GATE 2021 Electrical Engineering

A $1 \mu \mathrm{C}$ point charge is held at the origin of a cartesian coordinate system. If a second point charge of $10 \mu \mathrm{C}$ is moved from $(0,10,0)$ to $(5,5,5)$ and...

In a single phase transformer, the total iron loss is 2500 W at nominal voltage of 440 V and frequency 50 Hz . The total iron loss is 850 W at 220 V and 25 Hz . Then, at nominal vo...

For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is

A 16 -bit synchronous binary up-counter is clocked with a frequency $f_{c l k}$. The two most significant bits are ORed together to form an output $Y$. Measurements shows that $Y$...

An 8 pole, $50 \mathrm{~Hz}, 3$ phase, slip-ring induction motor has an effective rotor resistance of $0.08 \Omega$ per phase. Its speed at maximum torque is 650 rpm . The addition...

Let $p$ and $q$ be real numbers such that $p^2+q^2=1$. The eigen values of the matrix $\left[\begin{array}{cc}p & q \\ q & -p\end{array}\right]$ are

Let $X$ is a continuous random variable denoting the temperature measured. The range of temperature is $[0,100]$ degree Celsius and let the probability density function of $X$ be $...

Two generators have cost functions $F_1$ and $F_2$. Their incremental-cost characteristics are $$ \frac{d F_1}{d P_1}=40+0.2 P_1 \text { and } \frac{d F_2}{d P_2}=32+0.4 P_2 $$ The...

The importance of sleep is often overlooked by students when they are preparing for exams. Research has consistently shown that sleep deprivation greatly reduces the ability to rec...

Let $A$ be a $10 \times 10$ matrix such that $A^5$ is null matrix and let $I$ be the $10 \times 10$ identity matrix. The determinant of $A+I$ is $\_\_\_\_$ .

One Coulomb of point charge moving with a uniform velocity $10 \hat{x} \mathrm{~m} / \mathrm{s}$ enters the region $x \geq 0$ having a magnetic flux density $\vec{B}=(10 y \hat{x}+...

Oasis is to sand as island is to $\_\_\_\_$ . Which one of the following options maintains a similar logical relation in the above sentence?

Which one of the following numbers is exactly divisible by $\left(11^{13}+1\right) ?$

Let $P(z)=z^3+(1+j) z^2+(2+j) z+3$, where $z$ is complex number. Which one of the following is true?

$$ \text { The state space representation of a first-order system is given as } $$ $$ \begin{aligned} & \dot{x}=-x+u \\ & y=x \end{aligned} $$ Where, $x$ is the state variable, $u$...

Suppose the probability that a coin toss shows "head" is $p$, where $0

Consider a power system consisting of $N$ number of buses. Buses in this power system are categorized into slack bus. $P V$ buses and $P Q$ buses for load flow study. The number of...

$$ \text { Consider the table given : } $$ Constructional feature Machine type Mitigation P. Damper bars S. Induction motor X. Hunting Q. Skewed rotor slots T. Transformer Y. Magne...

Suppose the circles $x^2+y^2=1$ and $(x-1)^2+(y-1)^2=r^2$ intersect each other orthogonally at the point $(u, v)$. Then $u+v=$ $\_\_\_\_$ .

The people $\_\_\_\_$ were at the demonstration were from all sections of society.

Which one of the following vector functions represents a magnetic field $\vec{B}$ ? ( $\hat{x}, \hat{y}$, and $\hat{z}$ are unit vectors along $x$-axis, $y$-axis and $z$-axis respe...

A signal generator having a source resistance of $50 \Omega$ is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across...

A belt-driven DC shunt generator running at 300 rpm delivers 100 kW to a 200 V DC grid. It continues to run as a motor when the belt breaks, taking 10 kW from the DC grid. The arma...

Let $(-1-j),(3-j),(3+j)$ and $(-1+j)$ be the vertices of rectangle $C$ in the complex plane. Assuming that $C$ is traversed in counter-clockwise direction, the value of contour int...

Let $f(x)$ be a real-valued function such that $f^{\prime}\left(x_0\right)=0$ for some $x_0 \in(0,1)$ and $f^{\prime \prime}\left(x_0\right)>0$ for all $x \in(0,1)$. Then $f(x)$ ha...

The power input to a $500 \mathrm{~V}, 50 \mathrm{~Hz}, 6$ pole, 3 phase induction motor running at 975 rpm is 40 kW . The stator losses are 1 kW . If the total friction and windag...

In the open interval $(0,1)$, the polynomial $p(x)=x^4-4 x^3+2$ has

Seven Cars $P, Q, R, S, T, U$ and $V$ are parked in a row not necessarily in that order. The cars $T$ and $U$ should be parked next to each other. The cars $S$ and $V$ also should...

Suppose $I_A, I_B$ and $I_C$ are a set of unbalanced current phasors in a three-phase system. The phase-B zero-sequence current $I_{B 0}=0.1 \angle 0^0$ p.u. If phase-A current $I_...

Two single-core power cables have total conductor resistances of $0.7 \Omega$ and $0.5 \Omega$ respectively and their insulation resistances (between core and sheath) are $600 \mat...

A counter is constructed with three D flip-flops. The input-output pairs are named as $\left(D_0, Q_0\right)$, $\left(D_1, Q_1\right)$ and $\left(D_2, Q_2\right)$, where the subscr...

Consider a large parallel plate capacitor. The gap $d$ between the two plates is filled entirely with a dielectric slab of relative permittivity 5 . The plates are initially charge...

An alternator with an internal voltage of $1 \delta_1$ pu and synchronous reactance of 0.4 pu is connected by a transmission line of reactance 0.1 pu to a synchronous motor having...

Consider a continuous time signal $x(t)$ defined by $x(t)=0$ for $|t|>1$ and $x(t)=1-|t|$ for $|t| \leq 1$ Let the Fourier transform of $x(t)$ be defined as $X(\omega)=\int_{-\inft...

If the input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\max [0, x(t)]$, then the system is

Inductance is measured by,

The causal signal with $z$-transform $z^2(z-a)^{-2}$ is ( $u[n]$ is the unit step signal)

Let $f(t)$ be an even function, i.e., $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F(\omega)=\int_{-\infty}^{\infty} f(t) e^{-j \omega t} d t$. Supp...

Two discrete-time linear time-invariant systems with impulse responses $h_1\lfloor n\rfloor=\delta\lfloor n-1\rfloor+\delta\lfloor n+1\rfloor$ and $h_2[n]=\delta[n]+\delta[n-1]$ ar...