GATE ECE 2018
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## GATE ECE

The figure below shows the Bode magnitude and phase plots of a stable transfer function $$G(s) = {{{n_0}} \over {{s^3} + View Question The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability o View Question Consider p(s) = s3 +$${a_2}$$s2 +$${a_1}$$s +$${a_0}$$with all real coefficients. It is known that its derivative p View Question For a unity feedback control system with the forward path transfer function$$G(s) = {K \over {s\left( {s + 2} \right)}}
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The state equation and the output equation of a control system are given below: $$\mathop x\limits^. = \left[ {\matrix{ View Question A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by F =  View Question A four-variable Boolean function is realized using 4$$ \times $$1 multiplexers as shown in the figure. The minimized View Question The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for LOW logic level at the outp View Question A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 s View Question In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data Din using clock CK. Th View Question A 2$$ \times $$2 ROM array is built with the help of diodes as shown in the circuit below. Here W0 and W1 are signals View Question Consider matrix$$A = \left[ {\matrix{ k &amp; {2k} \cr {{k^2} - k} &amp; {{k^2}} \cr } } \right]$$and vect View Question Let M be a real 4$$ \times $$4 matrix. Consider the following statements : S1: M has 4 linearly independent eigenvecto View Question The position of a particle y(t) is described by the differential equation :$${{{d^2}y} \over {d{t^2}}} = - {{dy} \over
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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),
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A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation $${{dy} \over {dx}} = {{ View Question Let$$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where$$a$$and$$b$$are constants. If$${{\partial f}
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The contour C given below is on the complex plane $$z = x + jy$$, where $$j = \sqrt { - 1}$$. The value of the integra
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Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ arou
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Let X1 , X2 , X3 and X4 be independent normal random variables with zero mean and unit variance. The probability that X4
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Consider the network shown below with R1 = 1 $$\Omega$$, R2 = 2 $$\Omega$$ and R3 = 3 $$\Omega$$. The network is conn
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The ABCD matrix for a two-port network is defined by : $$\left[ {\matrix{ {{V_1}} \cr {{I_1}} \cr } } \right View Question For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 View Question For the circuit given in the figure, the voltage VC (in volts) across the capacitor is : View Question Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among th View Question Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎 View Question Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n], where X[k] =$$\sum\limits_{n = 0}^{N - 1} {x\left[ n \ri
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A discrete time all-pass system has two of its poles at 0.25$$\angle 0^\circ$$ and $$\angle 30^\circ$$. Which one of t
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## General Aptitude

If the number 715 ■ 423 is divisible by 3 (■ denotes the missing digit in the thousandths place), then the smallest whol
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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 ca
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"Even though there is a vast scope for its __________, tourism has remained a/an _________ area." The words that best fi
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What is the value of $$1 + {1 \over 4} + {1 \over {16}} + {1 \over {64}} + {1 \over {256}} + ......$$?
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"By giving him the last __________ of the cake, you will ensure lasting ________ in our house today." The words that bes
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A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt
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Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal masses of alloy
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The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field temper has always
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Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should depos
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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 t
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