GATE 2022 EC – Previous Year Questions with Solutions
All 65 questions of GATE 2022 EC with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Mr. X speaks Japanese Chinese.
- Question 2 – A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively. If R gets ₹ 1000 more than S, what is the…
- Question 3 – A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, PQ = 11…
- Question 4 – The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of…
- Question 5 – An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where…
- Question 6 – Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used…
- Question 7 – Consider the following inequalities. (i) 2x-1>7 (ii) 2x-9<1 Which one of the following expressions below satisfies the above two inequalities?
- Question 8 – Four points P(0, 1), Q(0, −3), R(−2, −1), and S(2, −1) represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?
- Question 9 – In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the…
- Question 10 – Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively. Let X, Y and Z represent the following…
- Question 11 – Consider the two-dimensional vector field F(x,y)=x\,+y\,, where and denote the unit vectors along the x-axis and the y-axis, respectively. A contour C…
- Question 12 – Consider a system of linear equations Ax=b, where A=bmatrix1&-2&3\\-1&2&-3bmatrix, b=bmatrix1\\3bmatrix. This system of equations admits .
- Question 13 – The current I in the circuit shown is .
- Question 14 – Consider the circuit shown in the figure. The current I flowing through the 10\ resistor is .
- Question 15 – The Fourier transform X(j) of the signal x(t)=t(1+t2)2 is .
- Question 16 – Consider a long rectangular bar of direct bandgap p-type semiconductor. The equilibrium hole density is 1017\ cm-3 and the intrinsic carrier…
- Question 17 – In a non-degenerate bulk semiconductor with electron density n=1016\ cm-3, the value of E C-E Fn=200 meV, where E C and E Fn denote the bottom of the…
- Question 18 – Consider the CMOS circuit shown in the figure (substrates are connected to their respective sources). The gate width (W) to gate length (L) ratios (…
- Question 19 – Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for A 0, A 1, A 2, and A 3 are .
- Question 20 – The ideal long channel nMOSFET and pMOSFET devices shown in the circuits have threshold voltages of 1 V and −1 V, respectively. The MOSFET substrates…
- Question 21 – Consider a closed-loop control system with unity negative feedback and KG(s) in the forward path, where the gain K=2. The complete Nyquist plot of the…
- Question 22 – The root-locus plot of a closed-loop system with unity negative feedback and transfer function KG(s) in the forward path is shown in the figure. Note…
- Question 23 – The frequency response H(f) of a linear time-invariant system has magnitude as shown in the figure. Statement I: The system is necessarily a pure…
- Question 24 – In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is…
- Question 25 – Consider the following partial differential equation (PDE) a2f(x,y) x2+b2f(x,y) y2=f(x,y), where a and b are distinct positive real numbers. Select…
- Question 26 – An ideal OPAMP circuit with a sinusoidal input is shown in the figure. The 3 dB frequency is the frequency at which the magnitude of the voltage gain…
- Question 27 – Select the Boolean function(s) equivalent to x+yz, where x, y, and z are Boolean variables, and + denotes logical OR operation.
- Question 28 – Select the correct statement(s) regarding CMOS implementation of NOT gates.
- Question 29 – Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are…
- Question 30 – Consider the following wave equation, 2f(x,t) t2=10000\,2f(x,t) x2. Which of the given options is/are solution(s) to the given wave equation?
- Question 31 – The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in 17 of her matches, the bowler…
- Question 32 – A simple closed path C in the complex plane is shown in the figure. If C2zz2-1\,dz=-i A, where i=-1, then the value of A is (rounded off to two…
- Question 33 – Let x 1(t)=e-tu(t) and x 2(t)=u(t)-u(t-2), where u() denotes the unit step function. If y(t) denotes the convolution of x 1(t) and x 2(t), then ty(t)=…
- Question 34 – An ideal MOS capacitor (p-type semiconductor) is shown in the figure. The MOS capacitor is under strong inversion with V G=2 V. The corresponding…
- Question 35 – A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the…
- Question 36 – The function f(x)=8 e x-x2+3 attains its minimum over the interval [1,e] at x= . (Here e x is the natural logarithm of x.)
- Question 37 – Let , be two non-zero real numbers and v 1,v 2 be two non-zero real vectors of size 31. Suppose that v 1 and v 2 satisfy v 1Tv 2=0, v 1Tv 1=1, and v…
- Question 38 – For the circuit shown, the locus of the impedance Z(j) is plotted as increases from zero to infinity. The values of R 1 and R 2 are:
- Question 39 – Consider the circuit shown in the figure with input V(t) in volts. The sinusoidal steady state current I(t) flowing through the circuit is shown…
- Question 40 – Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10\ m and width 100\ m. The product of electron mobility ( n) and oxide…
- Question 41 – For the following circuit with an ideal OPAMP, the difference between the maximum and the minimum values of the capacitor voltage (V C) is .
- Question 42 – A circuit with an ideal OPAMP is shown. The Bode plot for the magnitude (in dB) of the gain transfer function (A V(j)=V out(j)/V in(j)) of the circuit…
- Question 43 – For the circuit shown, the clock frequency is f 0 and the duty cycle is 25%. For the signal at the Q output of the Flip-Flop, .
- Question 44 – Consider an even polynomial p(s) given by p(s)=s4+5s2+4+K, where K is an unknown real parameter. The complete range of K for which p(s) has all its…
- Question 45 – Consider the following series: n=1ndcn For which of the following combinations of c,d values does this series converge?
- Question 46 – The outputs of four systems (S 1, S 2, S 3, and S 4) corresponding to the input signal (t), for all time t, are as follows. S 1: input (t), output…
- Question 47 – Select the CORRECT statement(s) regarding semiconductor devices.
- Question 48 – A state transition diagram with states A, B, and C, and transition probabilities p 1,p 2,,p 7 is shown in the figure (e.g., p 1 denotes the…
- Question 49 – Consider a Boolean gate (D) where the output Y is related to the inputs A and B as, Y=A+ B, where + denotes logical OR operation. The Boolean inputs…
- Question 50 – Two linear time-invariant systems with transfer functions G 1(s)=10s2+s+1and G 2(s)=10s2+s10+10 have unit step responses y 1(t) and y 2(t),…
- Question 51 – Consider an FM broadcast that employs the pre-emphasis filter with frequency response H pe()=1+j 0, where 0=104 rad/sec. For the network shown in the…
- Question 52 – A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10-4 cm, with air as the dielectric. Assume the speed of…
- Question 53 – The value of the integral D 3(x2+y2)\,dx\,dy, where D is the shaded triangular region shown in the diagram, is (rounded off to the nearest integer).
- Question 54 – A linear 2-port network is shown in Fig. (a). An ideal DC voltage source of 10 V is connected across Port 1. A variable resistance R is connected…
- Question 55 – For a vector x=[x[0],x[1],,x[7]], the 8-point discrete Fourier transform (DFT) is denoted by X=DFT( x)=[X[0],X[1],,X[7]], where X[k]=…
- Question 56 – A p-type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density…
- Question 57 – A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal voltage gain V out V in is…
- Question 58 – Consider the circuit shown with an ideal OPAMP. The output voltage V 0 is V (rounded off to two decimal places).
- Question 59 – Consider the circuit shown with an ideal long channel nMOSFET (enhancement-mode, substrate is connected to the source). The transistor is…
- Question 60 – The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals…
- Question 61 – The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition…
- Question 62 – Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with…
- Question 63 – Consider a channel over which either symbol x A or symbol x B is transmitted. Let the output of the channel Y be the input to a maximum likelihood…
- Question 64 – Consider a real valued source whose samples are independent and identically distributed random variables with the probability density function, f(x),…
- Question 65 – In an electrostatic field, the electric displacement density vector, D, is given by D(x,y,z)=(x3\,+y3\,+xy2\, k)\ C/m2, where ,, k are the unit…