GATE 2019 EC – Previous Year Questions with Solutions
All 65 questions of GATE 2019 EC with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – The strategies that the company to sell its products house-to-house marketing.
- Question 2 – The boat arrived dawn.
- Question 3 – 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…
- Question 4 – 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…
- Question 5 – When he did not come home, she him lying dead on the roadside somewhere.
- Question 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…
- Question 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…
- Question 8 – "Indian history was written by British historians – extremely well documented and researched, but not always impartial. History had to serve its…
- Question 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…
- Question 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…
- Question 11 – Which one of the following functions is analytic over the entire complex plane?
- Question 12 – The families of curves represented by the solution of the equation dydx=-( xy)n for n=-1 and n=+1, respectively, are
- Question 13 – Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P(z)=H(z)H(1z) has a zero at z=12+12j, and P(z) has a total of four zeros,…
- Question 14 – 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…
- Question 15 – Let Y(s) be the unit-step response of a causal system having a transfer function G(s)=3-s(s+1)(s+3) that is, Y(s)=G(s)s. The forced response of the…
- Question 16 – For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles N p and the number of system zeros N z…
- Question 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…
- Question 18 – 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?
- Question 19 – The correct circuit representation of the structure shown in the figure is
- Question 20 – 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…
- Question 21 – What is the electric flux ( E d a) through a quarter-cylinder of height H (as shown in the figure) due to an infinitely long line charge along the…
- Question 22 – 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…
- Question 23 – A standard CMOS inverter is designed with equal rise and fall times ( n= p). If the width of the pMOS transistor in the inverter is increased, what…
- Question 24 – In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?
- Question 25 – In the circuit shown, A and B are the inputs and F is the output. What is the functionality of the circuit?
- Question 26 – The value of the contour integral 12 j(z+1z)2dz evaluated over the unit circle z =1 is .
- Question 27 – The number of distinct eigenvalues of the matrix A=bmatrix2&2&3&3\\0&1&1&1\\0&0&3&3\\0&0&0&2bmatrix is equal to .
- Question 28 – If X and Y are random variables such that E[2X+Y]=0 and E[X+2Y]=33, then E[X]+E[Y]= .
- Question 29 – The value of the integral 0 y xx\,dx\,dy is equal to .
- Question 30 – Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by F Z(x)=cases1-e-x&if x0\\0&if…
- Question 31 – Consider the signal f(t)=1+2( t)+3(23t)+4(2t+4), where t is in seconds. Its fundamental time period, in seconds, is .
- Question 32 – The baseband signal m(t) shown in the figure is phase-modulated to generate the PM signal (t)=(2 f ct+k\,m(t)). The time t on the x-axis in the figure…
- Question 33 – The 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…
- Question 34 – In the circuit shown, V s is a square wave of period T with maximum and minimum values of 8 V and -10 V, respectively. R 1=R 2=50\ . The average value…
- Question 35 – In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz. The frequency of the signal at Q 2 is kHz.
- Question 36 – 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…
- Question 37 – Consider the line integral C(x\,dy-y\,dx), the integral being taken in a counterclockwise direction over the closed curve C that forms the boundary of…
- Question 38 – Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[1] is shown in the…
- Question 39 – It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form x[n]=c 1(-j n2)+c 2(j n2), where c 1 and…
- Question 40 – In the circuit shown, if v(t)=2(1000t) volts, R=1\ k and C=1\ F, then the steady-state current i(t), in milliamperes (mA), is
- Question 41 – Consider a causal second-order system with the transfer function G(s)=11+2s+s2 with a unit-step R(s)=1s as an input. Let C(s) be the corresponding…
- Question 42 – The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function H(s)=Y(s)X(s)…
- Question 43 – Let the state-space representation of an LTI system be x(t)=Ax(t)+Bu(t), y(t)=Cx(t)+du(t) where A,B,C are matrices, d is a scalar, u(t) is the input…
- Question 44 – 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 N 0/2.…
- Question 45 – The quantum efficiency () and responsivity (R) at a wavelength (in m) in a p-i-n photodetector are related by
- Question 46 – 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…
- Question 47 – The dispersion equation of a waveguide, which relates the wavenumber k to the frequency , is k()=(1/c)2- 02 where the speed of light c=3108 m/s, and 0…
- Question 48 – 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 R 1 and R L are…
- Question 49 – The state transition diagram for the circuit shown is
- Question 50 – 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…
- Question 51 – The RC circuit shown below has a variable resistance R(t) given by the following expression: R(t)=R 0(1- tT)for 0 t<T where R 0=1\ , and C=1 F. We are…
- Question 52 – Consider a unity feedback system, as in the figure shown, with an integral compensator Ks and open-loop transfer function G(s)=1s2+3s+2 where K>0. The…
- Question 53 – Consider the homogeneous ordinary differential equation x2d2ydx2-3xdydx+3y=0, x>0 with y(x) as a general solution. Given that y(1)=1 and y(2)=14, the…
- Question 54 – Let h[n] be a length-7 discrete-time finite impulse response filter, given by h[0]=4,\ h[1]=3,\ h[2]=2,\ h[3]=1,\ h[-1]=-3,\ h[-2]=-2,\ h[-3]=-1, and…
- Question 55 – Let a random process Y(t) be described as Y(t)=h(t)*X(t)+Z(t), where X(t) is a white noise process with power spectral density S X(f)=5 W/Hz. The…
- Question 56 – A voice signal m(t) is in the frequency range 5 kHz to 15 kHz. The signal is amplitude-modulated to generate an AM signal f(t)=A(1+m(t))2 f ct, where…
- Question 57 – A random variable X takes values -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so…
- Question 58 – 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…
- Question 59 – 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…
- Question 60 – Consider a long-channel MOSFET with a channel length 1\ m and width 10\ m. The device parameters are acceptor concentration N A=51016\ cm-3, electron…
- Question 61 – A rectangular waveguide of width w and height h has cut-off frequencies for TE 10 and TE 11 modes in the ratio 1 : 2. The aspect ratio w/h, rounded…
- Question 62 – In the circuit shown, V s 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…
- Question 63 – A CMOS inverter, designed to have a mid-point voltage V I equal to half of V dd, as shown in the figure, has the following parameters: V dd=3 V nC…
- Question 64 – In the circuit shown, the threshold voltages of the pMOS ( V tp ) and nMOS (V tn) transistors are both equal to 1 V. All the transistors have the same…
- Question 65 – In the circuit shown, V 1=0 and V 2=V dd. The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation…