GATE EC question library

Mr. $\text{X}$ speaks __________ Japanese ____________ Chinese.

A sum of money is to be distributed among $\text{P, Q, R,}$ and $\text{S}$ in the proportion $5:2:4:3,$ respectively. If $\text{R}$ gets ₹ $1000$ more than $\text{S},$ what is the share of $\text{Q (in ₹)}?$

A trapezium has vertices marked as $\text{P, Q, R}$ and $\text{S}$ (in that order anticlockwise). The side $\text{PQ}$ is parallel to side $\text{SR}.$ Further, it is given that, $\text{PQ = 11 cm, QR = 4 cm, RS = 6 cm}$ and $\text{SP = 3 cm.}$ What is the shortest distance between $\text{PQ}$ and $\text{SR (in cm)}?$

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a “hole in the interior” that can be formed within the $4 \times 4$ grid using the unit squares as building blocks?

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard. If …

Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences. Which one of the following is the correct logical inference …

Consider the following inequalities. $2x – 1 > 7$ $2x – 9 < 1$ Which one of the following expressions below satisfies the above two inequalities?

Four points $\text{P(0, 1), Q(0, – 3), R( – 2, – 1),}$ and $\text{S(2, – 1)}$ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?

In a class of five students $\text{P, Q, R, S}$ and $\text{T},$ only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below. $\text{Statement of P: R}$ has copied in the exam. $\text{Statement of Q: S}$ has copied in the exam. …

Consider the following square with the four corners and the center marked as $\text{P, Q, R, S}$ and $\text{T}$ respectively. Let $\text{X, Y}$ and $\text{Z}$ represent the following operations: $\text{X:}$ rotation of the square by $180$ degree with respect to the $\text{S – Q}$ axis. $\text{Y:}$ rotation of the square by $180$ degree with …

The bar graph shows the frequency of the number of wickets taken in a match by a bowler in her career. For example, in $17$ of her matches, the bowler has taken $5$ wickets each. The median number of wickets taken by the bowler in a match is _______________ (rounded off to one decimal place).

Consider the two-dimensional vector field $\overrightarrow{\rm F}(x, y) = x \overrightarrow{i} + y \overrightarrow{j},$ where $\overrightarrow{i}$ and $\overrightarrow{j}$ denote the unit vectors along the $x –$axis and the $y –$axis, respectively. A contour $\text{C}$ in the $x – y$ plane, as shown in the figure, is composed of two horizontal …

Consider a system of linear equations $Ax = b,$ where $A =\begin{bmatrix} 1 & – \sqrt{2} & 3 \\ – 1 & \sqrt{2} & – 3 \end{bmatrix}, \quad b = \begin{bmatrix} 1 \\ 3 \end{bmatrix}.$ This system of equations admits ______________.

The current $I$ in the circuit shown is ______________.

Consider the circuit shown in the figure. The current $I$ flowing through the $10 \; \Omega$ resistor is _____________.

The Fourier transform $X(j \omega)$ of the signal $$x(t) = \frac{t}{(1+t^{2})^{2}}$$ is ______________.

Consider a long rectangular bar of direct bandgap $p-$type semiconductor. The equilibrium hole density is $10^{17} \; \text{cm}^{-3}$ and the intrinsic carrier concentration is $10^{10} \; \text{cm}^{-3}.$ Electron and hole diffusion lengths are $2 \; \mu\text{m}$ and $1 \; \mu\text{m},$ respectively. The left side of the bar $(x = 0)$ is …

In a non-degenerate bulk semiconductor with electron density $n = 10^{16} \; \text{cm}^{-3},$ the value of $E_{c} – E_{Fn} = 200 \; \text{meV},$ where $E_{c}$ and $E_{Fn}$ denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as $26 \; \text{meV}$ and the intrinsic carrier …

Consider the $\text{CMOS}$ circuit shown in the figure (substrates are connected to their respective sources). The gate width $(W)$ to gate length $(L)$ ratios $\left( \frac{W}{L} \right)$ of the transistors are as shown. Both the transistors have the same gate oxide capacitance per unit area. For the $p\text{MOSFET},$ the threshold voltage is …

Consider the $\text{2–bit}$ multiplexer $\text{(MUX)}$ shown in the figure. For $\text{OUTPUT}$ to be the $\text{XOR}$ of $\text{C}$ and $\text{D},$ the values for $A_{0}, A_{1}, A_{2},$ and $A_{3}$ are _______________.