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GATE 2019 : Electronics and Communication Engineering (with Final Answer Keys)

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GATE 2019 General Aptitude (GA) Set-1 Q. 1 Q. 5 carry one mark each. Q.1 The strategies that the company ________ to sell its products ________ house-to-house marketing. (A) use, includes (C) used, includes Q.2 The boat arrived ________ dawn. (A) in Q.3 (D) under (B) 3/4 (C) 4/3 (D) 7/3 (B) 6 (C) 12 (D) 120 When he did not come home, she _________ him lying dead on the roadside somewhere. (A) concluded (C) notice GA (C) on Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is ___. (A) 2 Q.5 (B) at It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is ______ hours. (A) 2/3 Q.4 (B) uses, include (D) uses, including (B) looked (D) pictured 1/5 GATE 2019 General Aptitude (GA) Set-1 Q. 6 Q. 10 carry two marks each. Q.6 Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is an engineer, one is a doctor, one a teacher and another a dancer. You are told that: 1. 2. 3. 4. 5. Mathew is not standing next to Seema There are two people standing between Lohit and the engineer Rahul is not a doctor The teacher and the dancer are standing next to each other Seema is turning to her right to speak to the doctor standing next to her Who among them is an engineer? (A) Seema (C) Rahul GA (B) Lohit (D) Mathew 2/5 GATE 2019 General Aptitude (GA) Set-1 Q.7 The bar graph in Panel (a) shows the proportion of male and female illiterates in 2001 and 2011. The proportions of males and females in 2001 and 2011 are given in Panel (b) and (c), respectively. The total population did not change during this period. The percentage increase in the total number of literates from 2001 to 2011 is ____. Proportion of illiterates (%) 100 80 60 60 50 40 40 40 20 0 Female Male 2001 2011 Panel (a) 2011 2001 Female 40% Male 60% Panel (b) (A) 30.43 GA Male 50% Female 50% Panel (c) (B) 33.43 (C) 34.43 (D) 35.43 3/5 GATE 2019 General Aptitude (GA) Set-1 Q.8 Indian history was written by British historians extremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subservient to the glory of the Union Jack. Latter-day Indian scholars presented a contrary picture. From the text above, we can infer that: Indian history written by British historians ____________ (A) was well documented and not researched but was always biased (B) was not well documented and researched and was always biased (C) was well documented and researched but was sometimes biased (D) was not well documented and researched and was sometimes biased Q.9 Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants is USD 200 per hour and breaks are not paid. After paying the consultants, the client shall have USD ______ remaining in the budget. (A) 000.00 GA (B) 166.67 (C) 300.00 (D) 433.33 4/5 GATE 2019 General Aptitude (GA) Set-1 Q.10 Five people P, Q, R, S and T work in a bank. P and Q don t like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, who is currently sharing an office with T wants to move to the adjacent office with S, the handsome new intern. Given the floor plan, what is the current location of Q, R and T? (O = Office, WR = Washroom) (A) WR (C) O1 P, Q O2 Manager T O3 R O4 S WR O1 P, Q Teller 1 Teller 2 Manager Entry O4 S Teller 1 Teller 2 O3 R O4 S Teller 1 Teller 2 Garden (B) (D) O1 P, Q O2 Manager O3 T O4 R, S WR O1 P Teller 1 Teller 2 Manager Entry Garden O3 R, T Entry Garden WR O2 O2 Q Entry Garden END OF THE QUESTION PAPER GA 5/5 GATE 2019 EC-1 Q. 1 Q. 25 carry ONE mark each. Q.1 Which one of the following functions is analytic over the entire complex plane? (A) ln Q.2 (B) = and = + , respectively, are (A) Parabolas and Circles (C) Hyperbolas and Circles EC-1 (C) (D) cos The families of curves represented by the solution of the equation for Q.3 / = ( ) (B) Circles and Hyperbolas (D) Hyperbolas and Parabolas Let be the z-transform of a real-valued discrete-time signal [ ]. If = has a zero at = + , and has a total of four zeros, which one of the following plots represents all the zeros correctly? (A) (B) (C) (D) 1/27 GATE 2019 Q.4 EC-1 Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure). Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1? (A) 0.5 A Q.5 Let that is, (A) (C) EC-1 (B) 1 A (C) 2 A (D) 2.5 A be the unit-step response of a causal system having a transfer function = + + = . The forced response of the system is + (B) (D) + 2/27 GATE 2019 Q.6 EC-1 For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles and the number of system zeros in the frequency range Hz Hz is (A) Q.7 = , (B) = , = (C) = , = (D) = , = 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 EC-1 = (B) 1100001 (C) 1111000 (D) 1111111 3/27 GATE 2019 Q.8 EC-1 EC-1 Which one of the following options describes correctly the equilibrium band diagram at T=300 K of a Silicon pnn+p++ configuration shown in the figure? (A) (B) (C) (D) 4/27 GATE 2019 Q.9 EC-1 EC-1 The correct circuit representation of the structure shown in the figure is (A) (B) (C) (D) 5/27 GATE 2019 EC-1 Q.10 The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with ms = 0 V and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points (A) (B) (C) (D) P, Q, R Q, R, P R, P, Q Q, P, R Q.11 What is the electric flux ( ) 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) (C) EC-1 0 0 (B) (D) 0 0 6/27 GATE 2019 EC-1 Q.12 In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell s equations (in their standard form). Match the left-hand side with the corresponding right-hand side. List I 1 2 3 4 List II (A) 1 - P, 2 - R, 3 - Q, 4 - S (C) 1 - Q, 2 - S, 3 - P, 4 - R P Q R S 0 + (B) 1 - Q, 2 - R, 3 - P, 4 - S (D) 1 - R, 2 - Q, 3 - S, 4 - P Q.13 A standard CMOS inverter is designed with equal rise and fall times ( = ). If the width of the pMOS transistor in the inverter is increased, what would be the effect on the LOW noise margin ( ) and the HIGH noise margin ? (A) increases and decreases. (B) decreases and increases. (C) Both and increase. (D) No change in the noise margins. Q.14 In the circuit shown, what are the values of F for EN = and EN = , respectively? (A) (B) (C) (D) EC-1 0 and D Hi-Z and D 0 and 1 Hi-Z and D 7/27 GATE 2019 EC-1 Q.15 In the circuit shown, A and B are the inputs and F is the output. What is the functionality of the circuit? (A) (B) (C) (D) Latch XNOR SRAM Cell XOR Q.16 The value of the contour integral + evaluated over the unit circle | | = is _______. Q.17 The number of distinct eigenvalues of the matrix is equal to ______. EC-1 = [ ] 8/27 GATE 2019 EC-1 Q.18 If and are random variables such that [ [ ] + [ ] = ________. Q.19 The value of the integral i + ]= and [ + ]= , then , is equal to _______. Q.20 Let be an exponential random variable with mean 1. That is, the cumulative distribution function of is given by if ={ if < Then Pr > | > , rounded off to two decimal places, is equal to _______. Q.21 Consider the signal = + cos + sin + cos + , where is in seconds. Its fundamental time period, in seconds, is ______________. Q.22 The baseband signal shown in the figure is phase-modulated to generate the PM signal = cos + . The time on the x-axis in the figure is in milliseconds. If the carrier frequency is = kHz and = , then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is __________ (rounded off to 2 decimal places). EC-1 9/27 GATE 2019 EC-1 Q.23 Radiation resistance of a small dipole current element of length l at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation resistance, rounded off to two decimal places, is ____________ %. Q.24 In the circuit shown, is a square wave of period with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and = = . The average value of is ____ volts (rounded off to 1 decimal place). Q.25 In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is The frequency of the signal at Q is ____ kHz. EC-1 kHz. 10/27 GATE 2019 EC-1 Q. 26 Q. 55 carry TWO marks each. Q.26 Consider a differentiable function on the set of real numbers such that = and | | . Given these conditions, which one of the following inequalities is [ , ] ? necessarily true for all | + | (A) | | (C) | + | (B) | | (D) Q.27 Consider the line integral the integral being taken in a counterclockwise direction over the closed curve that forms the boundary of the region shown in the figure below. The region is the area enclosed by the union of a rectangle and a semi-circle of radius . The line integral evaluates to (A) EC-1 + / (B) + (C) + (D) + 11/27 GATE 2019 EC-1 Q.28 Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to [ ] is shown in the figure. Let . In the figure, what should be the values of the coefficients , , = exp terms of so that [ ] is obtained correctly? = , = , = = , = , = (A) (C) (B) (D) in = , = , = = , = , = Q.29 It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form where and and [ ]= )+ exp ( exp ( ), are arbitrary real numbers. The desired three-tap filter is given by [ ] = , [ ] = , [ ] = [ ] = for < or > . What are the values of the filter taps and if the output is [ ] = is as given above? (A) EC-1 = , = (B) = , = (C) = , = (D) for all , when [ ] = , = 12/27 GATE 2019 EC-1 Q.30 In the circuit shown, if = sin volts, steady-state current , in milliamperes (mA), is (A) sin (C) sin + cos + cos (B) sin (D) sin = k and = F, then the + cos + cos Q.31 Consider a causal second-order system with the transfer function = + + be the corresponding output. The time with a unit-step = as an input. Let taken by the system output to reach 94% of its steady-state value lim , rounded off to two decimal places, is (A) 5.25 (B) 4.50 (C) 3.89 (D) 2.81 Q.32 The block diagram of a system is illustrated in the figure shown, where and is the output. The transfer function = is (A) (B) (C) (D) EC-1 = = = = + + + is the input + + + + + + + + + + 13/27 GATE 2019 EC-1 Q.33 Let the state-space representation of an LTI system be = + , = + where , , are matrices, is a scalar, is the input to the ] and = . Which one of the following system, and is its output. Let = [ options for and will ensure that the transfer function of this LTI system is (A) (B) (C) (D) = [ = [ = [ = [ = + ] and = [ ] ] and = [ ] ] and = [ ] ] and = [ ] + + ? Q.34 A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density / . Binary signaling, with 0 and , is used for the transmission, along with an optimal receiver that minimizes the bit-error probability. form an orthonormal signal set. , Let , we would obtain a certain bit-error and = If we choose = probability . , for what value of would we , but take = If we keep = obtain the same bit-error probability ? (A) 0 (B) 1 (C) 2 (D) 3 Q.35 The quantum efficiency ( ) and responsivity (R) at a wavelength (in m) in a p-i-n photodetector are related by (A) EC-1 = . (B) = . (C) = . (D) = . 14/27 GATE 2019 EC-1 Q.36 Two identical copper wires W1 and W2, placed in parallel as shown in the figure, carry currents I and 2I, respectively, in opposite directions. If the two wires are separated by a between the wires at a distance r distance of 4r, then the magnitude of the magnetic field B from W1 is (A) (C) 0 (B) 0 (D) 0 0 Q.37 The dispersion equation of a waveguide, which relates the wavenumber k to the frequency , is = / where the speed of light = m/s, and o is a constant. If the group velocity is m/s, then the phase velocity is (A) . m/s (B) m/s (C) m/s (D) . m/s Q.38 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 and are 200 and 1 k , respectively. What is the range of Vi that will maintain the Zener diode in the on state? (A) (B) (C) (D) EC-1 22 V to 34 V 24 V to 36 V 18 V to 24 V 20 V to 28 V 15/27 GATE 2019 EC-1 Q.39 The state transition diagram for the circuit shown is (A) (B) (C) (D) EC-1 16/27 GATE 2019 EC-1 Q.40 In the circuits shown, the threshold voltage of each nMOS transistor is 0.6 V. Ignoring the effect of channel length modulation and body bias, the values of Vout and Vout , respectively, in volts, are (A) 1.8 and 1.2 (B) 2.4 and 2.4 (C) 1.8 and 2.4 Q.41 The RC circuit shown below has a variable resistance expression: = ( ) for given by the following < where = , and = F. We are also given that = = V. If the current at time = is A, then the current = / is ___________ (rounded off to 2 decimal places). EC-1 (D) 2.4 and 1.2 and the source voltage is , in amperes, at time 17/27 GATE 2019 EC-1 Q.42 Consider a unity feedback system, as in the figure shown, with an integral compensator and open-loop transfer function = + + where > . The positive value of for which there are exactly two poles of the unity feedback system on the axis is equal to ______ (rounded off to two decimal places). Q.43 Consider the homogeneous ordinary differential equation with + = , > as a general solution. Given that = and = the value of . , rounded off to two decimal places, is ______. Q.44 Let [ ] be a length-7 discrete-time finite impulse response filter, given by [ ] = , [ ] = , [ ] = , [ ] = , [ ] = , [ ] = , [ ] = , and [ ] is zero for | | . A length-3 finite impulse response approximation [ ] of [ ] has to be obtained such that , = | ( ) ( )| is minimized, where ( ) and ( ) are the discrete-time Fourier transforms of [ ] [ ] + [ ], and [ ], respectively. For the filter that minimizes , , the value of rounded off to 2 decimal places, is ________ . EC-1 18/27 GATE 2019 EC-1 Q.45 Let a random process be described as = + , where is a = W/Hz. The filter has a white noise process with power spectral density | = . for magnitude response given by | , and zero elsewhere. is a stationary random process, uncorrelated with , with power spectral density as shown in the figure. The power in , in watts, is equal to ________ W (rounded off to two decimal places). 1 -5 (W/Hz) 5 (Hz) Q.46 A voice signal is in the frequency range 5 kHz to 15 kHz. The signal is amplitudemodulated to generate an AM signal = + cos , where = kHz. The AM signal is to be digitized and archived. This is done by first sampling at 1.2 times the Nyquist frequency, and then quantizing each sample using a 256-level quantizer. Finally, each quantized sample is binary coded using bits, where is the minimum number of bits required for the encoding. The rate, in Megabits per second (rounded off to 2 decimal places), of the resulting stream of coded bits is _______ Mbps. Q.47 A random variable takes values and + with probabilities . and 0.8, respectively. It is transmitted across a channel which adds noise , so that the random variable at the channel output is = + . The noise is independent of , and is uniformly distributed over the interval [ , ]. The receiver makes a decision = { , if + , if > where the threshold [ , ] is chosen so as to minimize the probability of error Pr[ ]. The minimum probability of error, rounded off to 1 decimal place, is ___________. EC-1 19/27 GATE 2019 EC-1 Q.48 A Germanium sample of dimensions 1 cm 1 cm is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dioxideGermanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at 600 nm is cm-1 and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is ______ m. Q.49 In an ideal pn junction with an ideality factor of 1 at T=300 K, the magnitude of the reverse-bias voltage required to reach 75% of its reverse saturation current, rounded off to 2 decimal places, is ____mV. [ = . JK , = . J-s, = . C] Q.50 Consider a long-channel MOSFET with a channel length 1 m and width 10 m. The device parameters are acceptor concentration NA= cm-3, electron mobility n=800 cm2/V-s, oxide capacitance/area Cox= . F/cm2, threshold voltage VT=0.7 V. The drain saturation current (IDsat) for a gate voltage of 5 V is _____mA (rounded off to two decimal places). [ = . F/cm, = . ] Q.51 A rectangular waveguide of width w and height h has cut-off frequencies for TE and TE modes in the ratio 1: 2. The aspect ratio w/h, rounded off to two decimal places, is _____________________. EC-1 20/27 GATE 2019 EC-1 Q.52 In the circuit shown, V is a 10 V square wave of period, T = 4 ms with R = 500 and C = 10 F. The capacitor is initially uncharged at t=0, and the diode is assumed to be ideal. The voltage across the capacitor (V ) at 3 ms is equal to ____ volts (rounded off to one decimal place). Q.53 A CMOS inverter, designed to have a mid-point voltage VI equal to half of V , as shown in the figure, has the following parameters: V = V x= A/V ; x = A/V ; | The ratio of to = . V for nMOS | = . V for pMOS is equal to ____ (rounded off to 3 decimal places). Vdd Vdd EC-1 21/27 GATE 2019 EC-1 Q.54 In the circuit shown, the threshold voltages of the pMOS (| |) and nMOS ( ) transistors are both equal to 1 V. All the transistors have the same output resistance of 6 M . The other parameters are listed below: = x = / ; x = / ; MOS MOS = and are the carrier mobilities, and x is the oxide capacitance per unit area. Ignoring the effect of channel length modulation and body bias, the gain of the circuit is ____ (rounded off to 1 decimal place). EC-1 22/27 GATE 2019 EC-1 Q.55 In the circuit shown, V = and V = V . The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of I is _____mA (rounded off to 1 decimal place). EC-1 23/27 Q.No. Type Section Key/Range Marks 1 MCQ GA B 1 2 MCQ GA B 1 3 MCQ GA C 1 4 MCQ GA B 1 5 MCQ GA D 1 6 MCQ GA D 2 7 MCQ GA A 2 8 MCQ GA C 2 9 MCQ GA B 2 10 MCQ GA C 2 1 MCQ EC D 1 2 MCQ EC C 1 3 MCQ EC D 1 4 MCQ EC B 1 5 MCQ EC D 1 6 MCQ EC B 1 7 MCQ EC B 1 8 MCQ EC A 1 9 MCQ EC A 1 10 MCQ EC B 1 11 MCQ EC B 1 12 MCQ EC B 1 13 MCQ EC A 1 1/3 Q.No. Type Section Key/Range Marks 14 MCQ EC B 1 15 MCQ EC B 1 16 NAT EC 0.0001 to 0.0001 1 17 NAT EC 3 to 3 1 18 NAT EC 11 to 11 1 19 NAT EC 1.99 to 2.01 1 20 NAT EC 0.36 to 0.38 1 21 NAT EC 11.99 to 12.01 1 22 NAT EC 0.74 to 0.76 1 23 NAT EC 1.98 to 2.02 1 24 NAT EC 3.1 to 2.9 1 25 NAT EC 4 to 4 1 26 MCQ EC B 2 27 MCQ EC C 2 28 MCQ EC C 2 29 MCQ EC D 2 30 MCQ EC C 2 31 MCQ EC B 2 32 MCQ EC B 2 33 MCQ EC A 2 34 MCQ EC D 2 35 MCQ EC A 2 36 MCQ EC C 2 2/3 Q.No. Type Section Key/Range Marks 37 MCQ EC D 2 38 MCQ EC B 2 39 MCQ EC C 2 40 MCQ EC C 2 41 NAT EC 0.23 to 0.27 2 42 NAT EC 5.99 to 6.01 2 43 NAT EC 5.24 to 5.26 2 44 NAT EC 27.01 to 26.99 2 45 NAT EC 17.40 to 17.60 2 46 NAT EC 11.80 to 11.82 2 47 NAT EC 0.1 to 0.1 2 48 NAT EC 0.230 to 0.232 2 49 NAT EC 34.00 to 38.00 2 50 NAT EC 25.40 to 25.60 2 51 NAT EC 1.71 to 1.75 2 52 NAT EC 3.2 to 3.4 2 53 NAT EC 0.210 to 0.230 2 54 NAT EC 905.0 to 895.0 OR 895.0 to 905.0 2 55 NAT EC 5.9 to 6.1 2 3/3

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