GATE ECE 2018
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GATE ECE

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability o
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The figure below shows the Bode magnitude and phase plots of a stable transfer function $$G(s) = {{{n_0}} \over {{s^3} +
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Consider p(s) = s3 + $${a_2}$$s2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p
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For a unity feedback control system with the forward path transfer function $$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: $$\mathop x\limits^. = \left[ {\matrix{
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A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by F = $
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A four-variable Boolean function is realized using 4 $$ \times $$ 1 multiplexers as shown in the figure. The minimized
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The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for LOW logic level at the outp
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A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 s
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In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data Din using clock CK. Th
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A 2 $$ \times $$ 2 ROM array is built with the help of diodes as shown in the circuit below. Here W0 and W1 are signals
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Let M be a real 4 $$ \times $$ 4 matrix. Consider the following statements : S1: M has 4 linearly independent eigenvecto
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Consider matrix $$A = \left[ {\matrix{ k & {2k} \cr {{k^2} - k} & {{k^2}} \cr } } \right]$$ and vect
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The position of a particle y(t) is described by the differential equation : $${{{d^2}y} \over {d{t^2}}} = - {{dy} \over
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Let $$f\left( {x,y} \right) = {{a{x^2} + b{y^2}} \over {xy}}$$, where $$a$$ and $$b$$ are constants. If $${{\partial f}
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Let r = x2 + y - z and z3 - xy + yz + y3 = 1. Assume that x and y are independent variables. At (x, y, z) = (2, -1, 1),
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A curve passes through the point ($$x$$ = 1, $$y$$ = 0) and satisfies the differential equation $${{dy} \over {dx}} = {{
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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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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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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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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 : $$\left[ {\matrix{ {{V_1}} \cr {{I_1}} \cr } } \right
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For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5
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For the circuit given in the figure, the voltage VC (in volts) across the capacitor is :
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Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by 𝑎
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Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among th
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Let X[k] = k + 1, 0 ≤ k ≤ 7 be 8-point DFT of a sequence x[n], where X[k] = $$\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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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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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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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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