GATE 2020 Electronics and Communication Engineering Previous Year Paper

GATE 2020 Electronics and Communication Engineering Previous Year Paper

GENERAL APTITUDE

Section -A

Q.1 Time at quarter past three angle between hour hand and minute hand is

Ans. (7.5°)

Q.2 Radius of circle is ‘a’ and PQR is the maximum possible area of rectangle.

Find shaded area

(a) πa²– 2a²

(b) π 2a ²− a ²

(d) None of these

Ans. (a)

Q.3 Implicit : Explicit : : Express : __________?

(a) Compress

(b) Suppress

(d) Repress

Ans. (b)

Q.4 He was not only accused of theft _______ of conspiracy.

(a) Rather than

(b) Rather

(d) But even

Ans. (c)

Q.5 The untimely loss of life is a course of serious global concern as thousands of people get killed ________ accidents every year while many others die _____ disease like cardiovascular disease cancer etc.

(a) during, from

(b) in, of

(d) None of these

Ans. (b)

Q.6 The Canadian constitution requires equal importance to English and French. Last year air Canada lost a lawsuit and had to pay a six figure fine to French speaking couple after they filed a complaint about formal in-flight announcements in English lasting 15 seconds as compared to informal announcements in French lasting only for 5 seconds. The French speaking couples were upset at

(a) The English announcements being longer than French once

(b) The English announcements being clearer than French

(d) The in-flight announcement being made in English

Ans. (a)

Q.7 The global financial crisis in 2008 was considered to be the most serious worldwide FC. Which started with the subprime lending crisis (SPLC) in the USA in 2007? The SPLC led to a banking crisis in 2008 with the collapse of Lehman brothers in 2008. The SPL refers to the provision of loans to those borrowers. Who may have difficulties in repaying loans and its arises because of excess liquidity following the East Asian crisis. The correct precedence according to Paragraph is

(a) Banking crisis — Subprime lending crisis — Global financial crisis — East Asian crisis

(b) Subprime lending crisis — Global financial crisis — Banking crisis — East Asian crisis

(d) East Asian crisis — Subprime lending crisis — Banking crisis — Global financial crisis

Ans. (d)

Q.8 Following quadratic equation is ax²– bx + c = 0 and it has equal root which is β and a, b, c are the real number which is true

(a) β³= _{2 2}bC_a

(b) b ≠ 4ac

(d) β³= ₂ab

Ans. (a)

Section- B

Q.1 Given a binary number 1100 and p, q, r represents its sign magnitude, 1’s complement, 2’s complement representation respectively. Then 6 digit 2’s complement form of p + q + r is

Ans. (110101)

Given, binary number 1100

1’s complement of 1100 = –3 Sign magnitude of 1100 = –4 2’s complement of 1100 = –4 ∴ P + Q + R = –4 – 3 – 4 = –11 The 6 digit 2’s complement of (–11) = 110101

Q.2 Output of 4 × 1 MUX F(P, Q, R) is

Ans.

Output, F = PQR + PQR +

F = QR + PQ₀

Q.3 For 10 bit D/A converter, full range of voltage 0-10, then find the output value for V_input13A (in hexadecimal) in volts is ______V.

Ans. (3.066)

Given, n = 10

V_FS= 10 V Input voltage = (13A)₁₆= (314)₁₀Output voltage = Resolution × Decimal equivalent of input

V_o= ₂10 ₁₀× ₃₁₄= 3.066 V

Q.4 Given: y ( t ) = ∫ _−∞ W ( t ) ⋅ φ ( t )W(t) is the random variable having PSD 3W/Hz and .

Find the variance of y(t)?

Ans. (6)

Q.5 Given that m(t) = 4cos1000πt and c(t) = cos2πf_ct ; where f_c= 1 MHz. Given that s(t) = m(t) cos2πf_ct and s(t) is demodulated using a demodulator.

Then y(t) is

Ans.

cos [2 π ( f _c+ 40 ) t ] S(t) = m(t) cos 2πf_ct S(t) = 4 cos 1000πt cos 2π (10⁶)t Output of multiplier = [4 cos 1000πt cos 2π 10⁶t] cos 2π (f_ct + 40)t] = [2 [cos [2π (500 + 10⁶)t] + cos [2π (10⁶500)t] cos 2π(f_c+ 40)t = 2 cos 2π (500 + 10⁶)t cos 2π ((f_ct + 40)t) + 2 cos [2π (10⁶– 500)t) cos 2π (f_c+ 40)t = cos [2π (2f_c+540t) + cos(60t) + cos [2f_c– 460)t + cos(540t)] Output of Low pass filter

= cos [2π (460)]t = cos 920 πt

Q.6 Given phase modulated and frequency modulated signals

where, k_pis the phase deviation constant (rad/volt), k_fis the frequency deviation constant (rad/sec/volt). If the highest instantaneous frequencies of S_Pm(t) and S_Fm(t) are same, then the value of the ratio K_p/K_fis ________ sec.

Find Kp/K_f.

Ans. (2)

Q.7 A digital communication system is used to transmit a block of N-bits, if the probability of receiving 1-bit in error is α and all bits are transmitted independently. The received block is said to be erroneous if at least one bit in error. The probability of the block to be erroneous is ______.

(a) α^N

(b) 1 – (1 – α)^N

(d) 1 – α^N

Ans. (b)

Probability of error in decoding single bit = α Then probability of no error will be 1 – α. Total N-bits transmitted, so that probability of no error in received block

= (1 – α) (1 – α) … N times = (1 – α)^NThe probability of received block is erroneous = 1 – (1 – α)^N

Q.8 A binary random variable takes two values as +2 and –2 with probability P(X = 2) = α; then the value of α for which entropy will be maximum is ______.

Ans. (1/2)

Given that P(X = 2) = α Entropy will be maximum; provided probabilities are equal.

i.e. P(X = 2) = P ( X = − 2) = α =

₂¹α = ¹2

Q.9 Given that X(ω) is Fourier transform of x(t) then find

Ans.

Q.10 Given that

Then which one of the following is the correct pole zero plot of above given system?

Ans. (b)

Q.11 Discrete time signals output is y(n) = max[X(k)], –∞ ≤ K ≤ n

(a) unit impulse

(b) unit step function

(d) zero

Ans. (b)

Q.12 A finite duration discrete time signals x(n) is obtained by sampling x(t) = cos[200πt] of sample instant = n/400, n = 0, 1, 2, … 7. The 8-point DFT of x(n) is defined as

(a) X(3) and X(5) are non-zero

(b) X(4) is non-zero

(d) All X(k) are non-zero

Ans. (c)

Q.13 The transfer function of a stable discrete time LTI system is H( Z) ₌K(z − α) /( z + 0.5) when α and K are constants and |α| > 1. If the magnitude response is constant for all frequencies then the value of α is ____.

Ans. (–2)

Q.14 For the impedance Z = jX, having X values from –∞ to ∞, which of the following is correct in the Smith chart?

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

(b) A point at the centre of the Smith chart

(d) A line passing through the centre of the Smith chart

Ans. (a)

For given impedance Normalized impedance is Z⁼jX_Z0 Z = jX ⇒ Z=0 + jX Normalized resistance = 0 ⇒ r = 0 X = –∞ to ∞ r = 0 and X from –∞ to ∞ is a unit circle (radius 1) and centre (0, 0) on a complex reflection coefficient plane:

Q.15 Which one of the following is correct?

(a) ∇ ²0A = then ‘A’ is irrotational

(b) ∇ ( ∇ ·A ) = ∇× ( ( ∇× A ) −∇ ²A )

(d) ∇× A is also a vector quantity

Ans. (a)

Q.16 Given the magnetic field intensity of a uniform plane wave in vacuum is H ( x , y , z , t ) = ( aˆ_x+ 2 aˆ_y+ baˆ_z)cos( ω t + 3 x − y − z ) then find value of b _____.

Ans. (1)

Q.17 For a given two port ideal lossless transformer, the parameter S₂₁for a reference impedance of 1 Ω is

Ans. (0.8)

Q.18 For an infinitely small dipole in free space, the electric field ‘E’ in the far field is proportional to (e^{− jkr}/r sinθ). Where K = 2π/λ . A vertical infinite small dipole (δI << λ) is placed at a distance h(h > 0) above an infinite ideal condcutive plane as shown in figure. The minimum value of ‘h’, for which one of maximum in the far-field radiation pattern occurs at θ = 60° is _____.

(a) 0.5 λ

(b) λ

(d) 0.25 λ

Ans. (b)

Q.19 For a given transistor T₁, base region has uniform doping of 10¹⁷/cm³and transistor T₂has base region with doping varying linearly with x. If all other parameters of the transistor are the same, then find the ratio of common emitter current gain of transistor T₁to transistor T₂?

(a) 0.3 times that of T₂

(b) 0.7 times that of T₂

(d) 2.5 times that of T₂

Ans. (c)

Q.20 For a solar cell, P_in= 100 mW/cm², surface area = 1 cm², V_oc= 0.7V, fill factor = 0.8, efficiency = 15%. If thickness of the cell is 200 μm, then the light generation rate will be

Ans.

η = ( FF) V_OCI _SC / P_in

0.15 = 0.8 × 0.7 × I_SC /100 mW

⇒ I_SC= 15/ 0.56 mA

G_L= I_SC / q ×Area× thickness

= 15 × 10⁻³ / 0.56 × 1.6 × 10⁻¹⁹ × 1 × 200 × 10⁻⁴

= 0.837 × 10 ¹⁹/cm ³/second

Q.21 Given that a semiconductor has density of state function in conduction band N_Cis half of density of state function in valence band N_V, then the shift in the intrinsic fermi level from the centre of forbidden gap is ____ meV.

Ans. (9.01)

Q.22 In a MOS capacitor, threshold voltage is –0.16V, metal work function is 3.7V, bandgap of semiconductor is 1eV whose band diagram is shown below. C′_x= 100 pF/cm². Oxide is free from non-idealities. When the voltage across the capacitor is equal to threshold voltage, what will be the depletion charge present in the semiconductor?

Ans.

MOS capacitance

φ_m= 3.7, φ_s= 4.8, φ_ms= –1.1

V_T= φ_ms – Q_ox/C_ox – Q_d/C_ox+ 2 φ_Fp

φ_Fp= E_i– E_F= 0.5 – 0.2 = 0.3

–0.16 = -1.1-0 ₋Q′^d/C_ox + 2 × 0.3

Q′_d/C_ox= 0.6 + 0.16 – 1.1 = –0.34

Q_b= –0.34 × C_ox

= –0.34 × 100 × 10^–9

= -34 nC/cm²

Q.23 Consider the following MOSFET, find the equivalent Norton’s resistance

Ans.

v_π= –V_x

V_x= (I_x– g_mV_x) r_ds+ I_xR

V_x(1 + g_mr_ds) = (r_ds+ R)I_x

R_N= V_x/I_x = R +r_ds / 1+g_mr_ds

Q.24 A sinusoidal voltage is applied to the given circuit, then the steady state output voltage V_ois _______ V.

Ans. (650.4)

Voltage doubles, V_o=2 V_m= 2 × 230√2 ≅ 650.4V

Q.25 Consider the op-amp shown below:

The current “I₀” is ________ mA.

Ans. (6)

V_o= (1 + 1) × 2 = 4 V

2−4 /1 + I_o + 0− 4/1= 0

-2+I_o-4 =0

⇒ I_o= 6 mA

Q.26

The output V₀is

(a) square wave with an amplitude of 5V

(b) sinusoidal of amplitude 10V

(d) constant signal with either +5V and –5V

Ans. (a)

The given circuit is a Schmitt trigger, which produces a square wave at the output.

Q.27 Find the state matrix (consider v and i as state variables).

Ans.

From source transformation,

KVL in loop 1,

2I₁= 2 i + 0.5di/dt + v

di/dt= –2V + 4i + 4I₁ (i)

KCL at node,

i = 0.25 dv/dt +V − I₂/ 1

dv/dt = –4V + 4i + 4I₂(ii)

Q.28 When base current of given BJT is negligible. Given that V_t= 26 mV and V_BE= 0.7V.

Voltage gain at low frequencies is

Ans. (–89.423)

Q.29 In the given Nyquist contour the pole zero locations are indicated as shown. If the given contour is transformed from s-plane to G(s) H(s) plane then which one of the following is true

(a) encircles the origin in clockwise

(b) encircles the –1 + j0 in clockwise

(d) encircles the origin in anticlockwise

Ans. (b)

Q.30 Given op-amp circuit

R = 10 kΩ, C = 0.1 μF, then the 3dB cut-off frequency of op-amp circuit is ____ Hz.

Ans. (159.2)

Op-amp active filter (LPF) inverting type 3 dB cut-off frequency,

f_c= 1/2πRC

= 1 /2 π × 10⁴ × 10⁻⁷

= 1000 / 2π

= 159.2 Hz

Q.31 In the following circuit, assume that I_B= 0, V_BE= 0.7V for both the transistors. If V_in= 15V (unregulated) and V₀= 9V (regulated), then the resistance R is equal to _______ Ω.

Ans. (800)

Q.32 Consider the below figure.

G(s) = 1/( s + 1) ( s + α ) Find the value of α.

Ans. (4)

Q.33 Given: C(s) = K (s+1) / (s+3), G(s) = 1/ s(s +1) . If steady state error for ramp input is 0.1, then find the value of k or negative feedback unity gain system

Ans. (30)

Q.34 If the value of current i = 10 cos [5t− π /4 ] , the value of inductance L is

Ans. (2.828)

Q.35 For given open loop transfer function G(s)H(s)=k(s+11) / s(s+2) (s +8) . Find value of k for which system is marginally stable.

Ans. (160)

Q.36 A two port network has an impedance [Z] = find [Z_L] for maximum power transfer. Find Z_L= ?

Ans. (48)

Q.37 Find value of V_th

Ans. (3.6)

By applying source transformation

V_th= 3.6 V

Q.38 Find the value of I_o

Ans. (143.7)

Q.39 In a transmission line given Z₀= 50, Z_L= 400, l = 3λ/ 4, find Z_in

Ans. (6.25)

Z_infor (l = λ/4) = Z²₀ / ZL = 50²/400 = 25/4 = 6.25 Ω

Q.40 For the given characteristic equation

Q(s) = s³+ 3s²+ (K + 2)s + 3K = 0

The root locus plot will have breakaway or break-in point in the region.

(a) (0, –1)

(b) (–1, –3)

(d) None of these

Ans. (a)

Q(s) = 1 + G(s) H(s) = 0 s³+ 3s²+ 2s + ks + 3k = 0

–k = s³ + 3s² + 2s / s+3

− dk/ds = ( s + 3)(3s²+6s+2)− (s³+3s²+2s) / (s+ 3)² = 0

3s³+ 6s²+ 2s + 9s²+ 18s + 6 – s³– 3s²– 2s = 0

2s³+ 12s²+ 18s + 6 = 0

s = –0.46, –3.87, –1.65

Q.41 d²y /dx² − 6dy/dx + 9 = 0.Find the solution of differential equation.

(a) (C₁+ C₂x)e^3x

(b) (C₁+ C₂x)e^–3x

(d) None of these

Ans. (a)

Q.42 In sequential circuit, the maximum clock frequency at which given circuit can operate reliably?

Ans. (76.92)

Total propagation delay = (t_pd+ t_set-up)_max= 8ns = 5 ns = 13 ns

∴ Frequency of operations = 1000/13 MHz = 76.92 MHz

Q.43 f(x, y, z) = e^{(1 – x cosy)}+ x ze^{− 1/1+y2}partial differentiation of f(x, y, z) with respect to x

at point (1, 0, e) will be

Ans. (0)

Q.44 f(x₂+ x₂) ≥ f(x₁) + f(x₂)

(a) ¹x

(b) square root of x

(d) e ^–x

Ans. (c)

Q.45 ∫∫∫ xdxdydz

Ans. (9/4)

Q.46 If x is having uniform distribution between [– 2, 10] and y = 2x – 6 then P (y <7 / x >5 )

Ans. (0.3)

Q.47 dy / dx = ( y−1) x solution of equation satisfies.

(a) ln y − 1 = 0.5x²+ c and y = – 1

(b) ln y − 1 = 2x²+ c and y = 1

(d) ln y − 1 = 2x²+ c and y = –1

Ans. (a)

Q.48 Two sides of a fair coin are labelled as 0 and 1. The coin is tossed two times independently. Let M and N denote labels corresponding to the outcomes of those processes for random variable X, where X = min(M, N), E(X) = _______.

Ans. (0.25)

Q.49 In a digital communication system, 4 symbols are transmitted (s₁= –3, s₂= –1, s₃= 1, s₄= 2) through an AWGN channel. The variable at the input of decision device is s_i+ W, where W is a Gaussian random variable with mean zero and unit variance. ML decoding is used. The conditional error probability when symbol s_iis transmitted is P_i. The value of “i” that result in maximum P_iis _____.

Ans. (3)

Since the noise variable is Gaussian with zero mean and ML decoding is used, the decision boundary between two adjacent signal points will be their arithmetic mean. In the following graphs, the shaded area indicates the conditional probability of decoding a symbol correctly when it is transmitted.