GATE EC question library

​​​If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [ charm $\rightarrow$ enamor $\rightarrow$ bewitch] is analogous to [bored $\rightarrow \_\_\_\_\_\_ \longrightarrow$ weary] Which one of the given options is appropriate to fill the blank?

​​​​$\text{P, Q, R, S}$, and $\text{T}$ have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room. If $\text{S}$ and $\text{Q}$ are single children, and the room allocations shown below are acceptable to all. …

​​​​Five years ago, the ratio of Aman's age to his father's age was $1: 4$, and five years from now, the ratio will be $2:5$. What was his father's age when Aman was born?

​​​​For a real number $x>1$, $$\frac{1}{\log _{2} x}+\frac{1}{\log _{3} x}+\frac{1}{\log _{4} x}=1$$ The value of $x$ is

The greatest prime factor of $\left(3^{199}-3^{196}\right)$ is

​Sequence the following sentences $(\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S})$ in a coherent passage: $\text{P}$: Shifu's student exclaimed, "Why do you run since the bull is an illusion?" $\text{Q}$: Shifu said, "Surely my running away from the bull is also an illusion." $\mathrm{R}$ : Shifu once proclaimed that all life is illusion. …

​​​​​Four identical cylindrical chalk-sticks, each of radius $r=0.5 \mathrm{~cm}$ and length $l=10 \mathrm{~cm}$, are bound tightly together using a duct tape as shown in the following figure. The width of the duct tape is equal to the length of the chalk-stick. The area (in $\mathrm{cm}^{2}$ ) of the duct tape required to wrap the bundle of …

The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index $\text{(BMI)}$ in $2003$ and $2023$. Based on the data provided, which one of the following options is INCORRECT?

Examples of mirror and water reflections are shown in the figures below: An object appears as the following image after first reflecting in a mirror and then reflecting on water. The original object is

​​​Two identical sheets $\text{A}$ and $\text{B}$, of dimensions $24 \mathrm{~cm} \times 16 \mathrm{~cm}$, can be folded into half using two distinct operations, $\text{FO1}$ or $\text{FO2}$. In $\text{FO1}$, the axis of folding remains parallel to the initial long edge, and in $\text{FO2}$, the axis of folding remains parallel to the initial …

The general form of the complementary function of a differential equation is given by $y(t)=(A t+B) e^{-2 t}$, where $A$ and $B$ are real constants determined by the initial condition. The corresponding differential equation is

​​​​​In the context of Bode magnitude plots, $40 \mathrm{~dB} /$ decade is the same as $\_\_\_\_\_\_.$

​​​In the feedback control system shown in the figure below $G(s)=\frac{6}{s(s+1)(s+2)}$. $\text{R(s), Y(s)}$, and $\text{E(s)}$ are the Laplace transforms of $r(t), y(t)$, and $e(t)$, respectively. If the input $r(t)$ is a unit step function, then

A digital communication system transmits through a noiseless bandlimited channel $[-W W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t)=\sum_{n} b[n] x(t-n T)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t=m T$. The Fourier …

​​​​Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances $z_{\text{inA }}, z_{i n B}, z_{i n C}$, and $z_{i n D}$ (indicated in the figure) are $\_\_\_\_\_\_.$

​​​Let $\hat{i}$ and $\hat{j}$ be the unit vectors along $x$ and $y$ axes, respectively and let $A$ be a positive constant. Which one of the following statements is true for the vector fields $\overrightarrow{F_{1}}=A(\hat{i} y+\hat{j} x)$ and $\overrightarrow{F_{2}}=A(\hat{i} y-\hat{j} x) ?$ .

​​​​In the circuit below, assume that the long channel $\text{NMOS}$ transistor is biased in saturation. The small signal trans-conductance of the transistor is $g_{m}$. Neglect body effect, channel length modulation and intrinsic device capacitances. The small signal input impedance $Z_{i n}(j \omega)$ is $\_\_\_\_\_\_$

​​​​For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is $40$. All the transistors are biased in saturation. The current source $I_{S S}$ is ideal. Neglect body effect, channel length modulation and intrinsic device capacitances. The closed loop low frequency small signal voltage gain …

​​​​For the Boolean function $$F(A, B, C, D)=\sum m(0,2,5,7,8,10,12,13,14,15) \text{, }$$ the essential prime implicants are $\_\_\_\_\_\_$.

​​​​A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_{0}}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t=t_{k}$, the variance of the random variable $n\left(t_{k}\right)$ is $\_\_\_\_\_\_\_$.