# GATE – 2017 Electronics and Communication (part 1) Questions and Answers With Solutions

Question 1 :

Consider the 5×5 matrix

It is given that A has only one real eigenvalue. Then the real eigenvalue of A is

(A) -2.5                (B) 0               (C) 15                   (D) 25

Solution :

Question 2 :

The rank of matrix

(A) 0                  (B) 1                    (C) 2                    (D) 3

Solution :

Question 3 :

Consider the following statement about the linear dependence of the real valued functions

y= 1, y= x  and yx2, over the field of real numbers.

Which one among the following is correct ?

(A) Both I and II are true                           (B) Both I and III are true

(C) Both II and IV are true                         (D) Both III and IV are true

Solution :

Question 4 :

Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (upto third decimal place) ________ .

Solution :

Question 5 :

Consider the following statements for continuous-time linear time-invariant (LTI) systems .

I.  There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex                 plane.

II. There is no causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct ?

(A) Both I and II are true                           (B) Both I and II are not true

(C) Only I is true                                          (D) Only II is true

Solution :

Question 6 :

Consider a single input single output discrete-time system with x[n] as input and y[n] as output , where the two are related as

Which one of the following statement is true about the system ?

(A) It is causal and stable                     (B) It is causal but not stable

(C) It is not causal but stable              (D) It is neither causal nor stable

Solution :

Question 7 :

In the circuit shown, the positive angular frequency ω (in radians per second) at which the magnitude of the phase difference between the voltages V1  and  Vis Π/4 radians is  ______ .

Solution :

Question 8 :

A periodic signal x(t) has a trigonometric Fourier series expansion

If x(t) = -x(-t) = -x (t – Π/ω0) , we can conclude that

(A) an  are zero for alland bn  are zero for n even

(B) an  are zero for all n and bn  are zero for n odd

(C) an  are zero for  n even and bn  are zero for n odd

(D) an  are zero for  n odd and bn  are zero for n even

Solution :

Question 9 :

A bar of Gallium Asrenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal .

Which one of the following statement is true ?

(A) Silicon atoms act as p-type dopants in Arsenic sites and n-type dopants in Gallium sites

(B) Silicon atoms act as n-type dopants in Arsenic sites and p-type dopants in Gallium sites

(C) Silicon atoms act as p-type dopants in Arsenic as well as Gallium sites

(D) Silicon atoms act as n-type dopants in Arsenic as well as Gallium sites

Solution :

Question 10 :

An n+n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of

ND1 = 1× 1018 cm-3  and  ND2 = 1× 1015 cm-3 corresponding to the n+  and n regions respectively . At the operational temperature T , assume complete impurity ionization, kT/q =25 mV , and intrinsic carrier concentration to be n= 1× 1010 cm-3 . What is the magnitude of the built-in potential of this device ?

(A) 0.748 V                    (B) 0.460 V                        (C) 0.288 V                           (D) 0.173 V

Solution :

Question 11 :

For a narrow base PNP BJT , the excess minority carrier concentrations (ΔnE   for emitter , ΔpB  for base , Δnfor collector ) normalized to equilibrium minority carrier concentrations ( nE0 for  emitter , pB0 for base , nC0 for collector ) in the quasi-neutral emitter, base , 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

Solution :

Question 12 :

For the operational amplifier circuit shown, the output saturation voltages are ± 15 V . The upper and lower threshold voltages for the circuit are , respectively ,

(A) +5 V and -5 V              (B) +7 V and -3 V            (C) +3 V and -7 V            (D) +3 V and -3 V

Solution :

Question 13 :

A good transconductance amplifier should have

(A) High input resistance and low output resistance

(B) Low input resistance and high output resistance

(C) High input and output resistances

(D) Low input and output resistances

Solution :

Question 14 :

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

Solution :

Question 15 :

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 output X and Y are

(A)  X = ‘1’ , Y = ‘1’

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

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

(D) X = ‘0’ , Y = ‘0’

Solution :

Question 16 :

The clock frequency of an 8085 microprocessor is 5 MHz . If the time required to execute an instruction is 1.4 μs , then the number of T- states needed for executing the instruction is

(A) 1                         (B) 6                          (C) 7                         (D) 8

Solution :

Question 17 :

Consider the D-Latch shown in the figure , which is transparent when its clock input CK is high and has zero propagation delay . In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1 .The duty cycle at the output of the latch in percentage is _______ .

Solution :

Question 18 :

The open loop transfer function

where p is an integer , is connected in unity feedback configuration as shown in the figure .

Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is  ____ .

Solution :

Question 19 :

Consider a stable system with transfer function

where b1,……, bp  and a1,……, aare real valued constants. The slope of  the Bode log magnitude curve of G(s) converges to -60 dB/decade as ω →∞ . A possible pair of values for p and q is

(A) p = 0 and q = 3                           (B) p = 1 and q = 7

(C) p = 2 and q = 3                            (D) p = 3 and q = 5

Solution :

Question 20 :

Which of the following can be the pole-zero configuration of a phase-lag controller ( lag compensator ) ?

Solution :

Question 21 :

Let ( X,  X2 ) be independent random variables .  Xhas mean 0 and variance 1, while  Xhas mean 1 and variance 4 . The mutual information I ( X1  ; X2 ) between X  and  X2  in bits is _______ .

Solution :

Question 22 :

Which one of the following statements about differential pulse code modulation (DPCM) is true ?

(A) the sum of message signal sample with its prediction is quantized

(B) the message signal sample is directly quantized , and its prediction is not used

(C) the difference of message signal sample and a random signal is quantized

(D) The difference of message signal sample with its prediction is quantized

Solution :

Question 23 :

In a digital communication system , the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P( f ) . If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is the inter symbol interference zero ?

Solution :

Question 24 :

The voltage of an electromagnetic wave propagation in a coaxial cable with uniform characteristic impedance is  V(l) = eϒl+jωt Volts , where l is the distance along the length of the cable in meters, γ= ( 0.1+j40) m-1 is  the complex propagation constant  and ω = 2π×10rad/s is the angular frequency . The absolute value of the attenuation in the cable in dB/meter is _______ .

Solution :

Question 25 :

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 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

Solution :

Question 26 :

Let f(x)x+x²  for real x. From among the following , choose the Taylor series approximation of f(x)  around x =0 , which includes all powers of less than or equal to 3 .

(A) 1 + x + x² + x³                                         (B) 1+ x + 3x²/2 + x³

(C) 1+ x + 3x²/2 + 7x³/6                             (D)  1+ x + 3x² + 7x³

Solution :

Question 27 :

A three dimensional region R of finite volume is described by

x² +y² ≤ z³  ;  0 ≤ z ≤ 1,

where x, y, z are real . The volume of R  ( up to two decimal place) is ______ .

Solution :

Question 28 :

Let I = ∫( 2z dx +  2y dy + 2x dz ) where x,y,z  are real , and let be the straight line segment from point A:(0, 2, 1) to B: (4, 1, -1) . The value of I is _______ .

Solution :

Question 29 :

Which one of the following is the general solution of the first order differential equation

where x,y are real ?

(A) y = 1 + x + tan-1 (x+c) , where c is a constant

(B) y = 1 + x + tan (x+c) , where c is a constant

(C) y = 1 – x + tan-1 (x+c) , where c is a constant

(D) y = 1 – x + tan (x+c) , where c is a constant

Solution :

Question 30 :

Starting with x=1 , the solution of the equation x³+x=1 , after two iterations of Newton-Raphson’s method (up to two decimal places) is ________ .

Solution :

Question 31 :

Let x(t) be a continuous time periodic signal with fundamental period T = 1 second . Let { a} be the complex  Fourier series coefficients of x(t) , where k is integer valued . Consider the following statements about x(3t) :

I. The complex Fourier series coefficients of x(3t) are { a} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are { 3a} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6Π rad/s

For the three statements above , which one of the following is correct ?

(A) only II and III are true                             (B) only I and III are true

(C) only  III is true                                           (D) only  I is true

Solution :

Question 32 :

Two discrete-time signals x[n] and h[n] are both non-zero only for n=0, 1, 2 and are zero otherwise. It is given that x[0] = 1, x[1] = 2,  x[2] = 1,  h[0] = 1 .

Let y[n] be the linear convolution of  x[n] and h[n] . Given that y[1] = 3 and y[2] = 4, the value of the expression

( 10 y[3] + y[4] ) is ________ .

Solution :

Question 33 :

Let h[n] be the impulse response of a discrete-time linear time-invariant (LTI) filter . The impulse response is given by

h[0] = 1/3; h[1] = 1/3; and h[n] = 0 for n < 0 and n > 2.

Let H(ω) be the discrete-time Fourier transform (DTFT) of h[n] , where ω is the normalized angular frequency in radians. Given that H(ω0) = 0  and 0 < ω< π , the value of ω0( in radians ) is equal to _______ .

Solution :

Question 34 :

The figure shows an RLC circuit excited by the sinusoidal voltage 100 cos (3t) Volts , where t is in seconds. The ratio amplitude of V/ amplitude of V1  is _____.

Solution :

Question 35 :

In the circuit shown, the voltage VIN (t) is described by :

Where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is _____ .

Solution :

Question 36 :

The dependence of drift velocity of electrons on electric field in a semiconductor is shown below . The semiconductor has a uniform electron concentration of n = 1× 1016 cm-3  and electronic charge q = 1.6× 1019 C .  If a bias of 5V is applied across a 1 μm region of this semiconductor, the resulting current density in this region , in kA/cm2 , is _____ .

Solution :

Question 37 :

As shown, a uniformly doped Silicon (Si) bar of length L = 0.1 μm with a donor concentration N1016 cm-3 is illuminated at x=0 such that electron and hole pairs are generated at the rate of

Hole lifetime is 10-4 selectronic charge q = 1.6× 1019 C, hole diffusion coefficient Dp = 100 cm²/s and low level injection condition prevails . Assuming a linearly decaying steady state excess hole concentration that goes to 0 at x = L , the magnitude of the diffusion current density at x = L/2 , in A/cm², is ________ .

Solution :

Question 38 :

As shown, two silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentrations of  ND1 1014 cm-3 and ND2 1016 cm-3 in the n-regions of the diodes, and uniform acceptor doping NA1 1014 cm-3 and NA2 1016 cm-3 in the p-regions of the diodes respectively . Assuming that the reverse bias voltage is >> bulit-in potentials of the diodes, the ratio C/ C1  of their reverse bias capacitances for the same applied reverse bias is ________ .

Solution :

Question 39 :

In the figure shown, the npn transistor acts as a switch.

For the input Vin (t) as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to- emitter voltage at saturation VCE(Sat) =  0.2 V and base-to-emitter voltage VBE = 0.7 V. The minimum value  of the common-base current gain (α) of the transistor for the switching should be ______ .

Solution :

Question 40 :

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage Vtn = 1V and its transconductance parameter μnCox(W/L) = 1mV/V² . Neglect channel length modulation and body bias effects. Under these conditions, the drain current Iin mA is _______ .

Solution :

Question 41 :

For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector currents are equal . Given that V= 25mV, VBE = 0.7 V, and the BJT output resistance ris practically infinite .Under  these conditions , the midband voltage gain magnitude A= | vo v| V/V , is  ________ .

Solution :

Question 42 :

The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (Op-Amp), and has an open-loop voltage gain ,  A= 105  V/V and an open-loop cut-off frequency,  f= 8 Hz. The voltage gain of the amplifier at 15 kHz in V/V, is _________ .

Solution :

Question 43 :

Which one of the following gives the simplified sum of products expression for the Boolean function

F =m+ m+m+m5  , where m0,  m,  m3 and   m5  are minterms corresponding to the input A, B and C with A as the MSB and C as the LSB ?

Solution :

Question 44 :

A 4-bit shift register circuit configured for right-shift operation, i.e.  Din→ A, A → B, B → C, C → D, is shown. If the present state of the shift register is ABCD =1101, the number of clock cycles required to reach the state ABCD = 1111 is _______ .

Solution :

Question 45 :

The following FIVE instructions were executed on an 8085 microprocessor.

MVI A , 33H

MVI B, 78H

CMA

ANI 32H

The accumulator value immediately after the execution of the fifth instruction is

(A) 00H                          (B) 10H                             (C) 11H                             (D) 32H

Solution :

Question 46 :

A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below .The four possible states of the FSM are QAQB = 00, 01, 10, 11.

Assume that XIN is held at a constant  logic level throughout the operation of the FSM . When the FSM is initialized to the state QAQ= 00 and clocked, after a few clock cycles, it starts cycling through

(A) all of the four possible states if  XIN = 1

(B) three of the four possible states if XIN = 0

(C) only two of the four possible states if  XIN = 1

(D) only two of the four possible states if  XIN = 0

Solution :

Question 47 :

A linear time invariant (LTI) system with transfer function

is connected in unity feedback configuration as shown in the figure .

For the closed loop system shown, the root locus for 0 < K <  ∞ intersects the imaginary axis for K = 1.5 . The closed loop system is stable for

(A) K > 1.5                                                (B) 1 <  K  < 1.5

(C) 0 < K < 1                                            (D) no positive value of K

Solution :

Question 48 :

Which one of the following options correctly describes the location of the roots of the equation s+ s² + 1 = 0 on the complex plane ?

(A) Four left half plane (LHP) roots

(B) One right half plane (RHP) root , one LHP root and two roots on the imaginary axis

(C) Two RHP roots and two LHP roots

(D) All four roots are on the imaginary axis

Solution :

Question 49 :

The Nyquist Plot of the transfer function

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

Solution :

Question 50 :

In binary frequency shift keying (FSK), the given signal wave forms are

u0(t) = 5 cos (20000πt) ; 0 ≤ t ≤ T , and

u1(t) = 5 cos (22000πt) ; 0 ≤ t ≤ T,

where T is the bit-duration interval and t is in seconds. Both u0(t) and 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

Solution :

Question 51 :

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 lowpass filter  with the frequency response

as shown in figure (b) . The output of the lowpass filter is Y(t) .

Let E be the expectation operator and consider the following statements:

I. E( X (t) ) = E ( Y (t) )

II. E( X² (t) ) = E( Y² (t) )

III. E( Y² (t) ) = 2

Select the correct option :

(A) only I is true                                 (B) Only II and III are true

(C) Only I and II are true                 (D) Only I and III are true

Solution :

Question 52 :

A continuous time signal x(t)  = 4 cos (200πt) + 8 cos ( 400πt), where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response

Let y(t) be the output of this filter . The maximum value of |y(t)| is ________ .

Solution :

Question 53 :

An optical fiber is kept along the zˆ direction . The reflective indices for the electric field along xˆ and yˆ directions in the fiber are nx  = 1.5000 and  ny  = 1.5001, respectively (nx  ≠ ndue to the  imperfection in the fiber cross-section ). The free space wavelength of a light wave propagation in the fiber is 1.5 μm .If the light wave is circularly polarized at the input of the fiber , the minimum propagation distance after which it becomes linearly polarized , in centimeter is ________ .

Solution :

Question 54 :

The expression for an electric field in free space is

where x, y, z  represent the spatial coordinates, t represents time, ω and k are constants . This electric field

(A) does not represent a plane wave

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

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

(D) represents a linearly polarized plane wave

Solution :

Question 55 :

A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x-axis . Determine the direction of null in the radiation pattern 0 ≤ Φ ≤ π . Here the angle θ (0 ≤ θ ≤ π ) is measured from the z-axis, and the angle Φ ( 0 ≤ Φ ≤ 2π ) is measured from the x-axis in the x-y plane .

(A)  θ = 90° , Φ  = 45°                            (B)  θ = 45° , Φ  = 90°

(C)  θ = 90° , Φ  = 135°                          (D)  θ = 45° , Φ  = 135°

Solution :

Question 56 :

She has a sharp tongue and it can occasionally turn ________ .

(A) hurtful                        (B) left                    (C) methodical                   (D) vital

Question 57 :

(A) could have, been                          (B) would have, being

Question 58 :

In the summer, water consumption is known to decrease overall by 25% . A water board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.

Which of the following statement is correct ?

(A) The ratio of  household to other consumption is 8/17

(B) The ratio of  household to other consumption is 1/17

(C) The ratio of  household to other consumption is 17/8

(D) There are errors in the official statements

Solution :

Question 59 :

40% of death on city roads may be attributed to drunken driving . The number of degrees needed to represent this as a slice of a pie chart is

(A) 120                          (B) 144                           (C) 160                          (D) 212

Solution :

Question 60 :

Some tables are shelves. Some shelves are chairs. All chairs are benches . Which of the following conclusions can be deduced from the preceding sentences ?

i.     At least  one bench is a table

ii.    At least  one shelf is a bench

iii.    At least  one chair is a table

iv.    All benches are chairs

(A)   Only i                     (B) Only ii                (C) Only ii and iii                   (D) Only iv

Solution :

Question 61 :

” If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective sections, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters”.

Here, the word ‘antagonistic’ is closest in meaning to

(A) impartial                     (B) argumentative                      (C) separated                     (D) hostile

Question 62 :

S, T, U, V, W, X, Y, and Z are seated around a circular table. T’s neighbors are  Y and V . Z is seated third to the left of T and second to the right of S. U’s neighbors are S and Y ; and T and W are not seated opposite to each other. Who is third to the left of V ?

(A) X                   (B) W                  (C)  U                        (D) T

Question 63 :

Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars travel at a speed of 36 Km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour ?

(A) 1440                    (B) 1200                   (C) 720                       (D) 600

Solution :

Question 64 :

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian ?

(A) 56                     (B) 52                          (C) 48                            (D) 44

Solution :

Question 65 :

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals in this plot .

The path from P to Q is best described by

(A) Up-Down-Up-Down                                   (B) Down-Up-Down-Up

(C) Down-Up-Down                                          (D) Up-Down-Up