GATE 2016 EC (EC3) – Previous Year Questions with Solutions
All 65 questions of GATE 2016 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 – An apple costs Rs. 10 and an onion costs Rs. 8. Select the most suitable sentence with respect to grammar and usage.
- Question 2 – The Buddha said, “Holding on to anger is like grasping a hot coal with the intent of throwing it at someone else; you are the one who gets burnt.”…
- Question 3 – M has one son Q and one daughter R, with no other children. E is P’s mother and M’s daughter-in-law. How is P related to M?
- Question 4 – Which number least fits the set (324,441,97,64)?
- Question 5 – Two constant-speed trains take 10 s and 15 s respectively to pass a telegraph post completely. Their lengths are 120 m and 150 m respectively. The…
- Question 6 – A vehicle’s velocity along a straight line, in m/s, is plotted against time in seconds. How much does its odometer reading increase over the 7…
- Question 7 – The overwhelming number of people infected with rabies in India has been flagged by the World Health Organization as a concern. Inoculating 70% of…
- Question 8 – Four first-year undergraduates share a flat and give the oldest extra space. Manu is two months older than Sravan, who is three months younger than…
- Question 9 – Find the area bounded by 3x+2y=14 and 2x-3y=5 in the first quadrant.
- Question 10 – A straight line is fitted to ( x,y) data. It crosses the horizontal axis at x=0.1 and has slope −0.02. Its fitted y at x=5 is
- Question 11 – Consider the matrix A=bmatrix&x\\&bmatrix. If its eigenvalues are +j and -j, the unknown x equals
- Question 12 – For f(z)= z/z2, the residue at the pole z=0 is .
- Question 13 – A biased coin gives a head with probability 0.3. It is tossed independently until a head appears. The probability that the first head occurs on toss…
- Question 14 – The integral 01 dx/1-x equals .
- Question 15 – Consider y=y+2x-x2, y(0)=1, for 0 x<, with exact solution y(x)=x2+ex. At x=0.1, the percentage difference between the exact solution and one iteration…
- Question 16 – Let x(t)=(6 t)+(8 t), with t in seconds. The Nyquist sampling rate in samples/s for y(t)=x(2t+5) is
- Question 17 – If x(t)=[ t/( t)]*[ t/( t)], where * denotes convolution, x(t) is
- Question 18 – The signal x[n]=[n-3]+2[n-5] has z-transform X(z). If Y(z)=X(-z) is the transform of y[n], then
- Question 19 – For the RLC circuit shown, v i(t)=2(200t)+4(500t) V. The output voltage is
- Question 20 – The room-temperature I–V curves of diodes made from materials X,Y,Z are shown. They are uniformly doped and otherwise identical. With material band…
- Question 21 – The figure shows the band diagram of a metal–oxide–semiconductor structure. Its surface region is in
- Question 22 – The shown solar-cell I–V curve is measured under uniform illumination of 100\ mW/cm2. The cell area is 3\ cm2 and fill factor 0.7. Its maximum…
- Question 23 – D1 and D2 are ideal, and the two capacitors are identical. RC is much greater than the ac period and the diodes do not break down in reverse bias. The…
- Question 24 – For the circuit shown, assume V BE1=V EB2=0.7 V. The dc collector voltage V C2 in volts is .
- Question 25 – For the 555 astable multivibrator shown, the oscillation frequency at output pin 3 in kHz is .
- Question 26 – In an 8085, the accumulator is A7 hexadecimal and the carry flag is 0. After executing RLC, the accumulator and carry respectively are
- Question 27 – The logic function realized by the circuit below is
- Question 28 – The minimum number of 2-input NAND gates needed to implement a 2-input XOR is
- Question 29 – For the feedback block diagram shown, the overall closed-loop gain G is
- Question 30 – A unity-negative-feedback system has open-loop G(s)=2/[s(s+1)], as shown. Its steady-state error to a unit step is
- Question 31 – A superheterodyne receiver has intermediate frequency 15 MHz and local oscillator frequency 3.5 GHz. The received signal is above the oscillator…
- Question 32 – A 100 Hz bandlimited analogue baseband signal is sampled at the Nyquist rate. Samples are quantized into independent symbols with probabilities…
- Question 33 – A binary baseband system transmits the pulse p(t)=cases1/T s,&0 t T s,\\0,&otherwise.cases Which graphical choice shows its matched-filter output…
- Question 34 – A right-handed circularly polarized wave is normally incident on a plane perfect conductor. The reflected wave is
- Question 35 – Faraday’s law of electromagnetic induction is described by which equation?
- Question 36 – The initial-value problem y+12y+36y=0, y(0)=3, y(0)=-36 has solution
- Question 37 – An orthogonal basis of R3 is e 1=(1,0,2), e 2=(0,1,0), e 3=(-2,0,1). Express u=(4,3,-3) in this basis.
- Question 38 – A triangle in the xy plane is bounded by 2x=3y, y=0 and x=3. The volume above it and below x+y+z=6 is .
- Question 39 – The integral (2 j)-1 c ez/(z-2)\,dz is taken anticlockwise around a closed contour. Its values with z=2 (i) inside and (ii) outside c are respectively
- Question 40 – The signal 2(2 t/3)-( t) enters an LTI system with H(s)=es+e-s. If C k is the kth exponential Fourier-series coefficient of the output, C 3 equals
- Question 41 – The choices shade regions of convergence in the z plane. For x[n]=2 n , -<n<, which choice gives its z-transform ROC?
- Question 42 – The circuit has reached steady state before t=0, when the 3 Ω resistor burns out and becomes open. The current i(t), in amperes, at t=0+ is .
- Question 43 – In the circuit shown, the current i in amperes, with its indicated downward direction, is .
- Question 44 – The z-parameter matrix of the shown two-port network is
- Question 45 – A continuous speech signal sampled at 8 kHz is grouped into N-sample blocks. Each DFT must be computed in real time by radix-2 decimation-in-frequency…
- Question 46 – The direct-form FIR filter shown can be used to approximate a
- Question 47 – An active npn BJT has the linear excess-electron base profile shown. Emitter–base junction area is 0.001\ cm2, base electron mobility is 800\…
- Question 48 – Two unit-area MOS capacitors are shown. Figure I uses dielectric X of thickness t 1=1 nm and relative permittivity 4, and Y of thickness t 2=3 nm and…
- Question 49 – The Zener I–V curves are shown in Figure I and their series circuit in Figure II. As the supply varies from 0 to 100 V, breakdown occurs in
- Question 50 – In the shown circuit R 1=R 2=R 3=1\ , L=1 μH and C=1 μF. For V in=(106t), the overall voltage gain V out/V in is .
- Question 51 – All transistors in the shown circuit operate in saturation, have nonzero channel-length modulation and negligible body effect. Its small-signal…
- Question 52 – M1 in the shown circuit is saturated with g m=0.01 S. Ignore internal parasitic capacitances and set channel-length modulation to zero. The…
- Question 53 – The figure gives a five-variable K-map for P,Q,R,S,X. The minimum sum-of-products expression is
- Question 54 – In the shown circuit, NOR, multiplexer and inverter delays are 2 ns, 1.5 ns and 1 ns respectively. Inputs P,Q,R,S,T are applied simultaneously. The…
- Question 55 – In the circuit shown, the bubbled NAND gate delay is 2 ns and the counter delay is zero. At a clock frequency of 1 GHz, the counter behaves as a
- Question 56 – The first two rows of a cubic system's Routh table are arrayc ccs3&1&2K+3\2&2K&4array. The stable range of K is
- Question 57 – A second-order LTI system obeys x 1+2x 1=3u(t), x 2+x 2=u(t). The output is c(t)=x 1(t). The system is
- Question 58 – A single-loop negative-feedback system has G(s)=K(s+2)/(s2+2s+2) and H(s)=1, with real K>0. The breakaway-point location on its root locus is .
- Question 59 – A wide-sense stationary process X(t) passes through the shown delay-and-subtract LTI system. If its autocorrelation is R X(), the output…
- Question 60 – A voice-grade AWGN telephone channel has bandwidth 4.0 kHz and two-sided noise spectral density /2=2.510-5 W/Hz. To transmit at 52 kbps with…
- Question 61 – A memoryless binary symmetric channel has bit error probability 10-5. If 105 bits are sent, the probability that no more than one bit is wrong is .
- Question 62 – An air-filled rectangular waveguide has a=2.286 cm and b=1.016 cm. At 10 GHz, the propagation constant per metre of the propagating mode is .
- Question 63 – For an air-filled rectangular waveguide with a=2.286 cm and b=1.016 cm, the increasing order of cutoff frequencies is
- Question 64 – A 5 GHz radar uses one antenna for transmitting and receiving. The antenna gain is 150 and points at a target 1 km away with radar cross-section 3\…
- Question 65 – For the charge-density profile shown, which graphical choice best describes the resultant potential distribution?