GATE 2022 IN – Previous Year Questions with Solutions
All 65 questions of GATE 2022 IN with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Inhaling the smoke from a burning could you quickly.
- Question 2 – A sphere of radius r cm is packed in a cubical box. What is the minimum volume (in cm3) of a box enclosing the sphere?
- Question 3 – Pipes P and Q can fill a storage tank in full with water in 10 and 6 minutes, respectively. Pipe R draws the water out from the storage tank at a rate…
- Question 4 – Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following…
- Question 5 – A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially. What is the minimum…
- Question 6 – Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a…
- Question 7 – A game consists of spinning an arrow around a stationary disk as shown. At rest it has eight equally likely outcomes: sectors numbered 1 through 8.…
- Question 8 – Consider (i) 3p-q<4 and (ii) 3q-p<12. Which expression follows from the two inequalities?
- Question 9 – Given below are three statements and four conclusions drawn based on the statements. Statement 1: Some engineers are writers. Statement 2: No writer…
- Question 10 – Which one of the following sets of pieces can be assembled to form a square with a single round hole near the center? Pieces cannot overlap.
- Question 11 – The input x(t) and output y(t) satisfy dy(t)/dt+y(t)=3x(t-3)u(t-3), where u(t) is the unit-step function. The transfer function is .
- Question 12 – A pneumatic nozzle-flapper system is conventionally used to convert
- Question 13 – A periodic function of period 2 is f(x)=cases-1-x,&-1 x<0\\1-x,&0<x1cases. Its Fourier series contains .
- Question 14 – The output is related to the input by y(t)=x(t)(2 t). This system is .
- Question 15 – A unity-gain negative-feedback control system has loop gain L(s)=6/[s(s-5)]. The closed-loop system is .
- Question 16 – A sinusoidal carrier with amplitude A c and frequency f c is amplitude modulated by m(t) with 0<f m f c, giving s(t)=A c[1+m(t)](2 f ct). Which…
- Question 17 – A Hall sensor is based on the principle of
- Question 18 – The signal x(t) is band-limited between 100 Hz and 200 Hz. If y(t)=x(2t-5), which statement is always true?
- Question 19 – A Chromel–Alumel thermocouple has junction A at T A. An ideal voltmeter reads thermal emf E 1 between open ends B1 and B2, both at T B. Identical…
- Question 20 – The resistance of a pure copper wire of length 10 cm and diameter 1 mm is to be measured. The most suitable method from amongst the choices given…
- Question 21 – The logic block shown has output F given by .
- Question 22 – In which of the following bridge(s) is the balancing condition frequency-independent?
- Question 23 – The output F of the digital circuit shown can be written in the form(s) .
- Question 24 – Given M=bmatrix2&3&7\\6&4&7\\4&6&14bmatrix, which statements are correct?
- Question 25 – An analog-to-digital converter with resolution 0.01 V converts analog signals between 0 V to +10 V to an unsigned binary output. The minimum number of…
- Question 26 – Consider 24 voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at 12 kHz and represented by…
- Question 27 – A photodiode is made from a semiconductor of bandgap 1.42 eV. Given Planck’s constant 6.62610-34 J·s, vacuum light speed 3108 m/s, and 1 eV =1.610-19…
- Question 28 – The global minimum of x3e- x for x(-,) occurs at x= (one decimal place).
- Question 29 – A 440 V, 8 kW, 4-pole, 50 Hz, star-connected induction motor has a full load slip of 0.04. The rotor speed (in rpm) at full load is (round off to one…
- Question 30 – A system has transfer function (s+1)(s+3)/[(s+5)(s+7)(s+9)]. Its state-space representation requires at least state variables (integer).
- Question 31 – A Zener diode is used as a 4 V regulator in the circuit shown. It needs minimum current 4 mA for regulation. The maximum load current through R L is…
- Question 32 – A bag contains six red balls and four blue balls. If three balls are drawn in succession without replacement, the probability that the second and…
- Question 33 – For the bandpass-filter circuit shown, R 0=50\ , L 0=1 mH, and C 0=10 nF. Its Q factor is (two decimal places).
- Question 34 – Newton–Raphson is applied to f(x)=x- x=0. Starting with x 0=0, the next approximation x 1 is (two decimal places).
- Question 35 – An OPAMP with gain 104, input impedance 10 M, and output impedance 100 is used in a unity-gain feedback voltage buffer. Its closed-loop output…
- Question 36 – The shown V in(t) is applied from t=0 ms to 6 ms to the circuit. The capacitor initially has 0.3 V and the diode is ideal. The open-circuit V out at 5…
- Question 37 – The signal-flow graph is shown. The expression for Y(s)/X(s) is .
- Question 38 – Bilinear transformation with sampling period 0.1 s is used to obtain H d(z) from H c(s)=1/[(s+1)(s+3)]. Then H d(z) is .
- Question 39 – A car moves collinearly with a transceiver’s laser beam. A pulse emitted at t=0 returns after reflection from the car 100 ns later. A second pulse…
- Question 40 – The signal x(t)=(t-1)2u(t-1), where u is the unit step, has Laplace transform X(s). The value of X(1) is .
- Question 41 – A PID controller stably controls P(s)=1/[(s+1)(s+2)]. Its proportional gain is increased by factor 2, integral gain by factor 3, and derivative gain…
- Question 42 – The resistor-ladder DAC has the switch state shown for its digital input. Its output-node Thevenin voltage V th and resistance R th are .
- Question 43 – The Nyquist plot of stable open-loop G(j) for 0< intersects the unit circle at P=-0.77-0.64j. Points on the plot are Q=14.40+0.00j and R=-0.21+0.00j.…
- Question 44 – The enhancement n-channel MOSFET in the small-signal circuit is saturated with transconductance g m. Ignore channel-length modulation. The…
- Question 45 – For dy/dx+y y=0 with y(0)=e, the value of y(1) is .
- Question 46 – The digital circuit shown
- Question 47 – The enhancement n-channel MOSFET shown is saturated with transconductance g m. A low-frequency small-signal supply voltage v d causes output…
- Question 48 – A=a 1a 0 and B=b 1b 0 are unsigned two-bit binary numbers. Boolean F(a 1,a 0,b 1,b 0) is 1 exactly when A>B. Its minimized form is .
- Question 49 – Matrix A=bmatrix4&3\\9&-2bmatrix has eigenvalues −5 and 7. Select its eigenvector(s).
- Question 50 – For z=(a+jb)/(a-jb) with a>0,b>0, which statements are true?
- Question 51 – Monochromatic light of wavelength 532 nm is used to measure the absorption coefficient of a material in a UV-Visible Spectrophotometer. The measured…
- Question 52 – The load shown is driven by V 1=1000 V at 50 Hz. Given R 1=20\ , C 1=(1000/) μF, L 1=(20/) mH, and R 2=4\ , its power factor is (one decimal place).
- Question 53 – A unity-gain feedback system has plant P(s)=0.001/[s(2s+1)(0.01s+1)] and lag compensator C(s)=(s+10)/(s+0.1). The asymptotic Bode magnitude slope of…
- Question 54 – For Circuit A with shown currents I 1,I 2, the current I 3 in Circuit B is A (one decimal place).
- Question 55 – The balanced three-phase circuit shown has C 0=8.2 μF and line-to-line rms voltage 440 V at 50 Hz. The wattmeter reading is W (two decimal places).
- Question 56 – The circuit shown is driven by a sinusoidal input voltage, 𝑉, resulting in the output voltage, 𝑉௨௧. The frequency (in kilohertz) at which the…
- Question 57 – A conducting semicircular loop of radius R=0.1 m has its diameter centred at the origin and rotates in the x–y plane at =20 rad/s. A magnetic field…
- Question 58 – In the circuit shown, R 1=100 k and R 2=1 k. The npn BJT has base–emitter voltage 0.7 V and collector–emitter voltage 5.2 V. Its current gain is (two…
- Question 59 – A capacitor consists of two concentric spheres with air dielectric of permittivity 8.85410-12 F/m. Inner and outer radii are 10 cm and 15 cm. Its…
- Question 60 – A 1 kHz sine-wave generator with internal resistance 50 has open-circuit voltage 10 V peak-to-peak. A capacitor connected across its output reduces…
- Question 61 – For f(z)=1/[(z+1)(z+2)(z+3)], the residue at z=-1 is .
- Question 62 – The circuit has C 0=10 μF, L 0=1 mH, and an ideal diode. Initially the capacitor is charged to 10 V and inductor current is zero. The switch closes at…
- Question 63 – The bridge shown balances with R 1=100\ , R 2=210\ , C 2=2.9 μF, and R 4=50\ . The 2 kHz sine-wave generator supplies 10 V peak-to-peak. The value of…
- Question 64 – The switch is initially closed. It opens at t=0 and remains open. The time when comparator output V out becomes LOW is ms (three decimal places).
- Question 65 – The Wheatstone bridge has R 1=1.5 k and R 2=R 3=R 4=1 k. Initially the switch is open and the voltage between C and D is V CD. Closing it at t=0…