GATE 2021 EC – Previous Year Questions with Solutions
All 65 questions of GATE 2021 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 current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 years ago?
- Question 2 – p and q are positive integers and pq+ qp=3, then p2q2+q2p2=
- Question 3 – The least number of squares that must be added so that the line P-Q becomes the line of symmetry is .
- Question 4 – *Nostalgia* is to *anticipation* as is to . Which one of the following options maintains a similar logical relation in the above sentence?
- Question 5 – Consider the following sentences: (i) I woke up from sleep. (ii) I woked up from sleep. (iii) I was woken up from sleep. (iv) I was wokened up from…
- Question 6 – Given below are two statements and two conclusions. Statement 1: All purple are green. Statement 2: All black are green. Conclusion I: Some black are…
- Question 7 – Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI)…
- Question 8 – Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut…
- Question 9 – The number of minutes spent by two students, X and Y, exercising every day in a given week are shown in the bar chart above. The number of days in the…
- Question 10 – Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above. The ratio of the area of the regular…
- Question 11 – The vector function F( r)=-x\,+y\, is defined over a circular arc C shown in the figure. The line integral of C F( r) d r is
- Question 12 – Consider the differential equation given below. dydx+x1-x2\,y=x y The integrating factor of the differential equation is
- Question 13 – Two continuous random variables X and Y are related as Y=2X+3 Let X2 and Y2 denote the variances of X and Y, respectively. The variances are related…
- Question 14 – Consider a real-valued base-band signal x(t), band limited to 10 kHz. The Nyquist rate for the signal y(t)=x(t)\,x(1+ t2) is
- Question 15 – Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n] denotes the 16-point inverse…
- Question 16 – A bar of silicon is doped with boron concentration of 1016\ cm-3 and assumed to be fully ionized. It is exposed to light such that electron-hole pairs…
- Question 17 – The energy band diagram of a p-type semiconductor bar of length L under equilibrium condition (i.e., the Fermi energy level E F is constant) is shown…
- Question 18 – In the circuit shown in the figure, the transistors M 1 and M 2 are operating in saturation. The channel length modulation coefficients of both the…
- Question 19 – For the circuit with an ideal OPAMP shown in the figure, V REF is fixed. If V OUT=1 volt for V IN=0.1 volt and V OUT=6 volt for V IN=1 volt, where V…
- Question 20 – Consider the circuit with an ideal OPAMP shown in the figure. Assuming V IN V CC and V REF V CC , the condition at which V OUT equals to zero is
- Question 21 – If (1235) x=(3033) y, where x and y indicate the bases of the corresponding numbers, then
- Question 22 – Addressing of a 32K16 memory is realized using a single decoder. The minimum number of AND gates required for the decoder is
- Question 23 – The block diagram of a feedback control system is shown in the figure. The transfer function Y(s)X(s) of the system is
- Question 24 – The complete Nyquist plot of the open-loop transfer function G(s)H(s) of a feedback control system is shown in the figure. If G(s)H(s) has one zero in…
- Question 25 – Consider a rectangular coordinate system (x,y,z) with unit vectors a x, a y, and a z. A plane wave traveling in the region z0 with electric field…
- Question 26 – If the vectors (1.0,-1.0,2.0), (7.0,3.0,x) and (2.0,3.0,1.0) in R3 are linearly dependent, the value of x is .
- Question 27 – Consider the vector field F= a x(4y-c 1z)+ a y(4x+2z)+ a z(2y+z) in a rectangular system (x,y,z) with unit vectors a x, a y, and a z. If the field F…
- Question 28 – Consider the circuit shown in the figure. The current I flowing through the 7\ resistor between P and Q (rounded off to one decimal place) is A.
- Question 29 – Consider the circuit shown in the figure. The value of v 0 (rounded off to one decimal place) is V.
- Question 30 – An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0 V to 7.68 V. If the…
- Question 31 – The autocorrelation function R X() of a wide-sense stationary random process X(t) is shown in the figure. The average power of X(t) is .
- Question 32 – Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%. If the carrier and…
- Question 33 – A speech signal, band limited to 4 kHz, is sampled at 1.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and…
- Question 34 – A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz. The minimum step size…
- Question 35 – The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48, respectively. The critical propagation angle, which is defined…
- Question 36 – Consider the integral C(x)x2(x2+4)\,dx where C is a counter-clockwise oriented circle defined as x-i =2. The value of the integral is
- Question 37 – A box contains the following three coins. I. A fair coin with head on one face and tail on the other face. II. A coin with heads on both the faces.…
- Question 38 – The switch in the circuit in the figure is in position P for a long time and then moved to position Q at time t=0. The value of dv(t)dt at t=0+ is
- Question 39 – Consider the two-port network shown in the figure. The admittance parameters, in siemens, are
- Question 40 – For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity ( V T/ V BS ) is found to be 50 mV/V at a substrate voltage…
- Question 41 – The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are 4 ns, 2 ns and 1 ns, respectively. If…
- Question 42 – The content of the registers are R 1=25H, R 2=30H and R 3=40H. The following machine instructions are executed. PUSHR1 PUSHR2 PUSHR3 POPR1 POPR2 POPR3…
- Question 43 – The electrical system shown in the figure converts input source current i s(t) to output voltage v o(t). Current i L(t) in the inductor and voltage v…
- Question 44 – A digital transmission system uses a (7,4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword…
- Question 45 – The impedance matching network shown in the figure is to match a lossless line having characteristic impedance Z 0=50\ with a load impedance Z L. A…
- Question 46 – A real 22 non-singular matrix A with repeated eigenvalue is given as A=bmatrixx&-3.0\\3.0&4.0bmatrix where x is a real positive number. The value of x…
- Question 47 – For a vector field D=2\, a +z22\, a in a cylindrical coordinate system (,,z) with unit vectors a , a and a z, the net flux of D leaving the closed…
- Question 48 – In the circuit shown in the figure, the switch is closed at time t=0, while the capacitor is initially charged to -5 V (i.e., v c(0)=-5 V). The time…
- Question 49 – The exponential Fourier series representation of a continuous-time periodic signal x(t) is defined as x(t)= k=-a kejk 0t where 0 is the fundamental…
- Question 50 – For a unit step input u[n], a discrete-time LTI system produces an output signal (2[n+1]+[n]+[n-1]). Let y[n] be the output of the system for an input…
- Question 51 – Consider the signals x[n]=2n-1u[-n+2] and y[n]=2-n+2u[n+1], where u[n] is the unit step sequence. Let X(ej) and Y(ej) be the discrete-time Fourier…
- Question 52 – A silicon P-N junction is shown in the figure. The doping in the P region is 51016\ cm-3 and doping in the N region is 101016\ cm-3. The parameters…
- Question 53 – An asymmetrical periodic pulse train v in of 10 V amplitude with on-time T ON=1 ms and off-time T OFF=1\ s is applied to the circuit shown in the…
- Question 54 – For the transistor M 1 in the circuit shown in the figure, nC ox=100\ A/V2 and (W/L)=10, where n is the mobility of electron, C ox is the oxide…
- Question 55 – A circuit with an ideal OPAMP is shown in the figure. A pulse V IN of 20 ms duration is applied to the input. The capacitors are initially uncharged.…
- Question 56 – The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns. The propagation delay of all the flip-flops is assumed to…
- Question 57 – The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the…
- Question 58 – A unity feedback system that uses proportional-integral (PI) control is shown in the figure. The stability of the overall system is controlled by…
- Question 59 – A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant 2…
- Question 60 – Consider a superheterodyne receiver tuned to 600 kHz. If the local oscillator feeds a 1000 kHz signal to the mixer, the image frequency (in integer)…
- Question 61 – In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study…
- Question 62 – A message signal having peak-to-peak value of 2 V, root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code…
- Question 63 – Consider a polar non-return to zero (NRZ) waveform, using +2 V and -2 V for representing binary '1' and '0', respectively, is transmitted in the…
- Question 64 – A standard air-filled rectangular waveguide with dimensions a=8 cm, b=4 cm, operates at 3.4 GHz. For the dominant mode of wave propagation, the phase…
- Question 65 – An antenna with a directive gain of 6 dB is radiating a total power of 16 kW. The amplitude of the electric field in free space at a distance of 8 km…