# Electronics and Communication Engg - GATE 2018 Paper Solution

“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

“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

If the number $715\blacksquare423$ is divisible by 3 ($\blacksquare$ denotes the missing digit in the thousandths place), then the smallest whole number in the place of $\blacksquare$ is _________.

What is the value of $1+\frac14+\frac1{16}+\frac1{64}+\frac1{256}+........$ ?

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?

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?

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 ______.

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 Over the past three seasons though, that picture of John has been replaced by a cerebral, calculative and successful batsman-captain.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.

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?

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?

Two identical nMOS transistors M1 and M2 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. Vbias and VD are so adjusted that both transistors are in saturation. The transconductance of this combination is defined as $\style{font-family:'Times New Roman'}{g_m=\frac{\partial i_D}{\partial\nu_{GS}}}$ while the output resistance is $r_o=\frac{\partial v_{{}_{DS}}}{\partial i_D}$ , where $\style{font-family:'Times New Roman'}{i_D}$ is the current flowing into the drain of M2 . Let $\style{font-family:'Times New Roman'}{g_{m1},\;g_{m2}}$ be the transconductances and $\style{font-family:'Times New Roman'}{r_{o1},\;r_{o2}}$ be the output resistances of transistors M1 and M2, respectively

Which of the following statements about estimates for $\style{font-family:'Times New Roman'}{g_m}$ and $\style{font-family:'Times New Roman'}{r_o}$ is correct?

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. $\style{font-family:'Times New Roman'}{\nu_{IN}(t)=u(t)}$ volts. Also, at t = 0, the voltage across each of the capacitors is zero.
The time $\style{font-family:'Times New Roman'}t$, in milliseconds, at which the output voltage $v_{OUT}$ crosses −10 V is

A good transimpedance amplifier has

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:

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:

Consider $\begin{array}{l}p\left(s\right)=s^3+a_2s^2+a_1s+a_0\\\end{array}$ with all real coefficients. It is known that its derivative $\begin{array}{l}p\left(s\right)\\\end{array}$ has no real roots. The number of real roots of $p(s)$ is

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

The logic function $\begin{array}{l}f\left(X,\;Y\right)\\\end{array}$ realized by the given circuit is

A function $F\left(A,\;B,\;C\right)$ defined by three Boolean variables $A$, $B$ and $C$ when expressed as sum of products is given by

$F=\overline A\cdot\overline B\cdot\overline C\;+\;\overline A\cdot B\cdot\overline C\;+\;A+\overline B+\overline C$

where, $\begin{array}{l}\overline A,\;\overline B\\\end{array}$, and $\begin{array}{l}\overline C\\\end{array}$ are the complements of the respective variables. The product of sums (POS) form of the function F is

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