GATE 2018 EC – Previous Year Questions with Solutions
All 65 questions of GATE 2018 EC with answers and explanations. Read each question, then practise it by topic or as a full paper.
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- Question 1 – "By giving him the last of the cake, you will ensure lasting in our house today." The words that best fill the blanks in the above sentence are
- Question 2 – "Even though there is a vast scope for its , tourism has remained a/an area." The words that best fill the blanks in the above sentence are
- Question 3 – If the number 715■423 is divisible by 3 (■ denotes the missing digit in the thousandths place), then the smallest whole number in the place of ■ is .
- Question 4 – What is the value of 1+14+116+164+1256+?
- Question 5 – A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of…
- Question 6 – Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers…
- Question 7 – Two alloys A and B contain gold and copper in the ratios of 2:3 and 3:7 by mass, respectively. Equal masses of alloys A and B are melted to make an…
- Question 8 – The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field temper has always been a matter of concern for…
- Question 9 – A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. (i) 85% of cabs…
- Question 10 – A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has…
- Question 11 – Two identical nMOS transistors M 1 and M 2 are connected as shown below. The circuit is used as an amplifier with the input connected between G and S…
- Question 12 – In the circuit shown below, the op-amp is ideal and the Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e. v…
- Question 13 – A good transimpedance amplifier has
- Question 14 – Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a…
- Question 15 – The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers.…
- Question 16 – Consider p(s)=s3+a 2s2+a 1s+a 0 with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s)…
- Question 17 – In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?
- Question 18 – The logic function f(X,Y) realized by the given circuit is
- Question 19 – A function F(A,B,C) defined by three Boolean variables A, B and C when expressed as sum of products is given by F= A B C+ A B C+A B C where, A, B, and…
- Question 20 – The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure represent:
- Question 21 – Let M be a real 44 matrix. Consider the following statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M…
- Question 22 – Let f(x,y)=ax2+by2xy, where a and b are constants. If f x= f y at x=1 and y=2, then the relation between a and b is
- Question 23 – A discrete-time all-pass system has two of its poles at 0.250 and 230. Which one of the following statements about the system is TRUE?
- Question 24 – Let x(t) be a periodic function with period T=10. The Fourier series coefficients for this series are denoted by a k, that is, x(t)= k=-a kejk2Tt The…
- Question 25 – Consider the following amplitude modulated signal: s(t)=(2000 t)+4(2400 t)+(2800 t). The ratio (accurate to three decimal places) of the power of the…
- Question 26 – Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in…
- Question 27 – A binary source generates symbols X\-1,1\ which are transmitted over a noisy channel. The probability of transmitting X=1 is 0.5. Input to the…
- Question 28 – A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1 m at equilibrium. The forward voltage (in volts, correct to…
- Question 29 – A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on…
- Question 30 – There are two photolithography systems: one with light source of wavelength 1=156 nm (System 1) and another with light source of wavelength 2=325 nm…
- Question 31 – A lossy transmission line has resistance per unit length R=0.05\ /m. The line is distortionless and has characteristic impedance of 50\ . The…
- Question 32 – Consider matrix A=bmatrixk&2k\2-k&k2bmatrix and vector x=bmatrixx 1\ 2bmatrix. The number of distinct real values of k for which the equation Ax= 0…
- Question 33 – Let X 1, X 2, X 3, and X 4 be independent normal random variables with zero mean and unit variance. The probability that X 4 is the smallest among the…
- Question 34 – Taylor series expansion of f(x)= 0xe-(t22)dt around x=0 has the form f(x)=a 0+a 1x+a 2x2+ The coefficient a 2 (correct to two decimal places) is equal…
- Question 35 – The ABCD matrix for a two-port network is defined by: bmatrixV 1\ 1bmatrix=bmatrixA&B\&DbmatrixbmatrixV 2\\-I 2bmatrix The parameter B for the given…
- Question 36 – The circuit shown in the figure is used to provide regulated voltage (5 V) across the 1\ k resistor. Assume that the Zener diode has a constant…
- Question 37 – Let c(t)=A c(2 f ct) and m(t)=(2 f mt). It is given that f c5f m. The signal c(t)+m(t) is applied to the input of a non-linear system, whose output v…
- Question 38 – Consider a white Gaussian noise process N(t) with two-sided power spectral density S N(f)=0.5 W/Hz as input to a filter with impulse response…
- Question 39 – The state equation and the output equation of a control system are given below: x=bmatrix-4&-1.5\\4&0bmatrix x+bmatrix2\\0bmatrixu, y=[1.5\ \ 0.625]\,…
- Question 40 – Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having…
- Question 41 – A four-variable Boolean function is realized using 41 multiplexers as shown in the figure. The minimized expression for F(U,V,W,X) is
- Question 42 – A 22 ROM array is built with the help of diodes as shown in the circuit below. Here W0 and W1 are signals that select the word lines and B0 and B1 are…
- Question 43 – The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 m so that the amplitude of the wave attenuates by 20 dB, is
- Question 44 – A curve passes through the point (x=1,\ y=0) and satisfies the differential equation dydx=x2+y22y+ yx. The equation that describes the curve is
- Question 45 – For the circuit given in the figure, the voltage V c (in volts) across the capacitor is
- Question 46 – For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the…
- Question 47 – A dc current of 26\ A flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the…
- Question 48 – An op-amp based circuit is implemented as shown below. In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one…
- Question 49 – The input 4\,sinc(2t) is fed to a Hilbert transformer to obtain y(t), as shown in the figure below. Here, sinc(x)=( x) x. The value (accurate to two…
- Question 50 – A random variable X takes values -0.5 and 0.5 with probabilities 14 and 34, respectively. The noisy observation of X is Y=X+Z, where Z has uniform…
- Question 51 – For a unity feedback control system with the forward path transfer function G(s)=Ks(s+2) The peak resonant magnitude M r of the closed-loop frequency…
- Question 52 – The figure below shows the Bode magnitude and phase plots of a stable transfer function G(s)=n 0s3+d 2s2+d 1s+d 0. Consider the negative unity…
- Question 53 – In the circuit shown below, the (W/L) value for M 2 is twice that for M 1. The two nMOS transistors are otherwise identical. The threshold voltage V T…
- Question 54 – A solar cell of area 1.0 cm2, operating at 1.0 sun intensity, has a short circuit current of 20 mA, and an open circuit voltage of 0.65 V. Assuming…
- Question 55 – A junction is made between p- Si with doping density N A1=1015\ cm-3 and p Si with doping density N A2=1017\ cm-3. Given: Boltzmann constant…
- Question 56 – In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data D in using clock CK. The XOR gate outputs 3.3 volts…
- Question 57 – The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for LOW logic level at the outputs. When the pull-downs are…
- Question 58 – The cutoff frequency of TE 01 mode of an air filled rectangular waveguide having inner dimensions a cm b cm (a>b) is twice that of the dominant TE 10…
- Question 59 – A uniform plane wave traveling in free space and having the electric field E=(2 a x- a z)[63108t-2(x+2z)]\ V/m is incident on a dielectric medium…
- Question 60 – The position of a particle y(t) is described by the differential equation: d2ydt2=-dydt-5y4. The initial conditions are y(0)=1 and .dydt t=0=0. The…
- Question 61 – The contour C given below is on the complex plane z=x+jy, where j=-1. The value of the integral 1 j Cdzz2-1 is .
- Question 62 – Let r=x2+y-z and z3-xy+yz+y3=1. Assume that x and y are independent variables. At (x,y,z)=(2,-1,1), the value (correct to two decimal places) of r x…
- Question 63 – Consider the network shown below with R 1=1\ , R 2=2\ and R 3=3\ . The network is connected to a constant voltage source of 11 V. The magnitude of the…
- Question 64 – A band limited low-pass signal x(t) of bandwidth 5 kHz is sampled at a sampling rate f s. The signal x(t) is reconstructed using the reconstruction…
- Question 65 – Let X[k]=k+1, 0 k7 be 8-point DFT of a sequence x[n], where X[k]= n=0N-1x[n]e-j2 nk/N. The value (correct to two decimal places) of n=03x[2n] is .