GATE 2014 EC (EC3) – Previous Year Questions with Solutions
All 65 questions of GATE 2014 EC (EC3) with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – “India is a country of rich heritage and cultural diversity.” Which supplied fact best supports the claim?
- Question 2 – One US dollar costs ₹65 today compared with ₹60 last year. The Indian rupee has .
- Question 3 – “Advice” is .
- Question 4 – Find the next term: 81,54,36,24,…
- Question 5 – Which relation definitely implies P < M?
- Question 6 – Find the next term: 7G,11K,13M,…
- Question 7 – The hierarchical pie chart shows animal populations in a reserve forest. Which conclusions follow from the chart? (i) Butterflies are birds. (ii)…
- Question 8 – A man rows at 8 km/h in still water. Rowing upstream takes three times as long as rowing the same distance downstream. Find stream speed (km/h).
- Question 9 – An air-purifier firm sold 200 units in 2012. The chart shows manufacturing cost shares. Labour expenditure was ₹4,50,000. In 2013 raw-material…
- Question 10 – A batch of 100 bulbs is inspected by testing four randomly chosen bulbs. It is rejected if any tested bulb is defective. A batch typically contains…
- Question 11 – For x>-1, find the x maximizing f(x)=(1+x)-x.
- Question 12 – Which is a linear nonhomogeneous differential equation, with independent variable x and dependent variable y?
- Question 13 – Match applications P1: numerical integration; P2: transcendental equation; P3: system of linear equations; P4: differential equation with methods M1:…
- Question 14 – An unbiased coin is tossed infinitely many times. Find the probability that the fourth head appears on toss ten.
- Question 15 – If z=xy(xy), which derivative identity holds?
- Question 16 – A series RC circuit connects to DC source at t = 0, with V S=Ri(t)+1C 0ti(u)\,du. Which graph represents i(t)?
- Question 17 – Find current I (A) in the circuit shown.
- Question 18 – During which MOSFET fabrication process is channel length defined?
- Question 19 – A thin p-type silicon sample is uniformly illuminated, creating excess carriers. Recombination rate is directly proportional to .
- Question 20 – At 300 K, hole mobility is 500 cm²/(V·s) and kT/q = 26 mV. Find hole diffusion constant D p (cm²/s).
- Question 21 – A transconductance amplifier should have .
- Question 22 – The PNP transistor shown has V BE = 0.7 V and β = 50. R B = 100 kΩ. For output V₀ = 5 V, find R C (kΩ).
- Question 23 – The half-wave rectifier shown uses an ideal diode. Find approximate average steady-state diode current (A).
- Question 24 – An analog voltage range 0–8 V is divided into 16 equal intervals for a four-bit output. Find maximum quantization error (V).
- Question 25 – Identify the circuit shown.
- Question 26 – Which Boolean function does the multiplexer circuit realize?
- Question 27 – x(t)=(10 t)+(30 t) is sampled at 20 Hz and reconstructed using an ideal low-pass filter with cutoff 20 Hz. Which frequencies are present?
- Question 28 – An all-pass system has H(z)=(z-1-b)/(1-az-1), with H(e-j) =1 for every . If Re(a) and Im(a) are nonzero, find b.
- Question 29 – y(t)=m(t)(40000 t), where m(t) contains only frequencies below 5 kHz. Find the minimum sampling rate for y(t) that permits recovery of m(t) (kHz).
- Question 30 – Find C(s)/R(s) for the block diagram shown.
- Question 31 – Input -3e2tu(t), with unit step u(t), drives a system with transfer (s-2)/(s+3). Output initial value is −2. Find steady-state output.
- Question 32 – A received passband waveform has phase (f)=-2(f-f c)-2 f c, with center frequency f c and positive ,. Find actual signal propagation delay.
- Question 33 – For FM f(t)=[2 f ct+ 1(2 f 1t)+ 2(2 f 2t)], find maximum instantaneous-frequency deviation from f c.
- Question 34 – An air-filled rectangular waveguide has cross-section 5 cm × 3 cm. Find TE₂₁ cutoff frequency (MHz).
- Question 35 – Transmitter Tx sends a wideband modulated RF signal through the coaxial cable shown to receiver Rx. Transmitter output Z T, cable characteristic Z₀…
- Question 36 – Find the maximum of f(x)=2x3-9x2+12x-3 on 0 x3.
- Question 37 – Which statement is NOT true for a square matrix A?
- Question 38 – Toss a fair coin until both head and tail have appeared at least once. Find the average number of tosses required.
- Question 39 – X₁,X₂,X₃ are independent identically distributed uniform variables on [0,1]. Find PX₁ + X₂ ≤ X₃.
- Question 40 – Network N shown has C = 100 µF and R = 10 kΩ. Two such blocks are cascaded as shown. Find V₃(s)/V₁(s).
- Question 41 – Find node voltage V₂ in the circuit shown.
- Question 42 – Find angular frequency ω (rad/s) for which the Norton equivalent impedance seen at b–b′ is purely resistive.
- Question 43 – For the Y-network shown, find R₁ (Ω) in the equivalent Δ-network.
- Question 44 – An abrupt silicon PN diode has donor concentration 1016 cm⁻³ and acceptor concentration 51018 cm⁻³. At 300 K, n i=1.51010 cm⁻³, kT/q=26 mV and…
- Question 45 – For an n-channel MOSFET, the linear-regime slope of I D versus V GS is 10-3 Ω⁻¹ at V DS = 0.1 V. Neglect channel length modulation. Find…
- Question 46 – An ideal MOS capacitor has boron substrate doping 1015 cm⁻³. Applied gate voltage forms a 0.5 µm depletion region with surface potential 0.2 V. Given…
- Question 47 – The silicon BJT shown has β = 50, V BE = 0.7 V and V CE(sat) = 0.2 V. Which statement is correct?
- Question 48 – For the ideal op-amp circuit shown, find V₀.
- Question 49 – MOSFET M₁ shown has W/L = 2, V DD = 2 V, nC ox=100 µA/V² and V TH = 0.5 V. Find Vin (V) where M₁ changes from saturation to linear operation.
- Question 50 – WL denotes word line and BL bit line. Which diagram is an SRAM cell?
- Question 51 – W and Y are the most significant control-input bits of the respective multiplexers shown. Find output F.
- Question 52 – With inputs X,Y, difference D = X − Y and borrow B, which diagram implements a half-subtractor?
- Question 53 – H 1(z)=(1-pz-1)-1, H 2(z)=(1-qz-1)-1 and H(z)=H 1(z)+rH 2(z), with real p,q,r. For p = 1/2, q = −1/4 and r < 1, a zero of H lies on the unit circle.…
- Question 54 – A causal system has transfer 1/(s+1) and impulse response h(t). S1: It is stable. S2: h(t+1)/h(t) is independent of t for t > 0. S3: A noncausal…
- Question 55 – X(z)=1/(1-2z-1)2, ROC z > 2. Find x[2].
- Question 56 – Find the steady-state error of the system shown for a unit-step input.
- Question 57 – An unforced system obeys x=A x. Initial state (1,-1)T gives x(t)=(e-t,-e-t)T; initial state (0,1)T gives (e-t-e-2t,-e-t+2e-2t)T. Find the response to…
- Question 58 – The root-locus plot has its pole/zero marks and arrows removed. Which transfer function corresponds to it?
- Question 59 – A WSS process X(t) has PSD S X(f). For Y(t) = X(2t−1), find S Y(f).
- Question 60 – A real band-limited random process has two-sided PSD S X(f)=10-6(3000- f ) W/Hz for f ≤ 3000 Hz, and zero otherwise. It modulates (16000 t); the…
- Question 61 – A PCM system samples m(t)=(100 t)+(100 t) V at the Nyquist rate and uniformly quantizes with step 0.75 V. Find minimum data rate (bits/s).
- Question 62 – A binary X has P(X = 1) = 1/3 and enters the shown cascade of two independent identical BSCs, each crossover probability 1/2. Outputs are Y₁,Y₂. Find…
- Question 63 – A=( x)( y) a x+( x)( y) a y. Find A .
- Question 64 – The region shown contains a perfectly conducting half-space and air. Surface current is K s=2 x A/m. Find tangential H in air just above the…
- Question 65 – A plane wave in air has E=10( t-3x-3z) a y V/m. It strikes a nonmagnetic dielectric slab with relative permittivity 3 occupying z > 0. Find angle of…