GATE ECE 2018

## GATE ECE

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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The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for
determining the stability o

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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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Consider matrix $$A = \left[ {\matrix{
k & {2k} \cr
{{k^2} - k} & {{k^2}} \cr
} } \right]$$ and
vect

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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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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}} = {{

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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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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

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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 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(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 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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