GATE EC question library

Among the following options, the antonym of the word 'nocturnal' is $\_\_\_\_$.

The statements (S$1$), (S$2$), and (S$3$) pertain to the scores obtained by students in an exam. The maximum possible marks in the exam is $150$. (S$1$) The highest score is $100$. (S$2$) The fourth highest score is $76$. (S$3$) There are at least four students whose scores are within $25$ of each other. Which one of the following options …

The figure below has exactly three intersecting line segments with a rectangular portion $\text{WXYZ}$ missing. Which one of the following options $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, and S is the missing portion $\text{WXYZ}$?

Real numbers $y, p$, and $n$ (all greater than $1$ ) satisfy $$\left(\log _{p^{1 / n}} y\right)\left(\log _{y^{1 / n}} p\right)=16$$ where the logarithms are taken to the bases $p^{1 / n}$ and $y^{1 / n}$. The value of $n$ is $\_\_\_\_$

The following observation is made about the scores obtained by $100$ students in an exam: 'For each student, there exists another student in the class such that their scores are at most ten marks away.' If the above statement is false, which one of the following statements is necessarily true?

Each one of the following clues contains a keyword that is partially filled. Clue $1:$ Synonym of recognize ( $8$ letters): _ D _ NT_FY Clue $2:$ A story long enough to fill a book (5 letters): $\_\_\_\_$ EL Clue $3:$ Two of something ( $6$ letters): $\_\_\_\_$ PLE Clue $4:$ A fraction of something, split equally into two parts ($4$ …

Three children $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and two grown-ups $\mathrm{X}, \mathrm{Y}$ play a badminton doubles tournament. $\text{X}$ and $\text{Y}$ are parents to two of the children playing. The child of $\text{X}$ is not the same as the child of $\text{Y}.$ Exactly one of the children does not have a parent playing in the tournament. …

Let $P_{k}$ represent the perimeter of a square with sides of length $k$. The value of the expression $P_{1}+P_{2}+P_{3}+\cdots+P_{10}$ is $\_\_\_\_$

The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was $2.5$ stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length AB …

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Consider the differential equation $\dot{\vec{w}}=A \vec{w}$, with $\vec{w}(t=0)=\left[\begin{array}{l}1 \\ 1\end{array}\right]$. If $\vec{w}(t)=e^{t} \vec{u}_{x}+e^{-2 t} \vec{u}_{y}$ be the solution to the equation where $\vec{u}_{x}$ and $\vec{u}_{y}$ are unit vectors along the positive $x$ and $y$ axes respectively, then which of the …

A surface is given by $z^{2}=2 x^{2}-y^{2}$ and $\vec{n}$ and $-\vec{n}$ are unit normal vectors to the surface at the point $\vec{P}=\hat{\boldsymbol{\imath}}+\sqrt{2} \widehat{\boldsymbol{k}}$. Which of the following vectors can be $\vec{n}$, where $\hat{\boldsymbol{\imath}}, \hat{\boldsymbol{\jmath}}$ and $\widehat{\boldsymbol{k}}$ are the …

The Laplace Transform of the signal $x(t)=u(t-2) *(t u(t))$ is given by which of the following expressions? ["*" represents convolution operator]

Consider carrier transport in a Zener diode in the breakdown region. Which is the dominant transport mechanism for current flow in this case?

Two analog signals $x_{1}(t)$ and $x_{2}(t)(t$ in second $)$, are sampled at a rate $F_{s}=40 \mathrm{~Hz}$, where $$x_{1}(t)=\cos (20 \pi t), t \geq 0, \text{ and } x_{2}(t)=\cos (100 \pi t), t \geq 0$$ The first ten samples (starting from $t=0$ ) are considered for the analysis. Which of the following statements is TRUE?

The response of a discrete time system $y[n]$ obeys the following relation: $$y[n]=\frac{5}{6} y[n-1]-\frac{1}{6} y[n-2]+x[n] .$$ The input to the system is $x[n]=\delta[n]-\frac{1}{3} \delta[n-1]$. Which of the following options is TRUE for $y[n]$?

The ideal $\text{OP-AMP}$ circuit shown in the Figure produces output voltage $V_{o}=x$ when the Switch, $\text{S}$, is open. Which of the options represents the output voltage when $\text{S}$ is closed?

Consider the circuit shown in the Figure with $V_{i}=3 \mathrm{~V}$ and $V_{C C}=12 \mathrm{~V}$. Assume $V_{B E}=0.7 \mathrm{~V}$ and $\beta_{d c}=99$ for the BJT. Which of the following options is the correct value of the current $\boldsymbol{I}_{\boldsymbol{o}}$ ?

A control system is shown in the Figure. Which option represents the correct transfer function of the system?

In the circuit shown in the Figure, $A$ and $B$ are logic inputs and $Y$ is the logic output. Which of the following logic operations is realized by the circuit?