GATE Electrical Engineering Solved Papers

Kavya ______ go to work yesterday as she ______ feeling well.

Select the most appropriate option to complete the above sentence.

Good : Evil :: Genuine : ______

Select the most appropriate option to complete the analogy.

The relationship between two variables $x$ and $y$ is given by $x + py + q = 0$ and is shown in the figure. Find the values of $p$ and $q$.

Note: The figure shown is representative.

Each row of Column-I has three items and each item is represented by a circle in Column-II. The arrangement of circles in Column-II represents the relationship among the items in Column-I.

Identify the option that has the most appropriate match between Column-I and Column-II.

Note: The figures shown are representative.

What is the value of $$\left(\frac{3^{81}}{27^{4}}\right)^{\frac{1}{3}}$$ ?

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:

P. It is because deer, like most of the animals that tigers normally prey on, run much faster! It simply means, another day of empty stomach for the big cats.

Q. Tigers spend most of their life searching for food.

R. If they trace the scent of deer, tigers follow the trail, chase the deer for a mile or two in the dark, and yet may not catch them.

S. For several nights, they relentlessly prowl through the forest, hunting for a trail that may lead to their prey.

In the given figure, EF and HJ are coded as 30 and 80, respectively. Which one among the given options is most appropriate for the entries marked (i) and (ii) ?

Scores obtained by two students P and Q in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT?

Spheres of unit diameter are centered at $(l, m, n)$ where $l, m,$ and $n$ take every possible integer values.

The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, $x$ is the distance to its nearest sphere and $y$ is the distance to its next nearest sphere. The value of $\frac{y}{x}$ is:

In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2. ST is parallel to QR. Two semicircles are drawn with PS and PQ as diameters, as shown in the figure.

Which one of the following statements is true about the shaded area PQS?

Note: The figure shown is representative.

Consider the set $S$ of points $(x, y) \in \mathfrak{R}^2$ which minimize the real valued function

$$f(x, y) = (x + y - 1)^2 + (x + y)^2$$

Which of the following statements is true about the set $S$?

Let $v_1$ and $v_2$ be the two eigenvectors corresponding to distinct eigenvalues of a $3 \times 3$ real symmetric matrix. Which one of the following statements is true?

Let $A = \begin{bmatrix} 1 & 1 & 1 \\ -1 & -1 & -1 \\ 0 & 1 & -1 \end{bmatrix}$ and $b = \begin{bmatrix} 1/3 \\ -1/3 \\ 0 \end{bmatrix}$. Then, the system of linear equations $Ax = b$ has

Let $P = \begin{bmatrix} 2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and let $I$ be the identity matrix. Then $P^2$ is equal to

Consider discrete random variables $X$ and $Y$ with probabilities as follows:

$$P(X = 0\text{ and } Y = 0) = \frac{1}{4}$$

$$P(X = 1\text{ and } Y = 0) = \frac{1}{8}$$

$$P(X = 0\text{ and } Y = 1) = \frac{1}{2}$$

$$P(X = 1\text{ and } Y = 1) = \frac{1}{8}$$

Given $X = 1$, the expected value of $Y$ is

Which one of the following statements is true about the small signal voltage gain of a MOSFET based single stage amplifier?

Assuming ideal op-amps, the circuit represents a

The I-V characteristics of the element between the nodes X and Y is best depicted by

A nullator is defined as a circuit element where the voltage across the device and the current through the device are both zero. A series combination of a nullator and a resistor of value, R, will behave as a

Consider a discrete-time linear time-invariant (LTI) system $S$, where

$$y[n] = S\{x[n]\}$$

Let

$$S\{\delta[n]\} = \begin{cases} 1, & n \in \{0, 1, 2\} \\ 0, & \text{otherwise} \end{cases}$$

where $\delta[n]$ is the discrete-time unit impulse function. For an input signal $x[n]$, the output $y[n]$ is

Consider a continuous-time signal

$$x(t) = -t^2 \{u(t + 4) - u(t - 4)\}$$

where $u(t)$ is the continuous-time unit step function. Let $\delta(t)$ be the continuous-time unit impulse function. The value of

$$\int_{-\infty}^{\infty} x(t) \delta(t + 3) dt$$

is

Selected data points of the step response of a stable first-order linear time-invariant (LTI) system are given below. The closest value of the time-constant, in sec, of the system is

The Nyquist plot of a strictly stable $G(s)$ having the numerator polynomial as $(s - 3)$ encircles the critical point -1 once in the anti-clockwise direction. Which one of the following statements on the closed-loop system shown in figure, is correct?

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a Newton-Raphson load-flow formulation, the UPS would be represented as a

Which one of the following figures represents the radial electric field distribution $E_R$ caused by a spherical cloud of electrons with a volume charge density, $\rho = -3\rho_0$ for $0 \le R \le a$ (both $\rho_0$, $a$ are positive and $R$ is the radial distance) and $\rho = 0$ for $R > a$?