GATE 2021 IN – Previous Year Questions with Solutions
All 65 questions of GATE 2021 IN with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Getting to the top is than staying on top.
- Question 2 – The mirror image of the text TRIANGLE about the x-axis is which of the four choices shown?
- Question 3 – In a company, 35% of employees drink coffee, 40% drink tea, and 10% drink both. What percentage drinks neither tea nor coffee?
- Question 4 – Two operators are defined by p q=(p2+q2)/(pq) and p q=p2/q. If x y=22, then x= .
- Question 5 – Four persons P, Q, R, S sit in a row facing the same direction. P and R cannot sit adjacent; S must sit to the right of Q. The number of distinct…
- Question 6 – Statement: Either P marries Q or X marries Y. Which option is its logical negation?
- Question 7 – Two rectangular sheets M and N each measure 6 cm × 4 cm. Folding operation 1 halves the sheet by joining the short edges of its current shape.…
- Question 8 – Five equal-length segments PR, PS, QS, QT, RT form the star shown. The angle is degrees.
- Question 9 – Define (p,q)=cases(p-q)2,&p q\+q,&p<qcases. Evaluate (-(-3+2),(-2+3))-(-2+1).
- Question 10 – Humans have the ability to construct worlds entirely in their minds, which don’t exist in the physical world. So far as we know, no other species…
- Question 11 – Consider row vectors v=(1,0) and w=(2,0). The rank of M=2vTv+3wTw, where T denotes transpose, is .
- Question 12 – For x n=0.5x n-1+1, n=1,2,, with x 0=0, the value of nx n is .
- Question 13 – An infinitely long line with uniform positive charge density lies along the z-axis. In cylindrical coordinates (r,,z), the electric-field direction at…
- Question 14 – The input–output relationship of an LTI system is shown. For the input x[n] shown below it, the peak output value is .
- Question 15 – In an AC mains, measured rms voltage is 100 V ±1%, rms current 1 A ±1%, and power 50 W ±2%, with errors relative to readings. The percentage limiting…
- Question 16 – Let u(t) be the unit step. The bilateral Laplace transform of f(t)=etu(-t) is .
- Question 17 – Which temperature sensor has an exponential input–output characteristic?
- Question 18 – The signal (2 t) is .
- Question 19 – A circuit’s step response oscillates, with oscillations dying down after some time. Which inferences about its input–output transfer function are…
- Question 20 – For a 4-bit flash ADC with full-scale input range V, which statements are true?
- Question 21 – A 16-bit microprocessor has 20 address lines A0–A19 and 16 data lines. Its higher eight data lines connect to the eight data lines of a 16 Kbyte…
- Question 22 – A single-phase transformer has magnetizing inductance 250 mH and core-loss resistance 300 , referred to its primary. With a 230 V, 50 Hz sinusoidal…
- Question 23 – Take clockwise Nyquist encirclements as positive and counterclockwise as negative. The number N of encirclements of (-1,0) for G(s)=3/(s-1) is .
- Question 24 – The diode has fixed forward drop 0.6 V. The ideal OPAMP receives v s=0.4(100 t) as shown. At the positive peak of v s, OPAMP output v OA is V.
- Question 25 – Transistors Q 1,Q 2 have current gains 1=99, 2=49, respectively. For the shown circuit, current I B2 is μA.
- Question 26 – A 300 V, 5 A low-power-factor wattmeter has full-scale power 300 W. For loads on 300 V AC mains, the maximum power factor permitted at its rated…
- Question 27 – A 10-bit ADC has full scale 10.230 V at output (11\,1111\,1111) 2. Its quantization error is mV.
- Question 28 – A strain gauge of nominal resistance 1000 Ω has gauge factor 2.5. At applied strain 100 μm/m, its resistance becomes Ω (two decimal places).
- Question 29 – Given mercury density 13600 kg/m3, gravity 9.81 m/s2, and atmospheric pressure 101 kPa, a mercury U-tube manometer shows liquid-height difference 1…
- Question 30 – A piezoresistive pressure sensor has sensitivity 1 (mV/V)/kPa and DC excitation 10 V. Its output is read using a 3½-digit digital multimeter on the…
- Question 31 – A tone-modulated AM signal has modulation index 0.6. Its power efficiency is % (one decimal place).
- Question 32 – A Michelson interferometer’s movable arm is displaced 325 μm in vacuum (n = 1), and 1000 fringes cross the observation point. The laser wavelength is…
- Question 33 – The minimum of f(x)=-x2+10x+100 on [5,10] is .
- Question 34 – For f(z)=1/(z2+6z+9) in the complex plane, C f(z)\,dz around the circle centred at the origin with unit radius is .
- Question 35 – The determinant of M=bmatrix1&2&0&0\\3&4&0&0\\0&0&4&3\\0&0&2&1bmatrix is .
- Question 36 – The series (z-1)-1-1+(z-1)-(z-1)2+ represents .
- Question 37 – A single-phase transformer has maximum efficiency 98%, core loss 80 W, equivalent winding resistance 0.5 referred to the primary, and rated primary…
- Question 38 – A slip-ring induction motor is started by adding resistance to the rotor circuit. Compared with a shorted rotor, the benefit is .
- Question 39 – A unity negative-feedback system has plant G(s)=1/[(s+1)(s+3)] and PID controller C(s)=K(s+3-j)(s+3+j)/s, with scalar K. The closed loop is .
- Question 40 – The ideal OPAMP has output V o=5 V. The value of R L in the shown circuit is k.
- Question 41 – Boolean F(X,Y,Z)=(X+Y+Z)(X+Y+Z)(X+Y+Z)(X Y Z+X YZ+XYZ). Which expression is true?
- Question 42 – A 10½-digit counter-timer in frequency mode with gate time T s=1 s reads 1000 for a certain input. Without disconnecting it, switch to period mode in…
- Question 43 – A J-type thermocouple gives V =(13650+50 x) μV, with x in °C. It has reference-junction compensation as shown, amplifier gain G=20, reference…
- Question 44 – A laser pulse travels normally from ground level to the bottom of a concrete water tank and returns to a detector at ground level in 100 ns. Water…
- Question 45 – A 4×1 MUX realizes Boolean F(X,Y,Z,W). S 0 is the LSB and S 1 the MSB selector, connected as shown. I 0–I 3 are its inputs. Its canonical…
- Question 46 – The synchronous circuit contains JK and T flip-flops with outputs A and B, respectively, J A=A+B, K A=A+B, and T B=A. Starting at AB=00, its state…
- Question 47 – Independent continuous random variables have uniform distributions X U(2,3) and Y U(1,4). The probability P(Y X) is (two decimal places).
- Question 48 – For A=bmatrix2&5\\0&3bmatrix, the determinant (A4-5A3+6A2+2I) is .
- Question 49 – The electrically conductive square-section bar shown rests on a plane. Its mass is 1 kg and depth along y is 0.5 m. Friction coefficient is 0.1 and…
- Question 50 – A CRGO toroid has inner diameter 10 cm, outer diameter 14 cm, thickness 2 cm, and 200 copper-wire turns. Given 0=410-7 H/m and relative permeability…
- Question 51 – An air-cored coil of winding resistance 10 is in series with variable capacitor C x. A 10 V sinusoidal source has angular frequency 1000 rad/s. As…
- Question 52 – A household fan consumes 60 W and draws 0.3125 A rms from 230 V rms, 50 Hz single-phase mains. Its reactive power is VAR (nearest integer).
- Question 53 – Given y(t)=e-3tu(t)*u(t+3), where * denotes convolution, ty(t) is (two decimal places).
- Question 54 – The shown input signal passes through the filter with the shown taps. The number of nonzero output samples is .
- Question 55 – A sinusoid (2 t)u(t) is applied to G(s)=1/(s+1), where u is the unit step. The steady-state output amplitude is .
- Question 56 – A system G(s)=2/(s+1) receives a unit step u(t) and produces y(t). Define e(t)=y(t)-u(t). Then te(t) is .
- Question 57 – For the shown ideal OPAMP circuit, output Vo is V (one decimal place).
- Question 58 – All transistors shown are matched with current gain =20. Neglect the Early effect. Current I o4 is mA.
- Question 59 – A 400 V rms line-to-line, three-phase, three-wire RYB system is measured with two wattmeters as shown. R-line current is 560 A. R-line wattmeter W 1…
- Question 60 – A 3½-digit rectifier-type digital meter is on its 2000 V range. It measures a symmetrical 50 Hz square wave of amplitude ±100 V. Its reading is V.
- Question 61 – A bar-primary current transformer rated 1000/1 A, 5 VA, UPF has 995 secondary turns. At 1000 A and rated burden, its ratio error is zero and phase…
- Question 62 – The bridge voltmeter reads zero with R 1=100\ , R 2=110\ , R 3=90\ , and R 1/R 2=R A/R B. The value of R 4 is .
- Question 63 – The full bridge shown uses linear strain gauges with gauge factor 2. At 0 °C and zero strain, R 1=R 2=R 3=R 4=100\ . Their temperature coefficient is…
- Question 64 – A signal of bandwidth 5 MHz is transmitted by PCM. It is sampled 50% above the Nyquist rate and quantized into 256 levels. Its binary pulse rate is…
- Question 65 – A large multimode fibre has n core=1.5 and n clad=1.2. A section with cladding removed passes through a liquid of index n liquid. An LED illuminates…