GATE 2023 IN – Previous Year Questions with Solutions
All 65 questions of GATE 2023 IN with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – The village was nestled in a green spot, the ocean and the hills.
- Question 2 – Disagree : Protest : : Agree : (By word meaning)
- Question 3 – A ‘frabjous’ number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous…
- Question 4 – Which one among the following statements must be TRUE about the mean and the median of the scores of all candidates appearing for GATE 2023?
- Question 5 – In the given diagram, ovals are marked at different heights (h) of a hill. Which one of the following options P, Q, R, and S depicts the top view of…
- Question 6 – Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the…
- Question 7 – Ankita climbs five stairs from the ground. Each move is one or two stairs upward, and she cannot move down. Let F(N) count the ways to reach stair N;…
- Question 8 – The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides:…
- Question 9 – Which of the figures P, Q, R, S represents f(x)= x+2 - x-1 ?
- Question 10 – An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular…
- Question 11 – Choose the solution set S of x-2y+z=0 and x-z=0. Here R denotes the real numbers; tuples denote column vectors.
- Question 12 – Inductance of a coil is measured as 10 mH, using an LCR meter, when no other objects are present near the coil. The LCR meter uses a sinusoidal…
- Question 13 – Which flow meter offers the lowest resistance to flow? Source note: the published paper lists “Orifice flow meter” as option B. Its footnote states…
- Question 14 – Pair the quantities p–s with devices i–iv. Devices: i. Linear variable differential transformer (LVDT); ii. Thermistor; iii. Strain gauge; iv.…
- Question 15 – A parallel-plate capacitance is calculated as 20 pF using C= 0 rA/d, where 0 is free-space permittivity, r relative dielectric permittivity, A…
- Question 16 – The table gives present state, next state, and control input. Identify the flip-flop. Present Q(t) Next Q(t+1) Input ---: ---: ---: 0 0 0 0 1 1 1 0 1…
- Question 17 – Match XOR operations i–iv to results p–s, where X is a Boolean input. Operations: i. X X; ii. X X; iii. X0; iv. X1. Results: p. 1; q. 0; r. X; s. X.
- Question 18 – An LED emits light when it is biased. A photodiode provides maximum light sensitivity when it is biased.
- Question 19 – Expanding F(z)=1/(1-z) around z=2 gives F(z)= k=0 a k(z-2)k, with ROC z-2 <1. For k0, the coefficients are
- Question 20 – The solution of x=-k x, k>0, with x(0)=1, x(0)=0, for t0, is
- Question 21 – A system has Y(s)/X(s)=(s-)/(s+). If u(t) is the unit step, which input gives steady-state output y(t)=( t)?
- Question 22 – Choose the fastest logic family among the following:
- Question 23 – The limit x0x(1/x) is
- Question 24 – The number of zeros of P(s)=s3+2s2+5s+80 in the right half-plane is .
- Question 25 – The number of times the Nyquist plot of G(s)H(s)=12(s-1)(s-2)(s+1)(s+2) encircles the origin is .
- Question 26 – The opamp shown is ideal except for input bias current 1 nA and input offset voltage 10 μV. The worst-case output voltage is ± μV (nearest integer).
- Question 27 – The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them is 10 µN/m. When the gap is doubled, the…
- Question 28 – Let x[n]=u[-n+5]-u[n+3], where u[n]=1 for n0 and zero for n<0. The smallest n for which x[n]=0 is .
- Question 29 – A continuous-time periodic signal x(t) has fundamental period 100 s. If y(t)=x(4t), its fundamental period is s (nearest integer).
- Question 30 – When the bridge given below is balanced, the current through the resistor Ra is mA (rounded off to two decimal places).
- Question 31 – In the circuit given, the Thevenin equivalent resistance Rth across the terminals ‘a’ and ‘b’ is Ω (rounded off to one decimal place).
- Question 32 – A discrete random variable X takes values 0, 1, 2, with P(X=0)=0.25 and P(X=1)=0.5. If E[] denotes expectation, E[X]-E[X2] is (one decimal place).
- Question 33 – The diode shown is ideal and the source is i s(t)=(3000 t) mA. The magnitude of average current through resistor R is mA (two decimal places).
- Question 34 – The full-scale range of the wattmeter shown in the circuit is 100 W. The turns ratio of the individual transformers are indicated in the figure. The…
- Question 35 – The no-load steady-state output voltage of a DC shunt generator is 200 V when it is driven in the clockwise direction at its rated speed. If the same…
- Question 36 – An LTI system has impulse response h(t)=(t)+0.5(t-4), where is the continuous-time unit impulse. For x(t)=(7 t/4), its output is
- Question 37 – The Laplace transform of x(t)=e-3tu(t-5), where u is the unit step, is
- Question 38 – A p-i-n photodiode receives a light pulse containing 81012 photons at wavelength 0=1.55 μm. An average of 41012 electrons is collected at its…
- Question 39 – Let f(z)=j(1-z)/(1+z), where z is complex and j=-1. Its inverse f-1 maps the real axis to the .
- Question 40 – Simplify F(W,X,Y,Z)=(4,5,10,11,12,13,14,15) using the minimum number of terms and fewest literals per term.
- Question 41 – For the given digital circuit, A = B = 1. Assume that AND, OR, and NOT gates have propagation delays of 10 ns, 10 ns, and 5 ns respectively. All lines…
- Question 42 – In the circuit shown, the initial binary content of shift register A is 1101 and that of shift register B is 1010. The shift registers are…
- Question 43 – Which transfer function matches the magnitude and phase plots shown?
- Question 44 – A continuous real-valued signal x(t) has finite positive energy and is zero for all t<0. Select all signals whose continuous-time Fourier transform is…
- Question 45 – A silica-glass fibre has core index 1.47 and cladding index 1.44. The cladding is completely stripped off and the core immersed in water of index…
- Question 46 – For the circuit shown, =100 rad/s, R 1=R 2=2.2 Ω, and L=7 mH. The capacitance making input admittance Y in purely real is mF (two decimal places).
- Question 47 – The R–L circuit shown has R=10 kΩ, L=1 mH, and step-current excitation I 0u(t). At t=0-, inductor current is I L=I 0/5. The minimum time for inductor…
- Question 48 – A standard negative-feedback system has G(s)=1/[(s-2)(s-3)] and PID controller C(s)=K P+K I/s+K Ds. The root locus of G(s)C(s) is shown. Given C(j)=2…
- Question 49 – How many five-digit numbers can be formed using the integers 3, 4, 5 and 6 with exactly one digit appearing twice?
- Question 50 – The phase margin of G(s)=2(1-s)/(1+s)2 is degrees (nearest integer).
- Question 51 – A wire-wound ‘resistive potentiometer type' angle sensor with 72 turns is used in an application. The first turn of the potentiometer is connected to…
- Question 52 – The two secondaries of a linear variable differential transformer (LVDT) showed a magnitude of 2 V (RMS) for zero displacement position of the core.…
- Question 53 – Five measurements are made using a weighing machine, and the readings are 80 kg, 79 kg, 81 kg, 79 kg and 81 kg. The sample standard deviation of the…
- Question 54 – Four strain gauges R A,R B,R C,R D, each nominally R, form the bridge shown. Under force, R A,R D increase by R and R B,R C decrease by R. The…
- Question 55 – A 4 H inductor carries i 1(t)=(200 t) mA and is mutually coupled to a 5 H inductor carrying i 2(t)=2(200 t) mA, with dot polarities shown. The…
- Question 56 – The nMOS feedback amplifier shown has nC ox=1 mA/V2, threshold V T=1 V, and W/L=2. The drain bias voltage is 4 V. Capacitors C have zero…
- Question 57 – For g(x)=\(x-2)2,-2x+7\ on R, the minimum value is (one decimal place).
- Question 58 – A single-phase transformer is short-circuit tested at 1 kHz with its secondary shorted. The wattmeter reads 8 W, primary current is 2 A, and primary…
- Question 59 – The opamps shown are ideal. Inputs are V S1=3+0.10(300t) V and V S2=-2+0.11(300t) V. The mean output V 0 is V (two decimal places).
- Question 60 – The ideal switched-opamp circuit has V in=100 mV. At t=0, the 10 nF capacitor stores 1 nC with the shown polarity. A 1 kHz square wave V s controls…
- Question 61 – The sinusoidal source shown has frequency 50 Hz. The load voltage is 230 V RMS and impedance is 230/2+j230/2 Ω. Attenuator A 1=1/(502). The multiplier…
- Question 62 – In the circuit shown, assuming an ideal opamp, the value of the output voltage Vo = V (rounded off to one decimal place).
- Question 63 – The matrix A=bmatrix1&4\\-3&\\&6bmatrix has rank one. The ratio / is (nearest integer).
- Question 64 – A 1.999 V true-RMS 312-digit multimeter has accuracy ±0.1% of reading ±2 digits. It measures 100 A RMS line current through a 100:5 Class-1 current…
- Question 65 – The source V s=102(20000 t) V has internal resistance 50 Ω. The RMS current through R in the circuit shown is mA (one decimal place).