GATE 2018 Electrical Engineering
225 questions across 2 sessions
Gate Ee 2018
The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates c...
Functions F(a, b) and G(a, b) are defined as follows: F(a, b) = (a - b) 2 and G(a, b) = |a - b| , where |x| represents the absolute value of x. What would be the value of G(F(1, 3)...
In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?
A 1000 $$ \times $$ 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this...
The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are 𝑗0.1 pu, j0.05 pu and j0.01 pu respectively on the machi...
P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available. (i) The boat held two person...
The series impedance matrix of a short three-phase transmission line in phase coordinates is $$\left[ {\matrix{ {{Z_s}} & {{Z_m}} & {{Z_m}} \cr {{Z_m}} & {{Z_s}} & {{Z_m}} \cr {{Z_...
Consider a lossy transmission line with V 1 and V 2 as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectivel...
The three roots of the equation f(x) = 0 are x = {-2, 0, 3}. What are the three values of x for which f(x -3) = 0?
"Since you have gone off the ________, the _________ sand is likely to damage the car." The words that best fill the blanks in the above sentence are
A 3-phase 900 kVA, 3 kV / $$\sqrt 3 $$ kV (Δ/Y), 50 Hz transformer has primary (high voltage side) resistance per phase of 0.3 Ω and secondary (low voltage side) resistance per pha...
A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take $${\varepsilon _0} = 8.85 \tim...
"A common misconception among writers is that sentence structure mirrors thought; the more _________ the structure, the more complicated the ideas." The word that best fills the bl...
A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probabi...
A 0-1 Ampere moving iron ammeter has an internal resistance of 50 m$$\Omega $$ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operat...
Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (...
An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How ma...
A 200 V DC series motor, when operating from rated voltage while driving a certain load, draws 10 A current and runs at 1000 r.p.m. The total series resistance is 1 Ω. The magnetic...
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P = 1.4 sin $$\delta $$ + 0.15 sin 2$$\delta $$, where $$\d...
A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regula...
The positive, negative and zero sequence impedances of a three phase generator are Z 1 , Z 2 and Z 0 respectively. For a line-to-line fault with fault impedance Z f , the fault cur...
A separately excited dc motor has an armature resistance R $$a$$ = 0.05Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 50...
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is
For what values of k given below is $${{{{\left( {k + 2} \right)}^2}} \over {k - 3}}$$ an integer?
Set Combined
"Since you have gone off the ________, the ________ sand is likely to damage the car." The words that best fill the blanks in the above sentence are
A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regula...
An urn contains 5 red balls and 5 black balls. In the first draw, one ball is picked at random and discarded without noticing its colour. The probability to get a red ball in the s...
The matrix A = $\begin{bmatrix} 3/2 & 0 & 1/2 \ 0 & -1 & 0 \ 1/2 & 0 & 3/2 \end{bmatrix}$ has three distinct eigenvalues and one of its eigenvectors is $\begin{bmatrix} 1 \ 0 \ 1 \...
The man who is now Municipal Commissioner worked as ______________.
For a complex number z, $\lim_{z \to i} \frac{z^2+1}{z^3+2z-i(z^2+2)}$ is
Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia. Choose the option which is closest in meaning to the underlin...
"A common misconception among writers is that sentence structure mirrors thought; the more ________ the structure, the more complicated the ideas." The word that best fills the bla...
Consider a solid sphere of radius 5 cm made of a perfect electric conductor. If one million electrons are added to this sphere, these electrons will be distributed
In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is
The figures show diagramatic representations of vector fields $\vec{X}$, $\vec{Y}$, and $\vec{Z}$, respectively. Which one of the following choices is true?
A single phase fully controlled rectifier is supplying a load with an anti-parallel diode as shown in the figure. All switches and diodes are ideal. Which one of the following is t...
Find the odd one in the following group of words. mock, deride, praise, jeer
Let z(t) = x(t) * y(t), where "*" denotes convolution. Let c be a positive real-valued constant. Choose the correct expression for z(ct).
The three roots of the equation f(x) = 0 are x = {-2, 0, 3}. What are the three values of x for which f (x - 3) = 0?
Pick the odd one from the following options.
For what values of k given below is $\frac{(k+2)^2}{k-3}$ an integer?
A solid iron cylinder is placed in a region containing a uniform magnetic field such that the cylinder axis is parallel to the magnetic field direction. The magnetic field lines in...
Four power semiconductor devices are shown in the figure along with their relevant terminals. The device(s) that can carry dc current continuously in the direction shown when gated...
The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below. Which one of the following is TRUE about the frequency selectivity of these systems?
In a quadratic function, the value of the product of the roots (α, β) is 4. Find the value of $\frac{\alpha^n + \beta^n}{\alpha^{-n} + \beta^{-n}}$
Consider an electron, a neutron and a proton initially at rest and placed along a straight line such that the neutron is exactly at the center of the line joining the electron and...
Functions F(a, b) and G(a, b) are defined as follows: F(a,b) = $(a - b)^2$ and G(a,b) = $|a - b|$, where $|x|$ represents the absolute value of x. What would be the value of G(F(1,...
Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (...
If a synchronous motor is running at a leading power factor, its excitation induced voltage (E_f) is
Consider a lossy transmission line with V₁ and V₂ as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance of the line, respectively....
The transfer function of a system is given by, $V_o(s) / V_i(s) = (1-s) / (1+s)$. Let the output of the system be $v_o(t) = V_m sin(\omega t + \phi)$ for the input, $v_i(t) = V_m s...
When a unit ramp input is applied to the unity feedback system having closed loop transfer function $\frac{C(s)}{R(s)} = \frac{Ks+b}{s^2+as+b}$, $(a>0, b>0, K>0)$, the steady state...
An e-mail password must contain three characters. The password has to contain one numeral from 0 to 9, one upper case and one lower case character from the English alphabet. How ma...
Among 150 faculty members in an institute, 55 are connected with each other through Facebook® and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook® or Wh...
In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code?
Consider the system with following input-output relation $y[n] = (1+(-1)^n) x[n]$ where, $x[n]$ is the input and $y[n]$ is the output. The system is
The transfer function C(s) of a compensator is given below. $C(s) = \frac{(1+\frac{s}{0.1})(1+\frac{s}{100})}{(1+s)(1+\frac{s}{10})}$ The frequency range in which the phase (lead)...
The graph of a network has 8 nodes and 5 independent loops. The number of branches of the graph is
A 4 pole induction machine is working as an induction generator. The generator supply frequency is 60 Hz. The rotor current frequency is 5 Hz. The mechanical speed of the rotor in...
In the figure, the voltages are $v_1(t) = 100\cos(\omega t)$, $v_2(t) = 100\cos(\omega t + \pi/18)$ and $v_3(t) = 100\cos(\omega t + \pi/36)$. The circuit is in sinusoidal steady s...
A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probabi...
Two resistors with nominal resistance values $R_1$ and $R_2$ have additive uncertainties $\Delta R_1$ and $\Delta R_2$, respectively. When these resistances are connected in parall...
A source is supplying a load through a 2-phase, 3-wire transmission system as shown in figure below. The instantaneous voltage and current in phase-a are $v_{an} = 220 \sin (100\pi...
A stationary closed Lissajous pattern on an oscilloscope has 3 horizontal tangencies and 2 vertical tangencies for a horizontal input with frequency 3 kHz. The frequency of the ver...
Match the transfer functions of the second-order systems with the nature of the systems given below. Transfer functions P: 15 / (s² + 5s + 15) Q: 25 / (s² + 10s + 25) R: 35 / (s² +...
A designer uses marbles of four different colours for his designs. The cost of each marble is the same, irrespective of the colour. The table below shows the percentage of marbles...
P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only one set of oars. The following additional facts are available. (i) The boat held two person...
A positive charge of 1 nC is placed at (0, 0, 0.2) where all dimensions are in metres. Consider the x - y plane to be a conducting ground plane. Take \epsilon_0 = 8.85\times10^{-12...
For a 3-input logic circuit shown below, the output Z can be expressed as
A 3-bus power system is shown in the figure below, where the diagonal elements of Y-bus matrix are: $Y_{11} = -j12$ pu, $Y_{22} = -j15$ pu and $Y_{33} = -j7$ pu. The per unit value...
A closed loop system has the characteristic equation given by s³ + Ks² + (K+2)s + 3 = 0. For this system to be stable, which one of the following conditions should be satisfied?
A phase-controlled, single-phase, full-bridge converter is supplying a highly inductive DC load. The converter is fed from a 230 V, 50 Hz, AC source. The fundamental frequency in H...
Let f be a real-valued function of a real variable defined as f(x) = x² for x\ge0, and f(x) = -x² for x<0. Which one of the following statements is true?
In the circuit shown, the diodes are ideal, the inductance is small, and Io ≠ 0. Which one of the following statements is true?
The value of the directional derivative of the function \Phi(x, y, z) = xy² + yz² + zx² at the point (2, -1, 1) in the direction of the vector p = i + 2j + 2k is
The slope and level detector circuit in a CRO has a delay of 100 ns. The start-stop sweep generator has a response time of 50 ns. In order to display correctly, a delay line of
The Boolean expression AB + AC + BC simplifies to
The value of the integral \oint_C \frac{z+1}{z^2-4} dz in counter clockwise direction around a circle C of radius 1 with center at the point z = -2 is
A three-phase voltage source inverter with ideal devices operating in 180° conduction mode is feeding a balanced star-connected resistive load. The DC voltage input is Vdc. The pea...
For the circuit shown in the figure below, assume that diodes D1, D2 and D3 are ideal. The DC components of voltages v₁ and v₂, respectively are
In the logic circuit shown in the figure, Y is given by
A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is...
The figure shows the per-phase representation of a phase-shifting transformer connected between buses 1 and 2, where α is a complex number with non-zero real and imaginary parts. F...
For the power semiconductor devices IGBT, MOSFET, Diode and Thyristor, which one of the following statements is TRUE?
The op-amp shown in the figure is ideal. The input impedance $\frac{v_{in}}{i_{in}}$ is given by
The figure below shows the circuit diagram of a controlled rectifier supplied from a 230 V, 50 Hz, 1-phase voltage source and a 10:1 ideal transformer. Assume that all devices are...
A continuous-time input signal $x(t)$ is an eigenfunction of an LTI system, if the output is
Consider $g(t) = \begin{cases} t - \lfloor t \rfloor, & t \ge 0 \\ t - \lceil t \rceil, & \text{otherwise} \end{cases}$, where $t \in \mathbb{R}$. Here, $\lfloor t \rfloor$ represe...
Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arri...
Let $I = c \iint_R xy^2 \, dxdy$, where $R$ is the region shown in the figure and $c = 6 \times 10^{-4}$. The value of $I$ equals _________ (Give the answer up to two decimal place...
Consider a non-singular $2 \times 2$ square matrix $\mathbf{A}$. If $trace(\mathbf{A})=4$ and $trace(\mathbf{A}^2)=5$, the determinant of the matrix $\mathbf{A}$ is ________ (up to...
The power supplied by the 25 V source in the figure shown below is ________ W.
Let $f$ be a real-valued function of a real variable defined as $f(x)=x-[x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\int_{0.25}^{1.25} f(...
Consider a function f(x,y,z) given by f(x, y, z) = (x² + y² - 2z²) (y² + z²) The partial derivative of this function with respect to x at the point,x = 2, y = 1 and z = 3 is
In the two-port network shown, the h₁₁ parameter (where, h₁₁=V₁/I₁, when V₂=0) in ohms is ________ (up to 2 decimal places).
The equivalent resistance between the terminals A and B is ________ Ω.
Let x and y be integers satisfying the following equations 2x² + y² = 34 x + 2y = 11 The value of (x + y) is _________.
Let y² - 2y + 1 = x and √x + y = 5. The value of x + √y equals _________ (Give the answer up to three decimal places)
The series impedance matrix of a short three-phase transmission line in phase coordinates is [Zs Zm Zm; Zm Zs Zm; Zm Zm Zs]. If the positive sequence impedance is (1 + j 10) Ω, and...
A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor...
The positive, negative and zero sequence impedances of a 125 MVA, three-phase, 15.5 kV, star-grounded, 50 Hz generator are j0.1 pu, j0.05 pu and j0.01 pu respectively on the machin...
A 10-bus power system consists of four generator buses indexed as G1, G2, G3, G4 and six load buses indexed as L1, L2, L3, L4, L5, L6. The generator-bus G1 is considered as slack b...
For the given 2-port network, the value of transfer impedance z₂₁ in ohms is _________.
The initial charge in the 1 F capacitor present in the circuit shown is zero. The energy in joules transferred from the DC source until steady state condition is reached equals ___...
A 1000 × 1000 bus admittance matrix for an electric power system has 8000 non-zero elements. The minimum number of branches (transmission lines and transformers) in this system are...
Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30° is ______. (Give the answer up to two decimal places.)
The mean square value of the given periodic waveform f(t) is _____.
The following measurements are obtained on a single phase load: V = 220 V ±1%, I = 5.0 A ± 1% and W = 555 W ± 2%. If the power factor is calculated using these measurements, the wo...
The waveform of the current drawn by a semi-converter from a sinusoidal AC voltage source is shown in the figure. If Io = 20 A, the rms value of fundamental component of the curren...
A separately excited dc motor has an armature resistance R_a = 0.05 Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 500 Nm...
The nominal-π circuit of a transmission line is shown in the figure. Impedance Z = 100∠80° Ω and reactance X = 3300 Ω. The magnitude of the characteristic impedance of the transmis...
In the converter circuit shown below, the switches are controlled such that the load voltage $v_o(t)$ is a 400 Hz square wave. The RMS value of the fundamental component of $v_o(t)...
In a load flow problem solved by Newton-Raphson method with polar coordinates, the size of the Jacobian is 100 × 100. If there are 20 PV buses in addition to PQ buses and a slack b...
A 3-phase voltage source inverter is supplied from a 600V DC source as shown in the figure below. For a star connected resistive load of $20 \Omega$ per phase, the load power for 1...
Consider a unity feedback system with forward transfer function given by G(s) = 1 / ((s+1)(s+2)) The steady-state error in the output of the system for a unit-step input is _______...
A transformer with toroidal core of permeability μ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius r << R, and neglecting any...
A function $f(x)$ is defined as $f(x)=\begin{cases} e^x, & x<1 \ \ln x+ax^2+bx, & x\ge1 \end{cases}$, where $x \in \mathbb{R}$. Which one of the following statements is TRUE?
Let g(x) = { -x, x ≤ 1 and f(x) = { 1-x, x ≤ 0 x+1, x ≥ 1 x², x > 0 Consider the composition of f and g, i.e., (f∘g)(x) = f(g(x)). The number of discontinuities in (f∘g)(x) present...
Consider the differential equation $(t^2-81)\frac{dy}{dt}+5t y = \sin(t)$ with $y(1) = 2\pi$. There exists a unique solution for this differential equation when $t$ belongs to the...
A 0-1 Ampere moving iron ammeter has an internal resistance of 50 mΩ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating freque...
The value of the contour integral in the complex-plane ∫ (z³ - 2z + 3) / (z - 2) dz along the contour |z| = 3, taken counter-clockwise is
The positive, negative and zero sequence impedances of a three phase generator are Z₁, Z₂ and Z₀ respectively. For a line-to-line fault with fault impedance Zf, the fault current i...
The eigenvalues of the matrix given below are $$\begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & -3 & -4 \end{bmatrix}$$
Consider the line integral $I = \int_C (x^2 +iy^2)dz$, where $z = x + iy$. The line $C$ is shown in the figure below. The value of $I$ is
Consider the two bus power system network with given loads as shown in the figure. All the values shown in the figure are in per unit. The reactive power supplied by generator G1 a...
Two passive two-port networks are connected in cascade as shown in figure. A voltage source is connected at port 1. Given V₁ = A₁V₂ + B₁I₂ I₁ = C₁V₂ + D₁I₂ V₂ = A₂V₃ + B₂I₃ I₂ = C₂...
For the balanced Y-Y connected 3-phase circuit shown in the figure below, the line-line voltage is 208 V rms and the total power absorbed by the load is 432 W at a power factor of...
The per-unit power output of a salient-pole generator which is connected to an infinite bus, is given by the expression, P = 1.4 sin δ + 0.15 sin 2δ, where δ is the load angle. New...
Let a causal LTI system be characterized by the following differential equation, with initial rest condition $\frac{d^2y}{dt^2} + 7\frac{dy}{dt} + 10y(t) = 4x(t) + 5\frac{dx(t)}{dt...
In the circuit shown below, the value of capacitor C required for maximum power to be transferred to the load is
Let the signal $x(t) = \sum_{k=-\infty}^{+\infty} (-1)^k \delta (t - \frac{k}{2000})$ be passed through an LTI system with frequency response H($\omega$), as given in the figure be...
The output y(t) of the following system is to be sampled, so as to reconstruct it from its samples uniquely. The required minimum sampling rate is
A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t=0 as shown in the figure. Assume i(0) = 0, v(0) = 0. Which one of the following circul...
The equivalent impedance Zeq for the infinite ladder circuit shown in the figure is
In the system whose signal flow graph is shown in the figure, $U_1(s)$ and $U_2(s)$ are inputs. The transfer function $\frac{Y(s)}{U_1(s)}$ is
A cascade system having the impulse responses h₁(n) = {1, -1} and h₂(n) = {1, 1} is shown in the figure below, where symbol ↑ denotes the time origin. The input sequence x(n) for w...
The transfer function of the system Y(s)/U(s) whose state-space equations are given below is: $\begin{bmatrix} \dot{x_1}(t) \\ \dot{x_2}(t) \end{bmatrix} = \begin{bmatrix} 1 & 2 \\...
Consider a system governed by the following equations $\frac{dx_1(t)}{dt} = x_2(t) - x_1(t)$ $\frac{dx_2(t)}{dt} = x_1(t) - x_2(t)$ The initial conditions are such that $x_1(0) < x...
A 220 V, 10 kW, 900 rpm separately excited DC motor has an armature resistance Rₐ = 0.02 Ω. When the motor operates at rated speed and with rated terminal voltage, the electromagne...
The root locus of the feedback control system having the characteristic equation s² +6Ks +2s+5=0 where K > 0, enters into the real axis at
The load shown in the figure is supplied by a 400 V (line-to-line), 3-phase source (RYB sequence). The load is balanced and inductive, drawing 3464 VA. When the switch S is in posi...
The number of roots of the polynomial, $s^7 + s^6 + 7s^5 + 14s^4 + 31s^3 + 73s^2 + 25s + 200$, in the open left half of the complex plane is
The range of K for which all the roots of the equation s³ + 3s² + 2s + K = 0 are in the left half of the complex s-plane is
If C is a circle $|z| = 4$ and $f(z) = \frac{z^2}{(z^2-3z+2)^2}$, then $\oint_C f(z)dz$ is
The approximate transfer characteristic for the circuit shown below with an ideal operational amplifier and diode will be
Which of the following systems has maximum peak overshoot due to a unit step input?
The output expression for the Karnaugh map shown below is
Which one of the following statements is true about the digital circuit shown in the figure
For the circuit shown in the figure below, it is given that $V_{CE} = \frac{V_{CC}}{2}$. The transistor has $\beta = 29$ and $V_{BE} = 0.7$ V when the B-E junction is forward biase...
The logical gate implemented using the circuit shown below where, V₁ and V₂ are inputs (with 0 V as digital 0 and 5 V as digital 1) and VOUT is the output, is
Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean function $F = m_0 + m_2 + m_3 + m_5 + m_7$, where $m_i$ denotes the $i^{th}$ minter...
Consider the two continuous-time signals defined below: $x_1(t) = \begin{cases} |t|, & -1 \le t \le 1 \\ 0, & \text{otherwise} \end{cases}$, $x_2(t) = \begin{cases} 1-|t|, & -1 \le...
For the circuit shown below, assume that the OPAMP is ideal. Which one of the following is TRUE?
The input voltage V_DC of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous, and output voltage is...
The figure below shows a half-bridge voltage source inverter supplying an RL-load with R = 40 Ω and L= $\frac{0.3}{\pi}$ H. The desired fundamental frequency of the load voltage is...
A load is supplied by a 230 V, 50 Hz source. The active power P and the reactive power Q consumed by the load are such that 1 kW $\le P \le$ 2 kW and 1 kVAR $\le Q \le$ 2 kVAR. A c...
The signal energy of the continuous-time signal $x(t) = [(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)]$ is
A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var{Y}, wher...
The bus admittance matrix for a power system network is $[-j39.9 \quad j20 \quad j20 \\ j20 \quad -j39.9 \quad j20 \text{ pu.} \\ j20 \quad j20 \quad -j39.9]$ There is a transmissi...
The Fourier transform of a continuous-time signal x(t) is given by X(ω) = 1 / (10+jω)^2, -∞ < ω < ∞, where j=√-1 and ω denotes frequency. Then the value of |ln x(t)| at t =1 is ___...
For the network given in figure below, the Thevenin's voltage V_ab is
The switch in the figure below was closed for a long time. It is opened at t = 0. The current in the inductor of 2 H for t ≥ 0, is
In the circuit shown in the figure, the bipolar junction transistor (BJT) has a current gain β = 100. The base-emitter voltage drop is a constant, VBE = 0.7 V. The value of the The...
Only one of the real roots of f(x) = x^6 - x - 1 lies in the interval 1 ≤ x ≤ 2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required min...
As shown in the figure, C is the arc from the point (3,0) to the point (0,3) on the circle x² + y² = 9. The value of the integral ∫_C (y² + 2yx)dx + (2xy + x²)dy is ________ (up to...
A 120 V DC shunt motor takes 2 A at no load. It takes 7 A on full load while running at 1200 rpm. The armature resistance is 0.8 Ω, and the shunt field resistance is 240 Ω. The no...
A star-connected, 12.5kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator: R₁=0.3Ω, R₂=0.3Ω,...
Let f(x) = 3x³ −7x² + 5x + 6. The maximum value of f(x) over the interval [0, 2] is ________ (up to 1 decimal place).
In the circuit shown below, the maximum power transferred to the resistor R is _________ W.
The magnitude of magnetic flux density (B) in micro Teslas (µT), at the center of a loop of wire wound as a regular hexagon of side length 1 m carrying a current (I=1 A), and place...
A 25 kVA, 400 V, Δ-connected, 3-phase, cylindrical rotor synchronous generator requires a field current of 5 A to maintain the rated armature current under short-circuit condition....
Let A = $\begin{bmatrix} 1 & 0 & -1 \\ -1 & 2 & 0 \\ 0 & 0 & -2 \end{bmatrix}$ and $B = A^3 - A^2 - 4A + 5I$, where $I$ is the $3 \times 3$ identity matrix. The determinant of $B$...
The capacitance of an air-filled parallel-plate capacitor is 60 pF. When a dielectric slab whose thickness is half the distance between the plates, is placed on one of the plates c...
A 375 W, 230 V, 50 Hz, capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Zm = (12.50 + j15.75) Ω (main win...
If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA, Y-Δ transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere...
Two parallel connected, three-phase, 50Hz, 11 kV, star-connected synchronous machines A and B, are operating as synchronous condensers. They together supply 50 MVAR to a 11 kV grid...
The unit step response $y(t)$ of a unity feedback system with open loop transfer function $G(s)H(s) = \frac{K}{(s+1)^2(s+2)}$ is shown in the figure. The value of $K$ is ________ (...
Consider the system described by the following state space representation $\begin{bmatrix} \dot{x}_1(t) \\ \dot{x}_2(t) \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 0 & -2 \end{bmatrix...
A 220 V DC series motor runs drawing a current of 30 A from the supply. Armature and field circuit resistances are 0.4 Ω and 0.1 Ω, respectively. The load torque varies as the squa...
A three-phase load is connected to a three-phase balanced supply as shown in the figure. If $V_{an} = 100\angle 0^\circ$ V, $V_{bn} = 100\angle -120^\circ$ V and $V_{cn} = 100\angl...
A 10 ½ digit timer counter possesses a base clock of frequency 100 MHz. When measuring a particular input, the reading obtained is the same in: (i) Frequency mode of operation with...
A three-phase, three winding Δ/Δ/Y (1.1 kV/6.6 kV/400 V) transformer is energized from AC mains at the 1.1 kV side. It supplies 900 kVA load at 0.8 power factor lag from the 6.6 kV...
The voltage across the circuit in the figure, and the current through it, are given by the following expressions: v(t) = 5 - 10 cos(wt + 60°) V i(t) = 5 + X cos(wt) A where w = 100...
In the circuit shown in the figure, the diode used is ideal. The input power factor is _________. (Give the answer up to two decimal places.)
For the synchronous sequential circuit shown below, the output Z is zero for the initial conditions Q_A Q_B Q_C = Q'_A Q'_B Q'_C = 100. The minimum number of clock cycles after whi...
A phase controlled single phase rectifier, supplied by an AC source, feeds power to an R-L-E load as shown in the figure. The rectifier output voltage has an average value given by...
A separately excited DC generator supplies 150 A to a 145 V DC grid. The generator is running at 800 RPM. The armature resistance of the generator is 0.1Ω. If the speed of the gene...
For a system having transfer function G(s) = $\frac{-s+1}{s+1}$, a unit step input is applied at time t = 0. The value of the response of the system at t = 1.5 sec (rounded off to...
The figure shows two buck converters connected in parallel. The common input dc voltage for the converters has a value of 100 V. The converters have inductors of identical value. T...
In the circuit shown all elements are ideal and the switch S is operated at 10 kHz and 60% duty ratio. The capacitor is large enough so that the ripple across it is negligible and...
A 3-phase 900 kVA, 3 kV / √3 kV (Δ/Y), 50 Hz transformer has primary (high voltage side) resistance per phase of 0.3 Ω and secondary (low voltage side) resistance per phase of 0.02...
Consider a causal and stable LTI system with rational transfer function H(z), whose corresponding impulse response begins at n = 0. Furthermore, H(1) = $\frac{5}{4}$. The poles of...
Consider an overhead transmission line with 3-phase, 50 Hz balanced system with conductors located at the vertices of an equilateral triangle of length Dab = Dbc = Dca = 1m as show...
A 200 V DC series motor, when operating from rated voltage while driving a certain load, draws 10 A current and runs at 1000 r.p.m. The total series resistance is 1 Ω. The magnetic...
The circuit shown in the figure uses matched transistors with a thermal voltage V_T = 25 mV. The base currents of the transistors are negligible. The value of the resistance R in k...
A 3-phase, 50 Hz generator supplies power of 3MW at 17.32 kV to a balanced 3-phase inductive load through an overhead line. The per phase line resistance and reactance are 0.25$\Om...
A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value...
Two generating units rated 300 MW and 400 MW have governor speed regulation of 6% and 4% respectively from no load to full load. Both the generating units are operating in parallel...
The figure below shows an uncontrolled diode bridge rectifier supplied from a 220 V, 50 Hz, 1-phase ac source. The load draws a constant current I_o = 14 A. The conduction angle of...
The positive, negative, and zero sequence reactances of a wye-connected synchronous generator are 0.2 pu, 0.2 pu, and 0.1 pu, respectively. The generator is on open circuit with a...
A 3-phase, 2-pole, 50 Hz, synchronous generator has a rating of 250 MVA, 0.8 pf lagging. The kinetic energy of the machine at synchronous speed is 1000 MJ. The machine is running s...
The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are R₁ = R₂' = X₁₁ = X₁₂'=12 Ω, X_M=240 Ω and s is the slip. At no-load, the m...
The voltage v(t) across the terminals a and b as shown in the figure, is a sinusoidal voltage having a frequency ω = 100 radian/s. When the inductor current i(t) is in phase with t...
A thin soap bubble of radius R = 1 cm, and thickness a = 3.3 µm (a << R), is at a potential of 1 V with respect to a reference point at infinity. The bubble bursts and becomes a si...
The figure shows the single line diagram of a power system with a double circuit transmission line. The expression for electrical power is 1.5 sin δ, where δ is the rotor angle. Th...
After Rajendra Chola returned from his voyage to Indonesia, he ________ to visit the temple in Thanjavur.
Choose the option with words that are not synonyms.
Saturn is ________ to be seen on a clear night with the naked eye.
Research in the workplace reveals that people work for many reasons ________.
Rahul, Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs ar...
There are five buildings called V, W, X, Y and Z in a row (not necessarily in that order). V is to the West of W. Z is to the East of X and the West of V. W is to the West of Y. Wh...
A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each...
Find the smallest number y such that y × 162 is a perfect cube.
The probability that a k-digit number does NOT contain the digits 0, 5, or 9 is
There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is
"We lived in a culture that denied any merit to literary works, considering them important only when they were handmaidens to something seemingly more urgent – namely ideology. Thi...
"The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history." Which of the following statements b...
There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labelled. If you are p...
Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her...
The expression $\frac{(x+y)-|x-y|}{2}$ is equal to
X is a 30 digit number starting with the digit 4 followed by the digit 7. Then the number X³ will have
The number of roots of e^x + 0.5x² - 2 = 0 in the range [-5, 5] is
Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes...
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals...
An air pressure contour line joins locations in a region having the same atmospheric pressure. The following is an air pressure contour plot of a geographical region. Contour lines...