GATE 2014 EC (EC2) – Previous Year Questions with Solutions
All 65 questions of GATE 2014 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 – Communication and interpersonal skills are important in their own ways.
- Question 2 – She will feel much better if she .
- Question 3 – She could not the thought of the election to her bitter rival.
- Question 4 – A regular six-sided die is thrown a very large number of times. Observed frequencies are 1:0.167, 2:0.167, 3:0.152, 4:0.166, 5:0.168, 6:0.180. This…
- Question 5 – Fill the missing number: 2, 3, 6, 15, , 157.5, 630.
- Question 6 – Find the odd group of letters.
- Question 7 – Each ladder step has two lights, chosen from red, blue, green and yellow. Whenever a light is red, the other on its step is blue. Whenever one is…
- Question 8 – Eight consecutive odd numbers sum to 656. Four consecutive even numbers average 87. Find the sum of the smallest odd number and second-largest even…
- Question 9 – The pie charts show export quantity shares and export revenue shares by item. Total exports are 500 thousand tonnes, earning ₹250 crore. Which listed…
- Question 10 – A half-full tank empties in 30 minutes at a constant drain rate. Water is pumped in while draining continues. What pumping rate fills it completely in…
- Question 11 – det(A) = 5 and det(B) = 40. Find det(AB).
- Question 12 – X is chosen uniformly from the positive odd integers below 100. Find E[X].
- Question 13 – For 0 t<, where does f(t)=e-t-2e-2t attain its maximum?
- Question 14 – Evaluate x(1+1/x)x.
- Question 15 – The characteristic equation of d2y/dx2+2\,dy/dx+y=0 has equal roots. Find possible .
- Question 16 – Norton’s theorem replaces a complex network connected to a load by an equivalent impedance .
- Question 17 – The ideal switch shown has been open for a long time. It closes at t = 0. Find the magnitude of current through the 4 kΩ resistor at t = 0⁺ (mA).
- Question 18 – A silicon bar has donor doping N D=2.251015 atoms/cm³. At 300 K, n i=1.51010 cm⁻³. Assuming complete ionization, find equilibrium electron and hole…
- Question 19 – Increasing base recombination in a BJT increases .
- Question 20 – Shallow P-well or N-well regions in CMOS technology can be formed using .
- Question 21 – Identify the feedback topology of the amplifier shown. Base-bias circuitry is omitted for simplicity.
- Question 22 – In the differential amplifier shown, common-mode and differential-mode gain magnitudes are A cm and A d. If R E increases, which occurs?
- Question 23 – Two cascaded voltage amplifiers are shown. A1 has open-loop voltage gain 10, input resistance 10 kΩ, output resistance 1 kΩ. A2 has corresponding…
- Question 24 – For an n-variable Boolean function, the maximum number of prime implicants is .
- Question 25 – How many bytes represent decimal 1856357 in packed BCD?
- Question 26 – A half-subtractor has inputs X,Y and difference N = X − Y. Find borrow M and difference N.
- Question 27 – An FIR system has H(z)=1+72z-1+32z-2. Classify it.
- Question 28 – x[n]=x[-n], and X(z) is its z-transform. If 0.5+j0.25 is a zero, which must also be a zero?
- Question 29 – For the periodic square wave shown, find the approximate ratio of power in the seventh harmonic to that in the fifth.
- Question 30 – A second-order system has undamped natural frequency 40 rad/s and damping ratio 0.3. Find damped natural frequency (rad/s).
- Question 31 – For the system shown, find Y(s)/X₂(s) when X₁(s) = 0.
- Question 32 – AWGN capacity is C=W 2(1+P/(2W)) bps, where W is bandwidth, P average received power and 2 one-sided noise PSD. For fixed P/2=1000, find capacity as W…
- Question 33 – In sinusoidal AM without overmodulation, envelope maximum and minimum are 3 V and 1 V. Find modulation index µ.
- Question 34 – The shown lossless transmission line is matched to a resistive load by a λ/4 transformer. Find transformer characteristic impedance (Ω).
- Question 35 – Which TEM field pattern travels in the positive x direction?
- Question 36 – The linear system pmatrix2&1&3\\3&0&1\\1&2&5pmatrixpmatrixa\\pmatrix=pmatrix5\\-4\\14pmatrix has .
- Question 37 – The real part of analytic f(z), z = x + jy, is e-y x. Which is its imaginary part?
- Question 38 – Find the maximum determinant of a real symmetric 2 × 2 matrix with trace 14.
- Question 39 – Let r=x a x+y a y+z a z and r= r . Evaluate div(r2 r).
- Question 40 – A series LCR circuit operates off resonance with current leading supply voltage. Current magnitude is half its resonant value. Given L = 1 H, C = 1 F…
- Question 41 – For the two-port circuit shown, find hybrid parameter h₂₂ (S).
- Question 42 – The capacitor shown is initially uncharged. Find branch current I(t) (mA) for t > 0.
- Question 43 – In the coupled circuit shown, 56% of total flux from one coil links the other. Find mutual inductance (H).
- Question 44 – Given q=1.610-19 C, kT/q=25 mV and n=1000 cm²/(V·s), electrons injected into p-type silicon have concentration gradient 1021 cm⁻⁴. Find…
- Question 45 – The abrupt PN junction shown is at 300 K. N-side depletion width X n=0.2 µm and silicon permittivity si=1.04410-12 F/cm. Find peak junction electric…
- Question 46 – A reverse-biased silicon diode has N A=91016 cm⁻³, N D=1016 cm⁻³ and total depletion width 3 µm. Silicon permittivity is 1.0410-12 F/cm. Find p-side…
- Question 47 – The diode shown has V on = 0.7 V and is otherwise ideal. If Vi = 5 sin(ωt) V, find minimum and maximum Vo (V), respectively.
- Question 48 – The NMOS shown has threshold 0.8 V. Ignore channel length modulation. At drain voltage V D = 1.6 V, I D = 0.5 mA. Adjust R and V DD to obtain V D = 2…
- Question 49 – The MOSFETs shown have V t =2 V and K=12 C ox(W/L)=0.1 mA/V². Find I D (mA).
- Question 50 – For the circuit shown, select the output y timing diagram from W1,W2,W3,W4.
- Question 51 – Both flip-flop outputs Q₁,Q₂ start at 0. Find the sequence generated at Q₁ by the clock.
- Question 52 – The figure shows an 8085 interface for input of eight-bit digital data DI₀–DI₇ from an external device. Which instruction transfers it correctly?
- Question 53 – x[n]=n for 0 n10, and zero otherwise. If y[n] is x[n] convolved with itself, find y[4].
- Question 54 – A causal stable LTI system has y[n]= y[n-1]+ x[n]. Its impulse response satisfies n=0 h[n]=2. Find the relation between ,.
- Question 55 – Evaluate -sinc2(5t)\,dt.
- Question 56 – An unforced LTI system obeys x=pmatrix-1&0\\0&-2pmatrixx. For x 1(0)=1, x 2(0)=-1, find its state response.
- Question 57 – A minimum-phase system has the shown asymptotic Bode magnitude plot. Connected in unity negative feedback, find its closed-loop steady-state error for…
- Question 58 – For the state-space system represented by the signal-flow diagram, which property always holds?
- Question 59 – A one-bit quantizer input X has density f X(x)=2e-2x for x0, and zero otherwise. Find the threshold making the two outputs equiprobable.
- Question 60 – Coherent orthogonal binary FSK sends equiprobable s 1(t)=(2 f 1t) and s 2(t)=(2 f 2t), with =4 mV, through AWGN having two-sided PSD N 0/2=0.510-12…
- Question 61 – A real stationary process X(t) has PSD S X(f)=1/W for f W, and zero otherwise. Find E[ X(t)X(t-1/(4W))].
- Question 62 – The figure gives the message spectrum M(f), with A = 100 Hz and B = 40 Hz. Modulating signals are v(t)=(2 f ct) and w(t)=(2(f c+A)t), with f c>A. Both…
- Question 63 – A plane wave has E(z,t)=3 x( t-kz+30)-4 y( t-kz+45) mV/m. Find its polarization.
- Question 64 – For the transmission line shown, find impedance Zin (Ω) between node A and ground.
- Question 65 – A rectangular waveguide has internal dimensions a × b, a > b. TE₁₁ cutoff is the arithmetic mean of TE₁₀ and TE₂₀ cutoffs. Given a=5 cm, find b (cm).