GATE 2024 IN – Previous Year Questions with Solutions
All 65 questions of GATE 2024 IN with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – If ‘→’ denotes increasing order of intensity, then the meaning of the words [drizzle → rain → downpour] is analogous to [ → quarrel → feud]. Which one…
- Question 2 – Statements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes.…
- Question 3 – A student was supposed to multiply a positive real number p by another positive real number q. Instead, the student divided p by q. If the percentage…
- Question 4 – If the sum of the first 20 consecutive positive odd numbers is divided by 202, the result is
- Question 5 – The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of…
- Question 6 – Select the best match for blanks (i)–(iv). Yoko Roi stands (i) as an author for standing (ii) as an honorary fellow, after she stood (iii) her…
- Question 7 – Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container, as shown. The container has the same length as the…
- Question 8 – The plot shows the relationship between cardiovascular-disease mortality risk and the number of steps a person walks per day. Based on these data,…
- Question 9 – Five cubes of identical size and one smaller cube are assembled as shown in Figure A. Viewed from direction X, their planar image is Figure B. Which…
- Question 10 – Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view…
- Question 11 – Let z=x+iy be a complex variable and z its complex conjugate. The equation z2+z2=2 represents a
- Question 12 – The pressure drop across a control valve is constant. Its inherent characteristic has decreasing sensitivity. If x is the fraction of maximum stem…
- Question 13 – A discrete-time sequence is x[n]=[1,2,3,4] for 0 n3. Its zero-lag autocorrelation is
- Question 14 – Match the measuring devices to their principles. Device Principle --- --- P. Optical pyrometer I. Variation in mutual inductance Q. Thermocouple II.…
- Question 15 – The parallel-plate capacitor shown has plate area A. Its dielectric-layer thicknesses are d 1,d 2 and relative permittivities 1=1 (air), 2 (solid),…
- Question 16 – The simplified form of the Boolean function F=(A+ A B)+ A(A+ B)C is
- Question 17 – Consider x=Ax+Bu, where x is the state vector, u the input, A the system matrix, and B the input matrix. Which matrix A gives a system pole at the…
- Question 18 – The sinusoidal transfer function corresponding to the polar plot shown, for T>0, is
- Question 19 – A matrix M=[v 1\ v 2\ v 3] is formed by stacking three column vectors. Which set gives rank(M)=3? Tuples below denote column vectors.
- Question 20 – Two concentric spherical metal shells have radii x,y with y>x. If the intervening medium has permittivity , their capacitance is
- Question 21 – A linear transducer is calibrated over the ranges shown: input temperature 50–150 °C and output current 4–20 mA. Its gain is mA/°C (two decimal…
- Question 22 – A filter is defined by y[n]-0.5y[n-2]=a\,x[n-4], where x[n],y[n] are input and output. If H(/2) =0.5, the value of a is (two decimal places).
- Question 23 – Consider the circuit shown. The CMOS digital logic has infinite input impedance and the opamp is ideal. A 1.8 V Zener diode requires a minimum Zener…
- Question 24 – The figure shows an NMOS amplifier. The transistor operates in saturation with n C ox=250\ A/ V2, V T=0.65 V, and W/L=4. Neglect channel-length…
- Question 25 – The number of complex multiplications required for a 16-point DFT using the decimation-in-time radix-2 FFT is (integer).
- Question 26 – A real 33 matrix P has eigenvalues 1/4,1,-2. The determinant P-1 is (nearest integer).
- Question 27 – The Nyquist sampling frequency for x(t)=102(200 t) is Hz (nearest integer).
- Question 28 – A 20 kΩ resistor is measured six consecutive times using an LCR meter. The first five readings are 19, 18, 23, 21, and 17 kΩ. If the mean equals the…
- Question 29 – The figure shows the readout circuit of a piezoelectric sensor. A generated charge q p produces a change of -2 V at V x. The corresponding change in…
- Question 30 – A circuit has voltage v(t)=95+200(120 t)+90(360 t-60) V and current i(t)=4(120 t-60)+1.5(240 t-75) A. Its average absorbed power is W (nearest…
- Question 31 – The current drawn is i(t)=4+30 t-20 t+15(3t)-10(3t) A. Its RMS value is A (one decimal place).
- Question 32 – The 0–10 kΩ linear potentiometer shown measures water level. Resistance between A and C changes linearly from 0 to 10 kΩ as water level changes from 0…
- Question 33 – The switch shown has been closed for a long time (t<0) and opens at t=0. The initial voltage derivative dv C/dt at t=0+ is V/s (nearest integer).
- Question 34 – A system satisfies dy/dt=y+2t-t2, with y(0)=1 and 0 t<. Using improved Euler with step size h=0.1, the value of y(0.1) is (two decimal places).
- Question 35 – Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while…
- Question 36 – A circular wire of radius a has current density J=ks2, where k is constant and s is radial distance from the axis (0 s a). Its total current is
- Question 37 – The measured values from a flow instrument, whose range is between 0 and 2 flow units, are shown in the histogram. The systematic error (bias) and the…
- Question 38 – For x[n]=cases(0.2)n,&0 n7\\0,&otherwisecases, the region of convergence of its z-transform consists of
- Question 39 – In the bridge circuit shown in the figure, under balanced condition, the values of R and C respectively, are
- Question 40 – A signal has bilateral Laplace transform X(s)=1/(s2+13s+42) with region of convergence -7<Re(s)<-6. If u(t) is the unit step, which signal is x(t)?
- Question 41 – The opamps A 1,A 2 shown are ideal, except that A 1 has offset voltage V OS=1 mV. For V in=0 V, the output voltages V out1,V out2, respectively, are
- Question 42 – The positive-edge-triggered D flip-flops shown are initially reset to Q=0. Gates and multiplexers have no propagation delay. After reset, clock pulses…
- Question 43 – In the circuit shown, R = 1 kΩ and C = 0.1 μF. For a DC gain of −10, the 3 dB cutoff frequency (one decimal place) is as follows. Assume the opamp is…
- Question 44 – For the feedback control system shown, the steady-state error e ss= t[r(t)-y(t)] due to a unit-step reference r(t) is
- Question 45 – A system has G(s)= n2/(s2+2 n s+ n2). Choose the ranges of and n (rad/s) such that its poles lie in the shaded region of the s-plane shown.
- Question 46 – Let C be the counterclockwise boundary of the rectangle with vertices (0,0),(2,0),(2,1),(0,1). The value of C(-ey\,dx+ex\,dy) is
- Question 47 – For the wattmeter circuit shown, define the following angles: : between load current and load voltage; : lag of pressure-coil current behind its…
- Question 48 – In the ultrasonic measurement system shown, transmitter T sends x(t)=(2 f 1t) V toward an object vibrating as m(t)=0.5(2 f 2t) V. Neglecting other…
- Question 49 – Both f(z)=u(x,y)+iv(x,y) and f(z)=u(x,y)-iv(x,y) are analytic in a domain. Choose all correct statements.
- Question 50 – A 20-psig pressure gauge gives the following readings. Its regression line is y=0.04x+10.32. The coefficient of determination R2 is (three decimal…
- Question 51 – In the circuit shown, R=4.5 kΩ, R=1.5 kΩ, and the instrumentation amplifier INA is ideal. The equivalent resistance between A and B is kΩ (nearest…
- Question 52 – Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched ON at t = 0. Assuming the opamp to be…
- Question 53 – The 4-point DFTs of x[n],y[n] are X[k]=[1,-j,1,j] and Y[k]=[1,3j,1,-3j]. If z[n] is their 4-point circular convolution, z[0] is (nearest integer). The…
- Question 54 – Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor Rx is Ω (rounded off to nearest integer).
- Question 55 – A unity-negative-feedback system has the open-loop pole-zero map shown; crosses mark poles. If s=j, >0, lies on its root locus, is (nearest integer).
- Question 56 – A shielded cable with C stray=20 pF and R wire=10 Ω connects the inductive sensors shown. The RMS value of V out is V (two decimal places). All…
- Question 57 – The diode in the circuit shown obeys I D=I S e V D/T, where V D is in volts, T is absolute temperature in kelvin, =1.16104 K/V, and I S=10-15 A. The…
- Question 58 – An ADC has full-scale voltage 1.4 V, resolution 200 mV, and binary output. It samples a 500 MHz bandwidth signal at the Nyquist rate. A…
- Question 59 – In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time t = 2 ms is V (rounded off…
- Question 60 – The switch SW shown changes from position 1 to 0 when V C changes from logic HIGH to LOW, and vice versa. The PMMC voltmeter bandwidth is 1 Hz. For V…
- Question 61 – A 50 kVA transformer has efficiency 95% at full load and unity power factor. Core loss is negligible. Its efficiency at 75% of full load and power…
- Question 62 – A three-phase squirrel-cage induction motor has starting torque 100% of full-load torque and maximum torque 300% of full-load torque. Neglect stator…
- Question 63 – Two magnetically coupled coils have total inductance 500 mH in series aiding and 300 mH in series opposing. Their self-inductances are equal. The…
- Question 64 – The differential equation y+3y+3y+y=30e-t has solution y(t)=(c 0+c 1t-c 2t2+c 3t3)e-t. Given y(0)=3, y(0)=-3, y(0)=-47, the value of c 0+c 1+c 2+c 3…
- Question 65 – A random variable X has density f X(x)=e-x for x0 and zero otherwise. The probability P(X>2) is (three decimal places).