GATE 2017 EC (EC2) – Previous Year Questions with Solutions
All 65 questions of GATE 2017 EC (EC2) with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – The ninth and the tenth of this month are Monday and Tuesday .
- Question 2 – It is to read this year's textbook the last year's.
- Question 3 – A rule states that to drink beer one must be over 18 years old. In a bar, P is 16, Q is 25, R is drinking milkshake and S is drinking beer. What must…
- Question 4 – Fatima starts at P, travels north 3 km and east 4 km to Q. She turns to face P and travels 15 km in that direction, then travels north 6 km. How far…
- Question 5 – Five hundred students take one or more of Chemistry, Physics and Mathematics. Enrolments are Chemistry 329, Physics 186 and Mathematics 295. Chemistry…
- Question 6 – “If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the…
- Question 7 – Each of P,Q,R,S,W,X,Y and Z has been married at most once. X and Y are married and have children P and Q. Z is the grandfather of S, who is a daughter…
- Question 8 – 1200 men and 500 women can build a bridge in two weeks. Nine hundred men and 250 women take three weeks for the same bridge. How many men alone are…
- Question 9 – The number of three-digit numbers in which digit 1 is never immediately to the right of digit 2 is
- Question 10 – A contour line joins locations having the same height above mean sea level. The geographical contour plot shown has contours at 25 m intervals. Which…
- Question 11 – The rank of the matrix bmatrix1&-1&0&0&0\\0&0&1&-1&0\\0&1&-1&0&0\\-1&0&0&0&1\\0&0&0&1&-1bmatrix is .
- Question 12 – The general solution of the differential equation d2y/dx2+2dy/dx-5y=0, in terms of arbitrary constants K 1 and K 2, is
- Question 13 – The smaller angle (in degrees) between the planes x+y+z=1 and 2x-y+2z=0 is .
- Question 14 – The residues of the function f(z)=1/[(z-4)(z+1)3] are
- Question 15 – In the circuit shown, V is a sinusoidal voltage source. The current I is in phase with voltage V. The ratio of the amplitude of voltage across the…
- Question 16 – A connection consists of resistance A in series with a parallel combination of resistances B and C. Three resistors of values 10\ , 5\ and 2\ are…
- Question 17 – An LTI system with unit sample response h[n]=5[n]-7[n-1]+7[n-3]-5[n-4] is a
- Question 18 – The input x(t) and output y(t) of a continuous-time system are related by y(t)= t-Ttx(u)\,du. The system is
- Question 19 – An n-channel enhancement-mode MOSFET is biased at V GS>V TH and V DS>(V GS-V TH), where the symbols denote gate-to-source voltage, drain-to-source…
- Question 20 – An npn bipolar junction transistor is operating in the active region. If the reverse bias across the base–collector junction is increased, then
- Question 21 – Consider an n-channel MOSFET of width W, length L, channel electron mobility n and oxide capacitance per unit area C ox. Given V GS=0.7 V, V DS=0.1 V,…
- Question 22 – The output V o of the diode circuit shown is connected to an averaging DC voltmeter. The input is 10 t V at 50 Hz. Neglecting the voltage drop across…
- Question 23 – In the figure, D 1 is a real silicon pn-junction diode with a 0.7 V forward drop and D 2 is a Zener diode with breakdown voltage −6.8 V. The input V…
- Question 24 – Consider the circuit shown. Assume base-to-emitter voltage V BE=0.8 V and common-base current gain =1. The collector-to-emitter voltage V CE (in…
- Question 25 – For the circuit shown, P and Q are the inputs and Y is the output. The logic implemented by the circuit is
- Question 26 – Consider the multiplexer circuit shown. The Boolean expression F implemented by the circuit is
- Question 27 – In a DRAM,
- Question 28 – For the system shown in the figure, Y(s)/X(s)= .
- Question 29 – Consider the state-space realization bmatrix x 1\\ x 2bmatrix=bmatrix0&0\\0&-9bmatrixbmatrixx 1\ 2bmatrix+bmatrix0\\45bmatrixu(t), with x 1(0)=x…
- Question 30 – Which of the following statements is incorrect?
- Question 31 – Which of the following graphs shows the Shannon capacity (channel capacity), in bits, of a memoryless binary symmetric channel with crossover…
- Question 32 – Consider the random process X(t)=U+Vt, where U is a zero-mean Gaussian random variable and V is uniform between 0 and 2. Assume U and V are…
- Question 33 – A sinusoidal message signal is converted to PCM using a uniform quantizer. The required signal-to-quantization-noise ratio at the quantizer output is…
- Question 34 – Two conducting spheres S1 and S2, of radii a and b with b>a, are far apart and connected by a long thin conducting wire as shown. For some charge…
- Question 35 – A two-wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power reflected from the…
- Question 36 – The values of the iterated integrals 01( 01x-y(x+y)3\,dy)dx and 01( 01x-y(x+y)3\,dx)dy are
- Question 37 – An integral over a counterclockwise circle C is I= C[(z2-1)/(z2+1)]ez\,dz. If C is defined by z =3, its value is
- Question 38 – If F= a x(3y-k 1z)+ a y(k 2x-2z)- a z(k 3y+z) is irrotational, the constants k 1,k 2,k 3, respectively, are
- Question 39 – Passengers repeatedly try to reserve a seat in any train between two stations until successful. If a passenger has a 40% chance of getting a…
- Question 40 – The minimum value of f(x)=13x(x2-3) on -100 x100 occurs at x= .
- Question 41 – The switch in the circuit shown was open for a long time and is closed at t=0. The current i(t) through the switch, in amperes, at t=0.5 s is .
- Question 42 – Consider the circuit shown, including the dependent voltage source of value 3i 0. The Thevenin equivalent resistance (in Ω) across P–Q is .
- Question 43 – Consider an LTI system with magnitude response H(f)=cases1- f/20,& f20,\\0,& f>20,cases and phase response H(f)=-2f. The input is x(t)=8(20 t+/4)…
- Question 44 – A causal LTI system has transfer function H(s)=1/s. Its input is x(t)=[(t)/( t)]u(t), where u(t) is the unit step. The output y(t) as t is .
- Question 45 – Consider the parallel combination of LTI systems shown. Their impulse responses are h 1(t)=2(t+2)-3(t+1) and h 2(t)=(t-2). If x(t) is a unit step, the…
- Question 46 – A MOS capacitor is fabricated on p-type Si. The metal work function is 4.1 eV, the electron affinity of Si is 4.0 eV, and E C-E F=0.9 eV. The oxide…
- Question 47 – For a particular incident-light intensity on a silicon pn-junction solar cell, photocurrent density J L=2.5 mA/cm² and open-circuit voltage V OC=0.451…
- Question 48 – Two n-channel MOSFETs T1 and T2 are identical except that T2 has twice the width of T1. Both operate in saturation, and T2 has twice the gate…
- Question 49 – An abrupt pn junction at x=0 is uniformly doped on both p and n sides. Its depletion-region width is W, and E(x) is the electric field in the x…
- Question 50 – Assume the transistors M1 and M2 in the circuit shown are identical and each has threshold voltage 1 V. The states of M1 and M2, respectively, are
- Question 51 – In the circuit shown, Q1 and Q2 are each biased at collector current 2.6 mA. Assume their current gains are sufficiently large that collector and…
- Question 52 – In the voltage-reference circuit shown, the op-amp is ideal. Transistors Q1,Q2,…,Q32 are identical and have infinite common-emitter current gain.…
- Question 53 – The state diagram shown is an FSM for detecting an overlapping three-bit sequence. Its input is In, output is Out, and initial state is S0. For input…
- Question 54 – Figure I is a 4-bit ripple-carry adder built from full adders; Figure II shows one full-adder circuit. XOR, AND and OR propagation delays are 20 ns,…
- Question 55 – A programmable logic array is shown. The Boolean function F implemented is
- Question 56 – A unity-feedback control system has open-loop transfer function G(s)=2(s+1)/(s3+ks2+2s+1). The value of k for which the system oscillates at 2 rad/s…
- Question 57 – A second-order LTI system satisfies x 1(t)-x 2(t)=0 and x 2(t)+2x 1(t)+3x 2(t)=r(t). The variables x1 and x2 are states, r(t) is the input, and the…
- Question 58 – A unity-feedback control system has G(s)=10K(s+2)/(s3+3s2+10). Its Nyquist path and Nyquist plot are shown. For 0<K<1, the number of closed-loop poles…
- Question 59 – The signal x(t)=(14000 t), with t in seconds, is sampled at 9000 samples/s. The sampled signal passes through an ideal low-pass filter with H(f)=1 for…
- Question 60 – An AM transmitter has unmodulated carrier power 5 kW and is modulated by a sinusoidal signal. Its maximum modulation percentage is 50%. If this is…
- Question 61 – A modulating signal x(t)=5[4103t-10(2103t)] V is fed to a phase modulator with phase-deviation constant k p=5 rad/V. The carrier frequency is 20 kHz.…
- Question 62 – Consider the binary memoryless channel characterized by the transition-probability diagram shown. The channel is
- Question 63 – An electron q1 moves in free space at 105 m/s toward a stationary electron q2 far away. The closest distance reached before repulsion diverts the…
- Question 64 – Air-filled rectangular waveguides with dimensions a=2.29 cm and b=1.02 cm are intended for radar. They must operate only in the dominant TE10 mode, at…
- Question 65 – Water has optical-frequency permittivity 1.75 0. An isotropic light source at depth d illuminates a circular area of radius 5 m at the surface, as…