GATE 2014 EC (EC1) – Previous Year Questions with Solutions
All 65 questions of GATE 2014 EC (EC1) with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – The aircraft take off as soon as its flight plan was filed. Choose the most appropriate phrase.
- Question 2 – All women are entrepreneurs. Some women are doctors. Which conclusion follows logically?
- Question 3 – Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped such notions.
- Question 4 – Runs scored in a series have these (average, standard deviation) statistics: K(31.2,5.21), L(46.0,6.35), M(54.4,6.22), N(17.9,5.90). Who is the most…
- Question 5 – Find the next number: 12, 35, 81, 173, 357, .
- Question 6 – Find the odd group of letters.
- Question 7 – For tax returns, resident males with annual income below ₹10 lakh fill Form P; resident females below ₹8 lakh fill Form Q. All people above ₹10 lakh…
- Question 8 – A 280-metre train at uniform speed crosses a platform in 60 seconds and passes a man standing on it in 20 seconds. Find platform length (metres).
- Question 9 – The chart gives a country’s exports and imports (₹ crore) from 2000 to 2007. Trade deficit is imports minus exports. In which year is the deficit…
- Question 10 – Three coins have faces HH, TT and HT. Choose one at random and toss it; the result is a head. Find the probability that its other face is a tail.
- Question 11 – For same-dimension matrices M,N and scalar c, which property does NOT always hold?
- Question 12 – Half the families in a housing society have one child each; the remaining half have two each. Find the probability that a child picked at random has a…
- Question 13 – C is the closed path z =3. Evaluate Cz2-z+4jz+2j\,dz.
- Question 14 – A real 4 × 4 matrix A satisfies A2=I, where I is the identity. Find the positive eigenvalue of A.
- Question 15 – X₁,X₂,X₃ are independent identically distributed uniform random variables on [0,1]. Find PX₁ is the largest.
- Question 16 – For maximum power transfer between cascaded network sections, how should the first section’s output impedance Z₁ relate to the second section’s input…
- Question 17 – The figure is part of a larger electrical network. For R = 1 Ω, i₁ = 2 A, i₄ = −1 A and i₅ = −4 A, which is TRUE?
- Question 18 – A photodiode receives optical power 10 µW and has responsivity 0.8 A/W. Find generated photocurrent (µA).
- Question 19 – In the circuit, PN diode D₁ has forward drop 0.7 V and Schottky diode D₂ has forward drop 0.3 V. ON means conducting and OFF means nonconducting.…
- Question 20 – Fixed positive charges in the gate oxide of an n-channel enhancement MOSFET lead to .
- Question 21 – A good current buffer has .
- Question 22 – For the AC-equivalent circuit shown, iᵢₙ is the input current and R F is very large. Identify the feedback type.
- Question 23 – For the low-pass filter shown, find R₂ (kΩ) for a cutoff frequency of 5 kHz.
- Question 24 – The pass-transistor circuit uses identical NMOS devices with threshold 1 V. Ignore body effect. Find output voltages at P,Q,R, respectively.
- Question 25 – Simplify (X+Y)(X+ Y)+(X Y)+ X.
- Question 26 – Five JK flip-flops are cascaded as shown. Applied clock frequency is 1 MHz. Find the waveform frequency at Q₃ (kHz).
- Question 27 – For integer n, the discrete-time signal x[n]=(2n) is .
- Question 28 – Real signals x(t) and y(t) are band-limited to [−500,500] Hz and [−1,1] kHz, respectively. For z(t) = x(t)y(t), find the Nyquist sampling frequency…
- Question 29 – A continuous LTI filter has h(t)=3 for 0 t3, and zero otherwise. A constant input of value 5 is applied. Find steady-state output.
- Question 30 – A unity negative-feedback system has forward transfer G(s)=K/((s+2)(s-1)). Find K placing both closed-loop poles at the same location.
- Question 31 – The feedback system and Nyquist plot of G(s) are shown. Which conclusion is correct?
- Question 32 – A CDMA system has N = 8 chips per signature. Find the maximum users assignable mutually orthogonal signature sequences.
- Question 33 – Find the capacity of a binary symmetric channel with crossover probability 0.5.
- Question 34 – A two-port has S=pmatrixs 11&s 12\ 21&s 22pmatrix. Port 2 is shorted. Find the resulting one-port s 11 parameter.
- Question 35 – A point charge +q is distance d from an infinite grounded metal plate in a medium of permittivity . Find its force.
- Question 36 – Find the Taylor expansion of 3 x+2 x.
- Question 37 – For every real , - g(t)e-j t\,dt= e-22. Let y(t)= -t g()\,d. Evaluate - y(t)\,dt.
- Question 38 – Find the volume under z(x,y)=x+y above the triangle 0 y x, 0 x12.
- Question 39 – J 6=pmatrix0&0&0&0&0&1\\0&0&0&0&1&0\\0&0&0&1&0&0\\0&0&1&0&0&0\\0&1&0&0&0&0\\1&0&0&0&0&0pmatrix reverses the columns of I 6. For P=I 6+ J 6, 0, find…
- Question 40 – A Y-network has arm resistances 10 Ω,10 Ω,11 Ω. Find the lowest resistance (Ω) in its equivalent Δ-network.
- Question 41 – A 230 V rms source feeds two parallel loads: 10 kW at 0.8 leading power factor, and 10 kVA at 0.8 lagging power factor. Find complex power delivered…
- Question 42 – The figure shows periodic x as a function of time. Find its rms value.
- Question 43 – For the circuit shown, find capacitance C (mF) giving critically damped current response i(t).
- Question 44 – A forward-active BJT has V BE=0.7 V, kT/q=25 mV and reverse saturation current I S=10-13 A. Find transconductance (mA/V).
- Question 45 – A silicon diode has p-side doping 1016 cm⁻³ and n-side doping 1017 cm⁻³. Forward bias is 0.3 V. At 300 K, n i=1.51010 cm⁻³ and kT/q=26 mV. Find…
- Question 46 – A depletion N-channel MOSFET is stated to operate in its linear region as a voltage-controlled resistor. Given V TH=-0.5 V, V GS=2.0 V, V DS=5 V,…
- Question 47 – In the voltage regulator shown, the op-amp is ideal; the BJT has V BE = 0.7 V and β = 100. Zener voltage is 4.7 V. For regulated output 9 V, find R…
- Question 48 – The op-amp in the circuit has finite input impedance, infinite voltage gain and zero input offset voltage. Find Vout.
- Question 49 – For the amplifier shown, BJT parameters are V BE = 0.7 V, β = 200 and thermal voltage V T = 25 mV. Find voltage gain vo/vi.
- Question 50 – Find output F of the digital logic circuit shown.
- Question 51 – For F(w,x,y,z)=wy+xy+ wxyz+ w xy+xz+ x y z, find the complete set of essential prime implicants.
- Question 52 – The logic circuit realizes the shown state diagram when Q₁ connects to XOR input A. If XOR is replaced by XNOR, which connection preserves that state…
- Question 53 – Find the z-transform ROC of x[n]=(-1/9)nu[n]-(-1/3)nu[-n-1].
- Question 54 – For periodic x[n]=( n/5), complex Fourier-series coefficients a k are nonzero at k=Bm1, m any integer. Find B.
- Question 55 – A system obeys y(t)+5y(t)=u(t). With y(0) = 1 and unit-step input u(t), find y(t).
- Question 56 – A state-space model is x=pmatrix-1&1&0\\0&-1&0\\0&0&-2pmatrixx+pmatrix0\\4\\0pmatrixu, y=pmatrix1&1&1pmatrixx. The system is .
- Question 57 – Using asymptotic Bode plots, find phase margin (degrees) of G(s)=10/((s+0.1)(s+1)(s+10)).
- Question 58 – The feedback system has G(s)=1/((s+1)(s+2)). Its step response must have 2% settling time below 2 seconds. Which compensator C(s) achieves this?
- Question 59 – For real random variable X, E[X] and E[X²] are the mean values of X and X². Which relation always holds?
- Question 60 – X(t)=2(2 t+), where random phase is uniform on [0,2]. Find E[X(t 1)X(t 2)].
- Question 61 – A BPSK system on AWGN with two-sided noise PSD N 0/2 has BER Q(), where depends on bit energy and noise PSD. In the shown system the same modulated…
- Question 62 – A fair coin is tossed until the first head. L is the number of tosses. Find entropy H(L) (bits).
- Question 63 – In spherical coordinates, the far fields of a free-space dipole are E=(100/r)( t- r) a V/m and H=(0.265/r)( t- r) a A/m. Find average power (W)…
- Question 64 – A parallel-plate transmission line has propagation speed v and characteristic impedance Z. Neglect fringing. Halving plate spacing causes .
- Question 65 – A lossless line has characteristic impedance 50 Ω. The input impedance of a /8 section is real when terminated by Z L=R+jX Ω. For X = 30 Ω, find R…