GATE ECE 2018

## GATE ECE

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

View Question The figure below shows the Bode magnitude and phase plots of a stable transfer function
$$G(s) = {{{n_0}} \over {{s^3} +

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)}}

View Question 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 Let
M
be a real
4 $$ \times $$ 4
matrix. Consider the following statements :
S1:
M
has
4
linearly independent eigenvecto

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

View Question The position of a particle y(t) is described by the differential equation :
$${{{d^2}y} \over {d{t^2}}} = - {{dy} \over

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}

View Question 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),

View Question A curve passes through the point
($$x$$ = 1, $$y$$ = 0)
and satisfies the differential equation
$${{dy} \over {dx}} = {{

View Question The contour
C
given below is on the complex plane $$z = x + jy$$, where $$j = \sqrt { - 1} $$.
The value of the integra

View Question Let
X1
, X2
, X3
and
X4
be independent normal random variables with zero mean and unit
variance. The probability that
X4

View Question Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ arou

View Question Consider the network shown below with R1 = 1 $$\Omega $$, R2 = 2 $$\Omega $$ and R3 = 3 $$\Omega $$. The network is
conn

View Question 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 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this
series are denoted by 𝑎

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[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

View Question 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

View Question ## General Aptitude

If the number 715 ■ 423 is divisible by 3 (■ denotes the missing digit in the thousandths place), then the
smallest whol

View Question 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

View Question "Even though there is a vast scope for its __________, tourism has remained a/an _________ area."
The words that best fi

View Question What is the value of $$1 + {1 \over 4} + {1 \over {16}} + {1 \over {64}} + {1 \over {256}} + ......$$?

View Question "By giving him the last __________ of the cake, you will ensure lasting ________ in our house today."
The words that bes

View Question The Cricket Board has long recognized John's potential as a leader of the team. However, his on-field
temper has always

View Question A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs
and unspoilt

View Question 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

View Question 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

View Question 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

View Question