown. the NAND gates have non-zero. but unequal propagation delays. The present
input condition is: P = Q = '0'. If the input condition is changed simultaneously to P = Q = '1', the outputs X and Y

are

(A) X = ‘1’ , Y = ‘1’

(B) either X = ‘1’ , Y = ‘0’ , X = ‘0’, Y = ‘1’

(C) either X = ‘1’ , Y = ‘0’ , X = ‘0’, Y = ‘0’

(D) X = ‘0’ , Y = ‘0’

Answer: (B)

Q.No. 35 In binary frequency shift keying (FSK), the given signal wave-forms are
u 0 (t) = 5 cos(20000πt); 0 ≤ t ≤ T, and
where T is the bit-duration interval and t is in seconds. Both u₀(t) and
u 1 (t) = 5 cos(22000πt); 0 ≤ t ≤ T

u₁(t) are zero outside the interval 0 ≤ t ≤ T. With a matched filter (correlator) based receiver, the smallest
positive value of T (in milliseconds) required to have u₀(t) and u₁ (t) uncorrelated is

(A) 0.25 ms

(B) 0.5 ms

(C) 0.75 ms

(D) 1.0 ms

Answer: (B)

Q.No. 36 For the modulated signal x(t) = m(t) cos(2nfct), the message signal m(t) = 4 cos(1000πt) and the carrier
frequency fc is 1 MHz. The signal X(t) is passed through a demodulator, as shown in the figure below. The output

y(t) of the demodulator is

(A) cos(490πt)

(B) cos(920πt)

(C) cos(1000 πt)

(D) cos(540πt).

Answer: (B)

Q.No. 37 What is the electric flux ∫E→ ⋅ da
→ through a quarter-cylinder of height H (as shown in the figure) due to an

infinitely long line charge along the axis of the cylinder with a charge density of Q ?

(A) 𝐻𝑄/𝜀₀

(B) 𝐻𝑄/4𝜀₀

(C) 𝐻𝜀0/4Q

(D) 4H/Q𝜀₀

Answer: (B)

Q.No. 38 Consider a differentiable function 𝑓(𝑥) on the set of real numbers such that 𝑓(−1) = 0 and |𝑓′(𝑥)| ≤ 2. Given
these conditions, which one of the following inequalities is necessarily true for all 𝑥 ∈ [−2, 2]?

(A) 𝑓(𝑥) ≤ 1/2|𝑥 + 1|

(B) 𝑓(𝑥) ≤ 1/2|𝑥 + 1|

(C) 𝑓(𝑥) ≤ 1/2|𝑥|

(D) 𝑓(𝑥) ≤ 2|𝑥|

Answer: (B)
2 2

Q.No. 39 A curve passes through the point (x=1,y=0) and satisfies the differential equation The
dy x +y y
= +
dx 2y x

equation that describes the curve is \(
2
y
(A) ln(1 + x
2 ) = x − 1

2

(B) 1 y
ln(1 + 2
) = x − 1
2 x

(C) ln(1 +
y
) = x − 1
x

(D) 1 y
ln(1 + ) = x − 1
2 x

Q.No. 40 For an infinitesimally small dipole in free space, the electric field Eθ in the far field is proportional to (e-
jkr/r) sinθ, where k = 2π/λ. A vertical infinitesimally small electric dipole (δl << λ.) is placed at a distance h (h > 0)

above an infinite ideal conducting plane, as shown in the figure. The minimum value of h, for which one of the

maxima in the far field radiation pattern occurs at θ = 60°, is

(A) λ

(B) 0.5λ

(C) 0.25λ

(D) 0.75λ

Q.No. 41 A discrete-time all-pass system has two of its poles at 0.25∠0° and 2∠30° . Which one of the following
statements about the system is TRUE?

(A) It has two more poles at 0.5∠30° and 4∠0° .

(B) It is stable only when the impulse response is two-sided.

(C) It has constant phase response over all frequencies.

(D) It has constant phase response over the entire z-plane.

Answer: (B)

Q.No. 42 Let X(t) be a wide sense stationary random process with the power spectral density Sₓ(f) as shown in
Figure ( a), where f is in Hertz (Hz). The random process X(t) is input to an ideal Iowpass filter with the frequency
1
1, |f | ≤ Hz
response H (f ) = { 2

1
0, |f | > Hz
2

as shown in Figure ( b). The output of the Iowpass filter is Y(t). Select the correct option:

(A) only I is true

(B) only II and Ill are true

(C) only I and II are true

(D) only I and Ill are true

Q.No. 43 Let f (x ) = e for real x. From among the following. choose the Taylor series approximation of f (x)
2
x +x

around x = O, which includes all powers of x less than or equal io 3.

(A) 1 + x + x 2
+ x
3

(B) 1 + x + 3

2
x
2
+ x
3

(C) 1 + x + 3

2
x
2
+
7

6
x
3

(D) 1 + x + 3x 2
+ 7x
3

Q.No. 44 If the vector function F→ = ˆa (3y − k z ) + ˆ 1 y 2
a (k y + z ) is irrotational, then the value
a (k x − 2z ) − ˆ
x z 3

of the constants k1, k2 and k3 , respectively, are

(A) 0.3, -2.5, 0.5

(B) 0.0, 3.0, 2.0

(C) 0.3, 0.33. 0.5

(D) 4.0, 3.0,

Answer: (B)

Q.No. 45 Consider the recombination process via bulk traps in a forward biased pn homojunction diode. The
maximum recombination rate is Umax. If the electron and the hole capture cross-sections are equal, which one of
the following is FALSE? With all other parameters unchanged, Umax decreases if the intrinsic carrier density is
reduced. Umax occurs at the edges of the depletion region in the device. Umax depends exponentially on the
applied bias. With all other parameters unchanged, Umax increases if the thermal velocity of the carriers increases.

(A) With all other parameters unchanged, Umax decreases if the intrinsic carrier density is reduced

(B) Umax occurs at the edges of the depletion region in the device.

(C) Umax depends exponentially on the applied bias

(D) With all other parameters unchanged, Umax increases if the thermal velocity of the carriers increases.

Answer: (B)

Q.No. 46 In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?

(A) 0 and D

(B) Hi-Z and D

(C) 0 and 1

(D) Hi-Z and D̅

Answer: (B)

Q.No. 47 Consider the 5 x 5 matrix A =

Then the real eigenvalue of A is

(A) —2.5

(B) 0

(C) 15

(D) 25

i

(A) 0.25

(B) 0.5

(C) 1

(D) 2

Answer: (D)
o i i

⎢⎥
⎡

⎣
1

5

4

3

2
2

1

5

4

3
3

2

1

5

4
4

3

2

1

5
5

4

3

2

1
⎤

⎦
It is given that A has only one real eigenvalue.

Q.No. 48 Let c(t) = A cos(2πf t) and m (t) = cos(2πf t). It is given that f >> 5f The signal c(t)+m(t)
c c m c

is applied to the input of a non-linear device, whose output vₒ (t) is related to the input
m

v (t) as v (t) = av (t) + bv (t) Where a and b are positive constants. The output of the non-linear device is
2

passed through an ideal band-pass filter with center frequency f and bandwidth 3fₘ , to produce an amplitude

Q.No. 49 Consider the circuit shown in the figure.

(A) X̄ ȲZ̄ + X Y + ȲZ

(B) X̄ YZ̄ + X Z + ȲZ
c

modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power,
then a/b is

The Boolean expression F implemented by the circuit is

(C) X̄ YZ̄ + X Y + ȲZ

(D) X̄ ȲZ̄ + X Z + ȲZ

Answer: (B)

Q.No. 50 Let 𝐻(𝑧) be the z-transform of a real-valued discrete-time signal ℎ[𝑛]. If 𝑃(𝑧) = 𝐻(𝑧)𝐻 (1/2) has a zero at
𝑧 = ½ +½ 𝑗, and 𝑃(𝑧) has a total of four zeros, which one of the following plots represents all the zeros correctly?

(A)

(B)

(C)

(D)

Answer: (D)

Q.No. 51 The families of curves represented by the solution of the equation (dy/dx) = - (x/y)n for 𝑛 = −1 and 𝑛 =
+1, respectively, are

(A) Parabolas and Circles

(B) Circles and Hyperbolas

(C) Hyperbolas and Circles

(D) Hyperbolas and Parabolas

Q.No. 52 If v1,v2 ……...v6 are six vectors in R4, which one of the following statements is FALSE?

(A) It is not necessary that these vectors span R4

(B) These vectors are not linearly independent.

(C) Any four of these vectors form a basis for R4

(D) If {v1,v3,v5,v6} spans R4, then it forms a basis for R4.

Q.No. 53 The band diagram of a p-type semiconductor with a band-gap of 1 eV is shown. Using this
semiconductor, a MOS capacitor having Vth of -0.16 V, C’ax of 100 nF/cm2 and a metal work function of 3.87 eV
is fabricated. There is no charge within the oxide. If the voltage across the capacitor is Vth, the magnitude of

depletion charge per unit area (in C/cm2) is

(A) 1.70x10-8

(B) 0.52x10-8

(C) 1.41x10-8

(D) 0.93x10-8

Q.No. 54 The correct circuit representation of the structure shown in the figure is

(A)

(B)

(C)

(D)

Q.No. 55 The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining
the stability of feedback controllers. Identify which of the following statements is FALSE:

(A) Both the criteria provide information relative to the stable gain range of the system.

(B) The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase
systems.

(C) The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the
Nyquist criterion.

(D) The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

Answer: (D)