GATE EC question library

The propagation delay of the exclusive$-\text{OR}$ ($\text{XOR}$) gate in the circuit in the figure is $3\:ns$. The propagation delay of all the flip-flops is assumed to be zero. The clock ($\text{Clk}$) frequency provided to the circuit is $500\: \text{MHz}$. Starting from the initial value of the flip-flop outputs $Q_{2}Q_{1}Q_{0} = 1\;1\;1$ …

The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time $t = 0$. Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is …

A unity feedback system that uses proportional-integral ($\text{PI}$) control is shown in the figure. The stability of the overall system is controlled by tuning the $\text{PI}$ control parameters $K_{P}$ and $K_{I}$. The maximum value of $K_{I}$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable …

A sinusoidal message signal having root mean square value of $4\:V$ and frequency of $\text{1 kHz}$ is fed to a phase modulator with phase deviation constant $2$ rad/ volt. If the carrier signal is $c\left ( t \right )=2\cos\left ( 2\pi 10^{6} t\right )$, the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal …

Consider a superheterodyne receiver tuned to $600 \text{ kHz}$. If the local oscillator feeds a $1000 \text{ kHz}$ signal to the mixer, the image frequency (in integer) is ____________________ $\text{kHz}$.

In a high school having equal number of boy students and girl students, $75\%$ of the students study Science and the remaining $25\%$ students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to …

A message signal having peak-to-peak value of $2\:V$, root mean square value of $0.1\:V$ and bandwidth of $\text{5 kHz}$ is sampled and fed to a pulse code modulation ($\text{PCM}$) system that uses a uniform quantizer. The $\text{PCM}$ output is transmitted over a channel that can support a maximum transmission rate of $\text{50 kbps}$. Assuming …

Consider a polar non-return to zero ($\text{NRZ}$) waveform, using $+2\:V$ and $-2\:V$ for representing binary ‘$1$’ and ‘$0$’ respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance $0.4\:V^{2}$. If the a priori probability of transmission of a binary ‘$1$’ is $0.4$, the optimum threshold voltage …

A standard air-filled rectangular waveguide with dimensions $\text{a=8 cm, b=4 cm}$, operates at $\text{3.4 GHz}$. For the dominant mode of wave propagation, the phase velocity of the signal in $v_{p}$. The value (rounded off to two decimal places) of $v_{p}/c$, where $c$ denotes the velocity of light, is ________________________

An antenna with a directive gain of $6\text{ dB}$ is radiating a total power of $\text{16 kW}$. The amplitude of the electric field in free space at a distance of $\text{8 km}$ from the antenna in the direction of $\text{6 dB}$ gain (rounded off to three decimal places) is ____________________ $\text{V/m}$.

The untimely loss of life is a cause of serious global concern as thousands of people get killed ____ accidents every year while many other die ____ diseases like cardio vascular disease, cancer, etc.

He was not only accused of theft _____ of conspiracy.

Select the word that fits the analogy: Explicit: Implicit :: Express: _______

The Canadian constitution requires that equal importance be given to English and French. Last year, Air Canada lost a lawsuit, and had to pay a six-figure fine to a French-speaking couple after they filed complaints about formal in-flight announcements in English lasting $15$ seconds, as opposed to informal $5$ second messages in French. The …

A superadditive function $f(\cdot)$ satisfies the following property $$f\left ( x_{1} +x_{2}\right )\geq f\left ( x_{1} \right ) + f\left ( x_{2} \right )$$ Which of the following functions is a superadditive function for $x > 1$?

The global financial crisis in $2008$ is considered to be the most serious world-wide financial crisis, which started with the sub-prime lending crisis in $\text{USA}$ in $2007$. The sub-prime lending crisis led to the banking crisis in $2008$ with the collapse of Lehman Brothers in $2008$. The sub-prime lending refers to the provision of loans to …

It is quarter past three in your watch. The angle between the hour hand and the minute hand is ________.

A circle with centre $\text{O}$ is shown in the figure. A rectangle $\text{PQRS}$ of maximum possible area is inscribed in the circle. If the radius of the circle is $a$, then the area of the shaded portion is _______.

$a, b, c$ are real numbers. The quadratic equation $ax^{2}-bx+c=0$ has equal roots, which is $\beta$, then

The following figure shows the data of students enrolled in $5$ years $(2014\;\text{to}\; 2018)$ for two schools $P$ and $Q$. During this period, the ratio of the average number of the students enrolled in school $P$ to the average of the difference of the number of students enrolled in schools $P$ and $Q$ is _______.