GATE 2025 IN – Previous Year Questions with Solutions
All 65 questions of GATE 2025 IN with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Despite his initial hesitation, Rehman’s to contribute to the success of the project never wavered. Select the most appropriate option to complete the…
- Question 2 – Bird : Nest :: Bee : Select the correct option to complete the analogy.
- Question 3 – If Pex=Qe-x for all real values of x, which one of the following statements is true?
- Question 4 – The paper shown in the figure is folded to make a cube, where each square corresponds to a particular face. Which option correctly represents the…
- Question 5 – Let p 1 and p 2 denote two arbitrary prime numbers. Which statement is correct for all values of p 1 and p 2?
- Question 6 – Based only on the conversation below, identify the logically correct inference: “Even if I had known that you were in the hospital, I would not have…
- Question 7 – If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH ?
- Question 8 – Which option is correct for the data below? Iteration i 0 1 2 3 --- ---: ---: ---: ---: Input I 20 −4 10 15 Output X 20 16 26 41 Output Y 20 −80 −800…
- Question 9 – In the figure, PQRS is a square of side 2 cm and PLMN is a rectangle. Corner L of the rectangle lies on side QR. Side MN passes through corner S of…
- Question 10 – The diagram shows a river system with seven segments P, Q, R, S, T, U, and V, splitting the land into five zones Z1, Z2, Z3, Z4, and Z5. The zones…
- Question 11 – A 2n2n matrix A=[a ij] has elements a ij=cases,&i+j odd,\\-,&i+j even.cases Here n is any integer greater than 2 and is any nonzero real number. The…
- Question 12 – The solution of the differential equation dy/dx=9x/y represents
- Question 13 – The working of the hand-held metal detector most widely used by security personnel for human frisking is based on the principle of
- Question 14 – The primary coil of the LVDT shown is supplied with AC voltage. Its secondary coils are connected in series opposition, with output measured by a true…
- Question 15 – Four identical strain gauges S1, S2, S3, and S4 are mounted on the cantilever force transducer at equal distance from its base. S1 and S2 are on the…
- Question 16 – Let the continuous-time signal be x(t)=ej9t+ej5t, where j=-1 and t is in seconds. The fundamental period of x(t) , in seconds, is
- Question 17 – The minimized Boolean expression Y(P,Q,R) implemented by the shown multiplexer circuit is
- Question 18 – The 4-bit signed two’s-complement result of (5) 10+(5) 10 is
- Question 19 – An infinite uniform charge sheet with s=10\ C/m2 lies in the z=0 plane. The surrounding medium has relative permittivity 10. The electric flux density…
- Question 20 – For the ideal-opamp circuit shown, the ratio V/I is
- Question 21 – In a single-phase AC circuit, a wattmeter measures power consumed by load resistance R L under excitation V S. The same meter is connected in Topology…
- Question 22 – Match the sensors with their most suitable applications. Sensors: P. Rotary Variable Differential Transformer Q. Thermocouple R. Ionization Gauge S.…
- Question 23 – A 312-digit digital voltmeter has specified accuracy (0.5\%+1). If it measures 10 V DC, the error would be . Accuracy is expressed as (\% of…
- Question 24 – Figure (a) is represented by the equivalent T-model in Figure (b). The inductances L 1,L 2,L 3 in the T-model are
- Question 25 – Three admittances Y a=-j0.2 S, Y b=0.3 S, and Y c=j0.4 S are connected in parallel across V s=1045 V. Their currents are I a,I b,I c and the total…
- Question 26 – An oscilloscope has an input resistance of 1 MΩ. A 10X passive attenuating probe is connected to it to increase the input voltage range as well as the…
- Question 27 – For G(s)=1+2s-1s3+5s2+3s+22, the number of zeros in the left half of the s-plane is
- Question 28 – Consider the control-system block diagram in Figure (a). The loop transfer function G(s)H(s) has no poles on the j axis. The counterclockwise contour…
- Question 29 – A Boolean function is X= A B+ A C. The reduced form of X is
- Question 30 – A 60 V DC source with internal resistance R int=0.5\ is connected through a switch to infinitely long rails separated by l=1 m, as shown. They lie in…
- Question 31 – The circuits mentioned in the following options are realized using ideal opamp. Among these, the circuit(s) performing non-linear operation on the…
- Question 32 – One eigenvector of A=bmatrix-1&-1\&-4bmatrix is along bmatrix\\2bmatrix, where is any nonzero real number. The value of x is (in integer).
- Question 33 – For f(z)=2z+1z2-z, where z is complex, the sum of residues at its singular points is (in integer).
- Question 34 – A dual-slope ADC has fixed integration time 100 ms and reference voltage −5 V. Its total time to measure an input of 1.25 V is ms (rounded to the…
- Question 35 – In the shown circuit, assume very high BJT current gain , V BE=0.7 V, and Zener voltage V Z=4.7 V. The LED current I is mA (rounded to two decimal…
- Question 36 – The outward surface integral S(2x+z)\,dy\,dz+(2x+z)\,dx\,dz+(2z+y)\,dx\,dy over the sphere S:x2+y2+z2=9 is
- Question 37 – Newton-Raphson method is used to compute the inverse of the number 1.6. Among the following options, the initial guess of the solution that results in…
- Question 38 – The value of -(6x+4x)\,dx is
- Question 39 – The initially resting causal discrete-time LTI system obeys y[n]=1 y[n-1]+x[n], where >1 is real. If x[n]=[n-p] with p>10, the value of y[p+1] is
- Question 40 – The digital circuit shown has clock frequency 12 MHz. Its output F frequencies for Control = 0 and Control = 1, respectively, are
- Question 41 – The shown chopper amplifier processes a biomedical signal v in(t) into v out(t). Signals v in(t) and v os(t) are band limited to 50 Hz and 10 Hz,…
- Question 42 – An 8-bit microprocessor has 16-bit address bus (A15 − A0) where A0 is the LSB. As shown in Figure (a), it has a pre-installed 4 KB ROM whose starting…
- Question 43 – A 3-bit DAC uses an ideal opamp and switches, each closed when its corresponding digital input is 1, as shown. For input 110, the resistance R in seen…
- Question 44 – A balanced three-phase load is measured by the two-wattmeter method. Its per-phase average power is 30 kW at lagging power factor 3/2. The wattmeter…
- Question 45 – The bridge in Figure (a) has the equivalent circuit in Figure (b). The values of R 1, R 2, and V C are
- Question 46 – A 2-pole, 50 Hz, 3-phase induction motor supplies power to a certain load at 2970 rpm. The torque-speed curve of this machine follows a linear…
- Question 47 – The shown closed-loop system has plant G(s)=1/s2 and lead compensator C(s). The desired dominant closed-loop poles are -1.5 j27/2. The phase lead…
- Question 48 – Let f(t) and g(t) be continuous-time real signals. If h(t) is their cross-correlation using f(t) and g(-t), its Fourier transform H(j) equals . Here…
- Question 49 – Choose the correct statements about Cauchy’s theorem for C f(z)\,dz, where C is a simple closed path in a simply connected domain D.
- Question 50 – The feedback-system plant is P(s)=a/(s2-b2), with a>0 and b>0. Which controller types C(s) cannot stabilize this plant?
- Question 51 – Choose the eigenfunctions of stable linear time-invariant continuous-time systems.
- Question 52 – The probability of a student missing a class is 0.1. In a total number of 10 classes, the probability that the student will not miss more than one…
- Question 53 – A metallic strain gauge of resistance R SG is connected as shown, with lead resistances R L1,R L2,R L3. Gauge factor is 2 and nominal resistance R…
- Question 54 – A length-4 sequence has x[0]=1, x[1]=2, x[2]=2, x[3]=4 and DTFT X(ej). Sampling at k=2 k/3 gives a sequence periodic in integer k with period 3.…
- Question 55 – The shown Michelson interferometer measures a gas refractive index. Its transparent chamber contains gas of index n g1 at atmospheric pressure. A 532…
- Question 56 – The shown AC bridge has R=300\ , R 1=1000\ , R 2=500\ , L=30 mH, and detector D. At balance, excitation frequency is kHz (rounded to two decimal…
- Question 57 – The shown air-filled parallel-plate electrostatic actuator has plate area 100\ m100\ m. With zero charge and spring restoring force, the plate gap is…
- Question 58 – The resistance of a thermistor is measured to be 2.25 kΩ at 30 °C and 1.17 kΩ at 60 °C. Its material constant β is K (rounded off to two decimal…
- Question 59 – The shown feedback control system has disturbance input d(t) and output y(t). The maximum allowable integer n such that any step disturbance produces…
- Question 60 – The shown circuit is driven at 50 Hz by V s=25230 V. Both transformers are ideal. Average power in the 50 kΩ resistor is W (rounded to two decimal…
- Question 61 – The galvanometer G in the shown circuit has internal resistance 100 Ω. Its current I G is μA (rounded to the nearest integer).
- Question 62 – A series RLC circuit resonates at 7500 rad/s for inductance L = 20 mH and resistance R = 10 Ω. The uncertainties in the measurement of L and R are 0.8…
- Question 63 – In the shown circuit, the switch is opened at t=0. The current i(t) at t=2 ms is mA (rounded to two decimal places).
- Question 64 – A signal V M=5( t/3) V is applied to the shown switch-and-capacitor circuit with C=0.1\ F. Output V x feeds an ADC whose input is 10 MΩ in parallel…
- Question 65 – For the circuit shown, the active power supplied by the source is W (rounded to one decimal place).