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Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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

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Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 _________.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 4

What is the value of

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 the shadow is twice her height. What is the height of the lamp post in meters?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 10% annual rate of interest, if the interest was compounded annually?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 alloy C. The ratio of gold to copper in alloy C is ______.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 them since his junior days. While this aggression has filled stadia with die-hard fans, it has taken a toll on his own batting. Until recently, it appeared that he found it difficult to convert his aggression into big scores. Over the past three seasons though, that picture of John has been replaced by a cerebral, calculative and successful batsman-captain. After many years, it appears that the team has finally found a complete captain.

Which of the following statements can be logically inferred from the above paragraph?

(i) Even as a junior cricketer, John was considered a good captain.

(ii) Finding a complete captain is a challenge.

(iii) Fans and the Cricket Board have differing views on what they want in a captain.

(iv) Over the past three seasons John has accumulated big scores.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 in the city are green and the remaining cabs are blue.

(ii) A witness identified the cab involved in the accident as blue.

(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.

Which of the following options is closest to the probability that the accident was caused by a blue cab?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major city airport. Environmentalists are upset that this would lead to the region becoming crowded and polluted like any other major beach resorts.

Which one of the following statements can be logically inferred from the information given in the above paragraph?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 terminals and the output taken between D and S terminals. V_{bias} and V_{D} are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as while the output

resistance is where ��_{D} is the current flowing into the drain of M_{2} . Let g_{m1} , g_{m2} be the transconductances and r_{o1} , r_{o2} be the output resistances of transistors M_{1} and M_{2}, respectively.

Which of the following statements about estimates for gm and r_{o} is correct?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 12

In the circuit shown below, the op-amp is ideal and Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e. v_{IN} (t) = u(t) volts. Also, at t = 0, the voltage across each of the capacitors is zero.

The time t, in milliseconds, at which the output voltage v_{out }crosses −10 V is

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 13

A good transimpedance amplifier has

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 linear system:

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 15

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 16

Consider with all real coefficients. It is known that its derivative ��′(s) has no real roots. The number of real roots of ��(s) is

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 17

In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 18

The logic function f ( X , Y ) realized by the given circuit is

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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

where, are the complements of the respective variables. The product of sums (POS) form of the function F is

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 20

The points P, Q, and R shown on the Smith chart (normalized impedance chart) in the following figure represent:

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 21

Let M be a real 4x4 matrix. Consider the following statements:

S1: M has 4 linearly independent eigenvectors.

S2: M has 4 distinct eigenvalues.

S3: M is non-singular (invertible).

Which one among the following is TRUE?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 22

Let where a and b are constants. If at x = 1 and y= 2 , then the relation between a and b is

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 23

A discrete-time all-pass system has two of its poles at 0.25∠0 and 2∠30 . Which one of the following statements about the system is TRUE?

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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

The same function x(t) can also be considered as a periodic function with period T ′ = 40. Let b_{k }be the Fourier series coefficients when period is taken as then is equal to

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 25

Consider the following amplitude modulated signal:

The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is __________.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 this code is at least 2. The maximum number of codewords such a code can contain is _________.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 threshold detector is R = X + ��.

The probability density function f_{N} (n) of the noise �� is shown below.

If the detection threshold is zero, then the probability of error (correct to two decimal places) is __________.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 28

A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1 μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is _______.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - 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 for 5 seconds and the RED is turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is _______.

Electronics And Communication Engineering - (EC) 2018 GATE Paper (Practice Test) - Question 30

There are two photolithography systems: one with light source of wavelength λ_{1} = 156 nm (System 1) and another with light source of wavelength λ_{2} = 325 nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are L_{min1} and L_{min2} respectively, the ratio L_{min1}/L_{min2} (correct to two decimal places) is__________.

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