GATE 2016 EC (EC2) – Previous Year Questions with Solutions
All 65 questions of GATE 2016 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 – Mr. X is 6 feet tall and Mr. Y is 5 feet tall. Select the appropriate statement with respect to grammar and usage.
- Question 2 – The students the teacher on teachers’ day for twenty years of dedicated teaching.
- Question 3 – After India’s cricket world cup victory in 1985, Shrotria, who had been playing both tennis and cricket, decided to concentrate only on cricket. “And…
- Question 4 – Given (9\ inches)1/2=(0.25\ yards)1/2, which statement is TRUE?
- Question 5 – S, M, E and F work shifts on a project. M works at twice the efficiency of the others but for half as many days as E. S and M have 6-hour daily…
- Question 6 – The Venn diagram gives student preferences for reading books, watching TV and playing sports. The number who like reading books or playing sports is .
- Question 7 – Social science disciplines existed in an amorphous form until colonial times, when they were institutionalized, to varying degrees to further colonial…
- Question 8 – Two and a quarter hours ago, a numberless wall clock seen in a mirror appeared to show 1:30. What is the actual current time shown by the clock?
- Question 9 – M and N start at the same location. M travels 10 km east, then 10 km northeast. N travels 5 km south, then 4 km southeast. The shortest distance…
- Question 10 – A 340 mm wire is cut into two parts. One forms a square and the other a rectangle with side ratio 1:2. What square side length in mm minimizes their…
- Question 11 – The value of x for which the matrix A=bmatrix3&2&4\\9&7&13\\-6&-4&-9+xbmatrix has zero as an eigenvalue is .
- Question 12 – Consider the complex-valued function f(z)=2z3+b z 3, where z is a complex variable. The value of b for which f(z) is analytic is .
- Question 13 – As x varies from −1 to +3, which describes the behaviour of f(x)=x3-3x2+1?
- Question 14 – How many distinct values of x satisfy x=x/2, where x is in radians?
- Question 15 – Consider I=15 x( t)+5 y( t) in Cartesian coordinates, with constant >0. When I is minimum, the angle it makes with the x axis (in degrees, 0180) is .
- Question 16 – In the circuit, V S is a constant voltage source and I L is a constant current load. The value of I L that maximizes the power absorbed by the load is
- Question 17 – The switch has been in position 1 for a long time and changes abruptly to position 2 at t=0. With t in seconds, the capacitor voltage V C in volts for…
- Question 18 – The figure shows a parallel RLC circuit with a sinusoidal current source. At resonance, the ratio I L / I R of the inductor and resistor current…
- Question 19 – The z-parameter matrix of the shown two-port network is bmatrix2j&j\&3+2jbmatrix\ . If Z b(j)=R b+j, the value of R b in ohms is .
- Question 20 – The energy of the signal x(t)=(4 t)/(4 t) is .
- Question 21 – The Ebers–Moll model of a BJT is valid
- Question 22 – A long-channel NMOS is biased in the linear region with V DS=50 mV and used as a resistance. Which statement is NOT correct?
- Question 23 – The diode in the figure has V on=0.7 V but is otherwise ideal. The magnitude of current i 2 in mA is .
- Question 24 – Resistor R 1 has been adjusted so that I 1=1 mA. Transistors Q1 and Q2 are perfectly matched and have very high current gain, so their base currents…
- Question 25 – Which statement is correct about an ac-coupled common-emitter amplifier operating in the mid-band region?
- Question 26 – The transistor geometries of a CMOS inverter meet worst-case charge and discharge time requirements for load C. Convert it into the shown NOR circuit…
- Question 27 – All gates in the shown circuit are ideal. R=10\ k and the supply is 5 V. D1–D5 start with logic values 0,1,0,1,0, respectively. The clock has a 30%…
- Question 28 – A 4:1 multiplexer must generate the output carry of a full adder. A and B are the added bits and select inputs, with A most significant; C in is input…
- Question 29 – The response of G(s)=(s-2)/[(s+1)(s+3)] to unit step u(t) is y(t). The value of dy/dt at t=0+ is .
- Question 30 – The number and direction of encirclements of -1+j0 by the Nyquist plot of G(s)=(1-s)/(4+2s) are
- Question 31 – A discrete memoryless source has alphabet \a 1,a 2,a 3,a 4\ with probabilities \1/2,1/4,1/8,1/8\. The minimum average codeword length in bits for…
- Question 32 – A speech signal is sampled at 8 kHz and encoded in PCM with 8 bits/sample. The PCM data are transmitted over a baseband channel using 4-level PAM. The…
- Question 33 – A constant uniform magnetic field B= zB exists in vacuum. A particle of mass m and small charge q enters with v= xv x+ zv z. All of B,m,q,v x,v z are…
- Question 34 – A plane electromagnetic wave in a homogeneous medium has electric field E= xE x e-j( t- z). The real quantities () and E x are known. Which CANNOT be…
- Question 35 – Light from free space enters the end face of a large-core step-index optical fibre at angle i to the normal. Core and cladding indices are n 1=1.5 and…
- Question 36 – The equation dx/dt=-3x+2, x(0)=1, is solved by forward Euler. The largest time step that can be used without making the numerical solution unstable is…
- Question 37 – C is the circle x2+y2=1 oriented anticlockwise. The value of C(xy2\,dx+x2y\,dy) is .
- Question 38 – The joint density is f X,Y(x,y)=x+y for 0 x1 and 0 y1, and zero otherwise. The probability P(X+Y1) is .
- Question 39 – The matrix A=bmatrixa&0&3&7\\2&5&1&3\\0&0&2&4\\0&0&0&bbmatrix has A=100 and trA=14. The value of a-b is .
- Question 40 – Every resistor in the circuit is 1\ . The equivalent resistance between a and b is
- Question 41 – The magnitude of current through R 2 in the shown circuit, in amperes, is .
- Question 42 – A continuous-time filter H(s)=(2s+6)/(s2+6s+8) is converted to G(z)=2z2-0.5032zz2-0.5032z+k. Its impulse response, sampled at 2 Hz, equals the…
- Question 43 – The 4-point sequence x[n]=\3,2,3,4\ has DFT X[k]=\12,2j,0,-2j\. Let X 1[k] be the DFT of the 12-point sequence x 1[n]=\3,0,0,2,0,0,3,0,0,4,0,0\. The…
- Question 44 – The switch has been closed for a long time and opens at t=0, remaining open. The diode has zero forward drop and zero reverse current. The…
- Question 45 – A MOS capacitor has a metal gate and p-type silicon substrate at 300 K. Its inversion carrier sheet density is 21011\ cm-2 at V G=0.8 V and 41011\…
- Question 46 – For avalanche breakdown in a silicon p+n junction, the n region has uniform donor density N D. Breakdown occurs when the maximum field reaches E crit,…
- Question 47 – A silicon region contains no electrons or holes and has ionized donor density N D+=1017\ cm-3. The electric field is zero at x=0 and +50 kV/cm at x=L;…
- Question 48 – A long-channel NMOS has source and body tied together; electron mobility is independent of V GS and V DS. At V GS=2 V, g m=0.5\ A/V for V DS=50 mV,…
- Question 49 – A half-wave rectifier has a 475\ F filter capacitor and a constant 1 A load. The figure shows input V i, output V C and peak-to-peak ripple u. The…
- Question 50 – The Zener diodes in the op-amp circuit clamp V O to +5 V or −5 V. Switch S is initially closed and opens at t=0. The time in seconds when V O changes…
- Question 51 – The op-amp has finite open-loop gain 100 and input offset V ios=+5 mV modeled with the polarity shown. It is otherwise ideal. With V input=25 mV, the…
- Question 52 – An 8 Kbyte ROM with active-low chip select CS is used with an 8085. It must occupy addresses 1000H–2FFFH. Address bits run from A 15 (most…
- Question 53 – An N-bit flash ADC drives 2N-1 comparator inputs simultaneously. The input voltage source has resistance 75 Ω and each comparator input capacitance is…
- Question 54 – The figure shows a finite-state machine with states A, B and C and binary inputs X,Y,Z. Which statement is correct?
- Question 55 – The feedback system shown has G(s)=1/(s2+2s). Its closed-loop step response should have minimum settling time and no overshoot. The required gain k is…
- Question 56 – The feedback system has G(s)=1/[(s+1)(s+2)(s+3)]. Find the positive gain k for which loop gain margin is 0 dB and phase margin is 0°.
- Question 57 – The figure is the asymptotic Bode phase plot of G(s)=k/[(s+0.1)(s+10)(s+p 1)], with k and p 1 positive. The value of p 1 is .
- Question 58 – An iid binary sequence n takes ±1 equiprobably. It is precoded as n= n+k n-3. The baseband signal is X(t)= n=- n g(t-nT), where g(t)=1 for 0 t T and…
- Question 59 – A 500–2000 Hz ideal band-pass channel carries 4800 bits/s using 16-QAM. A raised-cosine pulse spectrum uses the entire channel bandwidth. Its roll-off…
- Question 60 – Let X(t)=3V(t)-8, where V is a zero-mean stationary process with autocorrelation R V()=4e-5 . The power in X is .
- Question 61 – A binary communication system has events x 0,x 1 for transmitting zero and one, and y 0,y 1 for receiving zero and one. Given P(x 0)=1/2, P(y 0 x…
- Question 62 – A movable parallel-plate capacitor initially stores energy E with plate separation d. It is electrically isolated, and the separation is increased to…
- Question 63 – A lossless microstrip has trace width w over a practically infinite ground plane, separated by a slab of thickness t and relative permittivity r>1.…
- Question 64 – The figure shows lossless lines T 1,T 2 and input reflection magnitude versus frequency. Phase velocity is 2108 m/s in both lines. The length L of T…
- Question 65 – A small positive charge q starts at rest at x=0 between infinite yz metal plates at x=−d and x=+d. Voltages +V and −V are applied respectively at t=0.…