GATE 2014 EC (EC4) – Previous Year Questions with Solutions
All 65 questions of GATE 2014 EC (EC4) with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – Which option is closest in meaning to “disagree” in the sentence: “In a democracy, everybody has the freedom to disagree with the government”?
- Question 2 – After the discussion, Tom said to me, “Please revert!”. He expects me to .
- Question 3 – While receiving the award, the scientist said, “I feel vindicated”. Which option is closest in meaning to “vindicated”?
- Question 4 – Let f(x,y)=xnym=P. If x is doubled and y is halved, what is the new value of f?
- Question 5 – In a sequence of 12 consecutive odd numbers, the sum of the first five is 425. Find the sum of the last five.
- Question 6 – Find the next term: 13M, 17Q, 19S, .
- Question 7 – If KCLFTSB stands for “best of luck” and SHSWDG stands for “good wishes”, which indicates “ace the exam”?
- Question 8 – Industrial consumption of power doubled from 2000–2001 to 2010–2011. Find the annual rate of increase (%) assuming it is uniform over the years.
- Question 9 – An air-purifier firm sold 200 units in 2012. The pie chart shows shares of raw material, labour, energy, plant & machinery, and transportation in…
- Question 10 – A five-digit number is formed using 1,3,5,7,9 without repetition. Find the sum of all such five-digit numbers.
- Question 11 – To what does n=01/n! converge?
- Question 12 – Find the magnitude of the gradient of f(x,y,z)=x2+3y2+z3 at (1,1,1).
- Question 13 – X is a zero-mean, unit-variance Gaussian random variable. Find E[ X ].
- Question 14 – If a,b are constants, find the most general solution of d2x/dt2+2dx/dt+x=0.
- Question 15 – Find the directional derivative of f(x,y)=xy2(x+y) at (1,1), in the unit-vector direction making angle /4 with the y-axis.
- Question 16 – What does the circuit shown represent?
- Question 17 – Find the magnitude of current through R₂ (mA) in the circuit shown.
- Question 18 – At 300 K, GaAs has bandgap 1.42 eV and intrinsic carrier concentration 106 cm⁻³. Which incident-wavelength range is most suitable for generating…
- Question 19 – The figure plots i against 1/T for silicon intrinsic resistivity i and temperature T. The plot is almost linear. What can its slope estimate?
- Question 20 – Find the cutoff wavelength (µm) for intrinsic excitation of a semiconductor with bandgap E g = 1.1 eV.
- Question 21 – If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will .
- Question 22 – Two silicon diodes with forward drop 0.7 V form the circuit shown. Find the input-voltage range for which V₀ = V i.
- Question 23 – What does the circuit shown represent?
- Question 24 – For a given sample-and-hold circuit, increasing the hold capacitor causes .
- Question 25 – For C = 0 in the circuit shown, find Y.
- Question 26 – Find output Y of the CMOS circuit shown.
- Question 27 – A Fourier-transform pair is printed as (2/3)nu[n+3] A e-j6 f/[1-(2/3)e-j2 f], where u[n] is the unit step. Find A.
- Question 28 – A real signal x(t) is band-limited to f W/2. It passes through an LTI system with H(f)=e-j4 f for f W/2 and zero otherwise. Find the output.
- Question 29 – x[n]=0.5nu[n] is convolved with itself to obtain y[n]. Find n=-y[n].
- Question 30 – What high-frequency Bode magnitude slope does a fourth-order all-pole system exhibit?
- Question 31 – Find the natural frequency (rad/s) of the second-order closed-loop system shown.
- Question 32 – Calls arrive at a telephone exchange with each arrival time independent of earlier and future arrivals. What distribution models the total number of…
- Question 33 – In double-sideband full-carrier AM, if modulation index doubles, by what factor does the ratio of total sideband power to carrier power increase?
- Question 34 – An antenna radiates in free space. Electric-field magnitude at 1 km is 12 mV/m. Given intrinsic impedance 120 Ω, find average power-density magnitude…
- Question 35 – Match 1: point electromagnetic source; 2: dish antenna; 3: Yagi–Uda antenna, with P: highly directional; Q: end fire; R: isotropic.
- Question 36 – Solve y+4y+4y=0 with y(0)=y(0)=1, and find y(1).
- Question 37 – A parcel goes sequentially through two post offices from S to R. Each independently loses an incoming parcel with probability 1/5. Given that a parcel…
- Question 38 – f(t) has unilateral Laplace transform 1/(s2+s+1). Find the unilateral transform of g(t) = tf(t).
- Question 39 – For a right triangle, the sum of the hypotenuse and one side is fixed. What angle between that side and the hypotenuse maximizes area?
- Question 40 – The circuit has steady-state output y(t)=A()[ t+()]. For A() =0.25, find ω.
- Question 41 – Find v₀(t) as t → ∞ (V) for the circuit shown.
- Question 42 – Find R e/R for the infinite ladder shown.
- Question 43 – Find the impedance matrix Z (Ω) for the two-port network shown.
- Question 44 – A silicon sample has N D=1015 cm⁻³ donors and n i=1.51010 cm⁻³. It is additionally doped with N A=1018 cm⁻³ acceptors. Find the approximate electron…
- Question 45 – Two BJTs have equal collector current and areas A 1=0.20.2 µm² and A 2=300300 µm². All other device parameters are identical; kT/q = 26 mV, n i=1010…
- Question 46 – A uniformly doped N-type semiconductor is biased as shown. E C is the conduction-band minimum, E V the valence-band maximum and E F the Fermi level.…
- Question 47 – The common-collector amplifier shown is in forward active operation; bias circuitry is omitted. I C is collector current, V BE base–emitter voltage, V…
- Question 48 – A common-base BJT amplifies a signal from a 50 Ω antenna. With kT/q = 25 mV, find collector bias current (mA) that matches amplifier input impedance…
- Question 49 – The common-collector amplifier shown has high β, negligible V CE(sat), and V BE = 0.7 V. Find maximum undistorted peak-to-peak output v₀ (V).
- Question 50 – Find Y implemented by the 8-to-1 multiplexer shown.
- Question 51 – A 16-bit ripple-carry adder uses 16 identical full adders as shown. Each has carry-propagation delay 12 ns and sum-propagation delay 15 ns. Find…
- Question 52 – An 8085 executes STA 1234H starting at address 1FFEH. STA copies the accumulator to the specified 16-bit address. During fetch and execution, what…
- Question 53 – A stable LTI system has H(s)=1/(s2+s-6). To make the cascade causal, select a transfer H₁(s) to cascade with it.
- Question 54 – A causal LTI system with zero initial conditions and impulse response h(t) obeys y(t)+ y(t)+2y(t)=x(t). Define g(t)=2 0th()d+h(t)+ h(t). If G(s) is…
- Question 55 – The normalized N-point DFT is X[k]=N-1/2 n=0N-1x[n]e-j2 nk/N for 0 k<N. For N = 4, which sequence satisfies DFT(DFT(x)) = x?
- Question 56 – Find the state-transition matrix for x=pmatrix0&1\\0&0pmatrix x.
- Question 57 – G p(s)=(ps2+3ps-2)/[s2+(3+p)s+(2-p)], with p positive real. Find the maximum value of p until which G p remains stable.
- Question 58 – A unity negative-feedback system has characteristic equation 1+KG(s)=0. G(s) has one pole at 0 and two at −1. The root locus is shown. The…
- Question 59 – A binary signal X has P(X = +1) = 0.75 and P(X = −1) = 0.25. Y = X + Z, with independent zero-mean Gaussian noise of variance σ². A detector outputs…
- Question 60 – The Z-channel shown has equiprobable inputs 0,1. Given that output is 0, find the probability input was 0.
- Question 61 – M-level PSK transmits independent binary digits through a 100 kHz bandpass channel at 200 kbps. The system has a raised-cosine spectrum with 100%…
- Question 62 – A discrete-time channel has Y = X + Z and X ∈ −a,+a. Conditional on X, independent noise Z is Gaussian with mean βX and unit variance. A…
- Question 63 – The one-dimensional electric field between A and B is shown. Their electrostatic potentials are ψ A and ψ B. Find ψ B − ψ A (V).
- Question 64 – F=z a x+x a y+y a z. S is the part of x2+y2+z2=1 with z ≥ 0. Find S( F) d S.
- Question 65 – E=-(2y3-3yz2) x-(6xy2-3xz2) y+6xyz z is described as the electric field in a source-free region. Find a valid electrostatic potential.