GATE 2020 IN – Previous Year Questions with Solutions
All 65 questions of GATE 2020 IN with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – He is known for his unscrupulous ways. He always sheds tears to deceive people.
- Question 2 – Jofra Archer, the England fast bowler, is than accurate.
- Question 3 – Select the word that fits the analogy: Build : Building :: Grow : .
- Question 4 – “I do not think you know the case well enough to have opinions. Having said that, I agree with your other point.” What does “having said that” mean in…
- Question 5 – Define [x] as the greatest integer less than or equal to x, for each x(-,). If y=[x], find the area under y for x[1,4].
- Question 6 – Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through…
- Question 7 – P, Q, R and S are to be uniquely coded using and . If P is coded and Q is coded , then R and S, respectively, can be coded as .
- Question 8 – Find the sum of the first n terms in the sequence 8, 88, 888, 8888, ….
- Question 9 – Select the graph that schematically represents BOTH y=xm and y=x1/m properly in 0 x1, for integral m > 1. The choices are arranged A, B in the top row…
- Question 10 – The bar graph shows students who appeared and passed in an examination for schools P, Q, R and S. Find the average success rate (percentage) of the…
- Question 11 – Unit vectors along the mutually perpendicular x,y,z axes are i, j, k. Two vectors a,b lie in z = 0 and satisfy a b for every scalar α. A vector…
- Question 12 – The recursion is X n+1=X n-h[F(X n)-X n], with X 0=1 and small positive h. It numerically solves which ODE?
- Question 13 – In Ax=b, A is a real 24 matrix and b0. Can multiplying by AT and inverting ATA always give a unique x?
- Question 14 – The series circuit shown has resistors rated 100 Ω, 1 W; 2 Ω, 0.5 W; and 1 Ω, 0.25 W. Find the safe maximum current I.
- Question 15 – A differentiator has a transfer function whose
- Question 16 – A phase-lead network has G(s)=(1+0.2s)/(1+0.05s). Its maximum phase shift occurs at angular frequency
- Question 17 – The circuit has ideal diodes, a 5 V Zener breakdown voltage, a 10 sin(100πt) V input through 50 Ω, and a 100 Ω branch to a +5 V source as shown. The…
- Question 18 – Let f(A,B,C,D)= m(0,1,2,6,8,9,10,11)+ d(3,7,14,15), where m denotes minterms and d don’t-cares. The minimal sum-of-products expression is
- Question 19 – A Q meter is best suited to measure the
- Question 20 – A Hall sensor carries current I and has perpendicular magnetic flux density B. Its Hall voltage is
- Question 21 – Choose the Boolean expression represented by the shaded Venn regions in the figure.
- Question 22 – For the shown 4:1 multiplexer with select bits S 1 (MSB) and S 0 (LSB), the output O is
- Question 23 – For x[n]=(2 n)u[n], where u[n]=1 for n=0,1,2, and 0 otherwise, the period is
- Question 24 – A closed-loop system has C(s)/R(s)=1/(s+1). For input r(t)= t, its steady-state output is
- Question 25 – For f(z)=1/(z+a) with a > 0, evaluate Cf(z)dz counterclockwise on any circle of radius R > 0 centred at (−a,0).
- Question 26 – A player scores a basket with probability 0.1 on each independent attempt. On two attempts, find the probability of scoring only on the second, to two…
- Question 27 – With both op-amps ideal, find output V₁ in volts in the circuit shown.
- Question 28 – Three 400 Ω resistors form a delta supplied by balanced 400 V RMS, 50 Hz, R-Y-B three-phase three-wire mains. Find line current in A, to one decimal…
- Question 29 – For x(t)=e- t and X(j)= - x(t)e-j tdt, find X(j0).
- Question 30 – A second-order system has closed-loop poles s=-3 j4. Find the time of the first maximum of its unit-step response, in seconds, to two decimal places.
- Question 31 – The ideal-op-amp circuit shown has an 8 kΩ feedback resistor to the positive input, and a 1 kΩ/2 kΩ divider to its negative input. Find V x/I x in kΩ.
- Question 32 – A 10 kHz sinusoid is sampled at 15 k samples/s. The sampled signal passes through an ideal low-pass filter with 25 kHz cutoff. Find the maximum output…
- Question 33 – A 200 mV full-scale dual-slope ADC uses 100 mV reference and a fixed first-integration time of 100 ms. In continuous-conversion mode, find the minimum…
- Question 34 – A capacitive sensor has C x=(1000x) pF and is excited by 10(100 t) V. It drives a high-input-impedance amplifier through a grounded shielded cable…
- Question 35 – Two 100 Ω resistors of tolerances 3% and 4% are connected in series. Find effective combination tolerance in percent, to one decimal place.
- Question 36 – For M=pmatrix1&-1&0\\1&-2&1\\0&-1&1pmatrix, which is an eigenvector?
- Question 37 – The ODE is dx/dt= x, with x(0) = 0. Its solution is
- Question 38 – A straight line intercepts the x-axis at −0.5 and y-axis at 1. Its equation is
- Question 39 – A negative-feedback system has loop transfer function G(s)H(s)=1/[s(s-2)]. Its Nyquist plot
- Question 40 – For mesh currents I₁,I₂,I₃ and source polarities in the circuit shown, which matrix equation is correct?
- Question 41 – Find the minimum of f(x,y)=x2+y2 on x+y=1, to one decimal place.
- Question 42 – Two equally likely bags each contain 10 balls. B1 has 7 red and 3 green; B2 has 3 red and 7 green. A randomly drawn ball is red. Find the probability…
- Question 43 – The series circuit shown has R = 100 Ω, L = 100 mH, C = 10 μF and source 1002(1000t) V. Find the RMS current in A.
- Question 44 – A balanced 400 V line-voltage three-phase supply feeds the shown unbalanced star: 300 Ω from each line to a floating star point, with an extra 100 Ω…
- Question 45 – Let g[n]=1 for n = 0 and zero otherwise, and h[n]=1 for n = 0,3,6,9,… and zero otherwise. If y[n]=h[n] g[n] with convolution denoted by ⊗, find y[2].
- Question 46 – A negative-feedback system has G(s)H(s)=K/[s(s+2)(s+6)], K > 0. Find K at the root-locus breakaway point, to one decimal place.
- Question 47 – The negative unity-feedback system shown has forward path K/( s+1) with K,τ positive. Its response to r(t)=10u(t) tends to 8. Find K.
- Question 48 – The ideal-op-amp precision-rectifier circuit shown is driven by 2(5000 t) V. Find the reading in volts of its 1 Hz bandwidth PMMC voltmeter.
- Question 49 – In the shown circuit both op-amps are ideal and Vₓ = 0.5 mV. Find the steady-state output Vₒ in V, to two decimal places.
- Question 50 – Two T flip-flops are connected as shown. Initially A = B = 1. Input x takes values 1,0,1 in the next three clock cycles. Find the decimal value of…
- Question 51 – A 10-bit DAC has 1.023 V full-scale output. Its address inputs A 9 A 2 connect to an 8-bit microprocessor’s D 7 D 0, while A 1,A 0 are grounded. If…
- Question 52 – A balanced three-phase load on 400 V, 50 Hz, three-wire RYB mains is measured by two wattmeters. W₁ is in line R, W₂ in line B. Line current is 1/3 A.…
- Question 53 – A 6½-digit timer-counter is in time-period mode with range set to ns. It displays 1000000. With the same input, it is changed to frequency mode with…
- Question 54 – The charge-amplifier circuit shown uses an ideal op-amp powered by VCC = 5 V and biased at VCC/2. A piezoelectric sensor generates q p=0.1(10000 t)…
- Question 55 – A metallic strain gauge has gauge factor 2 and unstressed resistance 1 kΩ. It is bonded to material with elastic modulus 200 GN/m² and forms a quarter…
- Question 56 – A 10 mm diameter laser beam is focused onto an optical fibre by a thin biconvex lens of refractive index 1.5. Fibre core and cladding indices are 1.55…
- Question 57 – A slab of refractive index 1.5 and thickness t is surrounded by air on both sides. Light of free-space wavelength 600 nm is incident normally. Find…
- Question 58 – The finite sequence is X = (1,1,1). Its inverse DFT is x = (x(0),x(1),x(2)). Find x(2).
- Question 59 – The capacitor network, DC source and amplifier of gain G = −5 are shown. Find effective capacitance between A and B in μF, to two decimal places.
- Question 60 – A state model is x 1=x 2, x 2=-6x 1-5x 2, with x 1(0)=0,x 2(0)=1. Find x₂(1), to two decimal places.
- Question 61 – Assume all diodes in the circuit are ideal. Find current Iₖ through the 3 kΩ resistor in mA, to one decimal place.
- Question 62 – A 1000/1 A, 5 VA, unity-power-factor current transformer has 1000 secondary turns. At primary current 1000 A, ratio error is −0.1% and phase error is…
- Question 63 – An LVDT has mutual inductances M₁,M₂ to its two secondary coils. Their self-inductances remain constant with displacement x. At x = 0, M₁ = M₂ = M₀.…
- Question 64 – The Maxwell–Wien bridge shown balances when C₁ = 100 nF and R₁ = 100 kΩ. Its excitation is √2 cos(1000t) V. Find the coil Q factor.
- Question 65 – A negative-feedback system has G(s)H(s)=2(s+1)/s2. Find phase margin in degrees, to one decimal place.