GATE 2014 Electrical Engineering

The fuel cost functions of two power plants are Plant $${P_1}:\,{C_1} = 0.05\,Pg_1^2 + AP{g_1} + B$$ Plant $${P_2}:\,{C_2} = 0.10\,Pg_2^2 + 3AP{g_2} + 2B$$ Where, $$P{g_1}$$ and $$...

Given a system of equations $$$x + 2y + 2z = {b_1}$$$ $$$5x + y + 3z = {b_2}$$$ Which of the following is true its solutions

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

An incandescent lamp is marked 40W, 240V. If resistance at room temperature $$\left(26^\circ\mathrm C\right)\;\mathrm{is}\;120\mathrm\Omega$$ and temperature coefficient of resista...

The following four vector fields are given in cartesian coordinate system. The vector field which does not satisfy the property of magnetic flux density is

A 15kW, 230V dc shunt motor has armature circuit resistance of 0.4 $$\Omega$$ and field circuit resistance of 230 $$\Omega$$. At no load and rated voltage, the motor runs at 1400 r...

The core loss of a single phase, 230/115 V, 50 Hz power transformer is measured from 230 V side by feeding the primary (230 V side) from a variable voltage variable frequency sourc...

An 8-pole, 3-phase, 50 Hz induction motor is operating at a speed of 700 rpm. The frequency of the rotor current of the motor in Hz is ________.

A 3 phase, 50 Hz, 6 pole induction motor has a rotor resistance of 0.1 Ω and reactance of 0.92 Ω. Neglect the voltage drop in stator and assume that the rotor resistance is constan...

A star connected 400 V, 50 Hz, 4 pole synchronous machine gave the following open circuit and short circuit test results: Open circuit test: V OC = 400 V (rms, line–to–line) at fie...

Let $$S$$ be the set of points in the complex plane corresponding to the unit circle. $$\left( {i.e.,\,\,S = \left\{ {z:\left| z \right| = 1} \right\}} \right.$$ Consider the funct...

A fair coin is tossed $$n$$ times. The probability that the difference between the number of heads and tails is $$(n-3)$$ is

A cascade of three identical modulo -$$5$$ counters has an over all modulus of

Let $$X\left( s \right) = {{3s + 5} \over {{s^2} + 10s + 20}}$$ be the Laplace Transform of a signal $$x(t).$$ Then $$\,x\left( {{0^ + }} \right)$$ is

In an unbalanced three phase system phase current $${{\rm I}_a} = 1\angle \left( { - {{90}^0}} \right)\,\,pu,\,\,$$ negative sequence current $$\,{{\rm I}_{b2}} = 4\angle \left( {...

The undesirable property of an electrical insulating material is

The line integral of function $$F=yzi,$$ in the counterclockwise direction, along the circle $${x^2} + {y^2} = 1$$ at $$z=1$$ is

Let $$f\left( x \right) = x{e^{ - x}}.$$ The maximum value of the function in the interval $$\left( {0,\infty } \right)$$ is

A system matrix is given as follows $$$A = \left[ {\matrix{ 0 & 1 & { - 1} \cr { - 6} & { - 11} & 6 \cr { - 6} & { - 11} & 5 \cr } } \right].$$$ The absolute value of the ratio of...

The solution for the differential equation $$\,\,{{{d^2}x} \over {d{t^2}}} = - 9x,\,\,$$ with initial conditions $$x(0)=1$$ and $${{{\left. {\,\,\,\,{{dx} \over {dt}}} \right|}_{t...

In an oscilloscope screen, linear sweep is applied at the

Let $$X\left(z\right)=\frac1{1-z^{-3}}$$ be the Z–transform of a causal signal x[n]. Then, the values of x[2] and x[3] are

x(t) is nonzero only for $$T_x\;<\;t\;<\;T_x^1$$ , and similarly, y(t) is nonzero only for $$T_y\;<\;t\;<\;T_y^1$$ . Let z(t) be convolution of x(t) and y(t). Which one of the foll...

For a periodic square wave, which one of the following statements is TRUE?

Let f(t) be a continuous time signal and let F($$\omega$$) be its Fourier Transform defined by $$F\left(\omega\right)=\int_{-\infty}^\infty f\left(t\right)e^{-j\omega t}dt$$. Defin...

Power consumed by a balanced $$3$$-phase, $$3$$-wire load is measured by the two wattmeter method. The first wattmeter reads twice that of the second. Then the load impedance angle...

The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected in series. The PMMC meter contains 100 turns in the coil, t...

Consider a die with the property that the probability of a face with $$'n'$$ dots showing up is proportional to $$'n'.$$ The probability of the face with three dots showing up is _...

A single phase induction motor draws $$12MW$$ power at $$0.6$$ lagging power. A capacitor is connected in parallel to the motor to improve the power factor of the combination of mo...

Two identical coupled inductors are connected in series. The measured inductances for the two possible series connections are 380 μH and 240 μH. Their mutual inductance in μH is __...

A 250 V dc shunt machine has armature circuit resistance of 0.6 $$\Omega$$ and field circuit resistance of 125 $$\Omega$$. The machine is connected to 250 V supply mains. The motor...

For a single phase, two winding transformer, the supply frequency and voltage are both increased by 10%. The percentage changes in the hysteresis loss and eddy current loss, respec...

A three-phase, 4-pole, self excited induction generator is feeding power to a load at a frequency $$f_1$$. If the load is partially removed, the frequency becomes $$f_2$$. If the s...

In a constant V/f control of induction motor, the ratio V/f is maintained constant from 0 to base frequency, where V is the voltage applied to the motor at fundamental frequency f....

Minimum of the real valued function $$f\left( x \right) = {\left( {x - 1} \right)^{2/3}}$$ occurs at $$x$$ equal to

The horizontally placed conductors of a single phase line operating at $$50$$ $$Hz$$ are having outside diameter of $$1.6$$ cm, and the spacing between centers of the conductors is...

There are two generators in a power system. No-load frequencies of the generators are $$51.5$$ $$Hz$$ and $$51$$ $$Hz,$$ respectively, and both are having droop constant of $$1$$ $...

A step-up chopper is used to feed a load at $$400$$ $$V$$ $$dc$$ from a $$250$$ $$V$$ $$dc$$ source. The inductor current is continuous. If the ‘off’ time of the switch is $$20\,\,...

The minimum value of the function $$f\left( x \right) = {x^3} - 3{x^2} - 24x + 100$$ in the interval $$\left[ { - 3,3} \right]$$ is

A system with the open loop transfer function $$G\left( s \right) = {K \over {s\left( {s + 2} \right)\left( {{s^2} + 2s + 2} \right)}}$$ is connected in a negative feedback configu...

The closed-loop transfer function of a system is $$T\left( s \right) = {4 \over {\left( {{s^2} + 0.4s + 4} \right)}}.$$ The steady state error due to unit step input is ________

A $$20$$-pole alternator is having $$180$$ identical stator slots with $$6$$ conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize...

A three phase, $$100$$ $$MVA,$$ $$25$$ $$kV$$ generator has solidly grounded neutral. The positive, negative, and the zero sequence reactance's of the generator are $$0.2$$ $$pu$$,...

Consider the differential equation $${x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - y = 0.\,\,$$ Which of the following is a solution to this differential equation for $$x >...

The state transition matrix for the system $$\left[ {\matrix{ {\mathop {{x_1}}\limits^ \bullet } \cr {\mathop {{x_2}}\limits^ \bullet } \cr } } \right] = \left[ {\matrix{ 1 & 0 \cr...

A three phase star-connected load is drawing power at a voltage of 0.9 pu and 0.8 power factor lagging. The three phase base power and base current are 100 MVA and 437.38 A respect...

A synchronous generator is connected to an infinite bus with excitation voltage $${E_f} = 1.3\,pu.$$ The generator has a synchronous reactance of $$1.1$$ $$pu$$ and is delivering r...

A $$JK$$ flip flop can be implemented by $$T$$ flip flops. Identify the correct implementation.

Shunt reactors are sometimes used in high voltage transmission systems to

For the transfer function $$G\left( s \right) = {{5\left( {s + 4} \right)} \over {s\left( {s + 0.25} \right)\left( {{s^2} + 4s + 25} \right)}}.$$ The values of the constant gain te...

Which one of the following statements is true for all real symmetric matrices?

The second order dynamic system $${{dX} \over {dt}} = PX + Qu,\,\,\,y = RX$$ has the matrices $$P,Q,$$ and $$R$$ as follows: $$P = \left[ {\matrix{ { - 1} & 1 \cr 0 & { - 3} \cr }...

To evaluate the double integral $$\int\limits_0^8 {\left( {\int\limits_{y/2}^{\left( {y/2} \right) + 1} {\left( {{{2x - y} \over 2}} \right)dx} } \right)dy,\,\,} $$ we make the sub...

A single-phase $$SCR$$ based $$ac$$ regulator is feeding power to a load consisting of $$5\,\,\Omega $$ resistance and $$16$$ $$mH$$ inductance. The input supply is $$230$$ $$V,$$...

The $$SOP$$ (sum of products) from of a Boolean function is $$\sum \left( {0,1,3,7,11} \right),$$ where inputs are $$A,B,C,D$$ ($$A$$ is $$MSB$$, and $$D$$ is $$LSB$$). The equival...

All the values of the multi valued complex function $${1^i},$$ where $$i = \sqrt { - 1} $$ are

Let $$X$$ be a random variable with probability density function $$f\left( x \right) = \left\{ {\matrix{ {0.2} & {for\,\left| x \right| \le 1} \cr {0.1} & {for\,1 < \left| x \right...

Consider an LTI system with transfer function $$H\left(s\right)=\frac1{s\left(s+4\right)}$$.If the input to the system is cos(3t) and the steady state output is $$A\sin\left(3t+\al...

Consider an LTI system with impulse response $$h\left(t\right)=e^{-5t}u\left(t\right)$$ . If the output of the system is $$y\left(t\right)=e^{-3t}u\left(t\right)-e^{-5t}u\left(t\ri...

A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is

An input signal x(t) = 2 + 5sin(100$$\mathrm\pi$$t) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by $$$\frac{Y\le...

A discrete system is represented by the difference equation $$$\begin{bmatrix}X_1\left(k+1\right)\\X_2\left(k+2\right)\end{bmatrix}=\begin{bmatrix}a&a-1\\a+1&a\end{bmatrix}\begin{b...

Suppose that resistors $${R_1}$$ ܴand $${R_2}$$ ܴare connected in parallel to give an equivalent resistor $$R.$$ If resistors ܴ$${R_1}$$ and $${R_2}$$ ܴ have tolerance of $$1$$% ea...

Two ammeters $$X$$ and $$Y$$ have resistances of $$1.2$$ $$\Omega $$ and $$1.5$$ $$\Omega $$ respectively and they give full-scale deflection with $$150$$ $$mA$$ and $$250$$ $$mA$$...

While measuring power of a three-phase balanced load by the two-wattmeter method, the readings are $$100$$ $$W$$ and $$250$$ $$W$$. The power factor of the load is ___________.

For a $$400$$ $$km$$ long transmission line, the series impedance is $$(0.0 + j0.5)$$ $$\Omega /km$$ and the shunt admittance is $$(0.0 + j5.0)$$ $$\mu \,mho/km.$$ The magnitude of...

The line A to neutral voltage is $$10\angle15^\circ\;V$$ for a balanced three phase star-connected load with phase sequence ABC. The voltage of line B with respect to line C is giv...

For a fully transposed transmission line

Let $$\,\,\nabla .\left( {fV} \right) = {x^2}y + {y^2}z + {z^2}x,\,\,$$ where $$f$$ and $$V$$ are scalar and vector fields respectively. If $$V=yi+zj+xk,$$ then $$\,V.\left( {\nabl...

The mean thickness and variance of silicon steel laminations are 0.2 mm and 0.02 respectively. The varnish insulation is applied on both the sides of the laminations. The mean thic...

A non-ideal voltage source V S has an internal impedance of Z S . If a purely resistive load is to be chosen that maximizes the power transferred to the load, its value must be

A series RLC circuit is observed at two frequencies. At $$\omega_1$$ = 1k rad / s, we note that source voltage $$V_1=100\angle0^\circ V$$ results in a current $$I_1=0.03\angle31^\c...

A hollow metallic sphere of radius r is kept at potential of 1 Volt. The total electric flux coming out of the concentric spherical surface of radius R(>r) is

The no-load speed of a 230 V separately excited dc motor is 1400 rpm. The armature resistance drop and the brush drop are neglected. The field current is kept constant at rated val...

A separately excited 300 V DC shunt motor under no load runs at 900 rpm drawing an armature current of 2 A. The armature resistance is 0.5 $$\Omega$$ and leakage inductance is 0.01...

A single phase induction motor is provided with capacitor and centrifugal switch in series with auxiliary winding. The switch is expected to operate at a speed of 0.7 Ns, but due t...

In a synchronous machine, hunting is predominantly damped by

A particle, starting from origin at $$t=0$$ $$s,$$ is traveling along $$x$$-axis with velocity $$v = {\pi \over 2}\cos \left( {{\pi \over 2}t} \right)m/s$$ At $$t=3$$ $$s,$$ the di...

A single-input single-output feedback system has forward transfer function $$𝐺(𝑠)$$ and feedback transfer function $$𝐻(𝑠).$$ It is given that $$\left| {G\left( s \right)H\left(...

A non-salient pole synchronous generator having synchronous reactance of $$0.8$$ $$pu$$ is supplying $$1$$ $$pu$$ power to a unity power factor load at a terminal voltage of $$1.1$...

In $$8085A$$ microprocessor, the operation performed by the instruction $$LHLD$$ $${2100_H}$$ is

Integration of the complex function $$f\left( z \right) = {{{z^2}} \over {{z^2} - 1}},$$ in the counterclockwise direction, around $$\left| {z - 1} \right| = 1,$$ is

Consider the system described by the following state space equations $$$\eqalign{ & \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] = \left[ {\matrix{ 0 & 1 \cr { - 1} & { - 1...

The function $$f\left( x \right) = {e^x} - 1\,\,$$ is to be solved using Newton $$-$$ Raphson method. If the initial value of $${x_0}$$ is taken $$1.0,$$ then the absolute error ob...

In a long transmission line with $$r, l, g$$ and $$𝑐$$ are the resistance, inductance, shunt conductance and capacitance per unit length respectively, the condition for distortion...

A 183-bus power system has 150PQ buses and 32 PV buses. In the general case, to obtain the load flow solution using Newton-Raphson method in polar coordinates, the minimum number o...

The complex power consumed by a constant-voltage load is given by $$\left( {{P_1} + {J_{q1}}} \right).\,\,$$ Where, $$\,1\,\,kW \le \,\,{P_1} \le \,\,\,1.5\,\,kW\,\,\,$$ and $$\,\,...

Lifetime of an electric bulb is a random variable with density $$f\left( x \right) = k{x^2},$$ where $$x$$ is measured in years. If the minimum and maximum lifetimes of bulb are $$...

$$A = \left[ {\matrix{ p & q \cr r & s \cr } } \right];B = \left[ {\matrix{ {{p^2} + {q^2}} & {pr + qs} \cr {pr + qs} & {{r^2} + {s^2}} \cr } } \right]$$ If the rank of matrix $$A$...

A periodic waveform observed across a load is represented by $$$V\left( t \right) = \left\{ {\matrix{ {1 + \sin \,\omega t} & {0 \le \omega t < 6\pi } \cr { - 1 + \sin \,\omega t}...

A signal is represented by $$$x\left(t\right)=\left\{\begin{array}{l}1\;\;\;\left|t\right|\;<\;1\\0\;\;\;\left|t\right|\;>\;1\end{array}\right.$$$ The Fourier transform of the conv...

A differentiable non constant even function x(t) has a derivative y(t), and their respective Fourier Transforms are X($$\omega$$) and Y($$\omega$$). Which of the following statemen...

For the signal f(t) = 3 sin8$$\mathrm\pi$$t + 6sin12$$\mathrm\pi$$t + sin14$$\mathrm\pi$$t, the minimum sampling frequency (in Hz) satisfying the Nyquist criterion is _________.

A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at 25 Hz. T...

An $$LPF$$ wattmeter of power factor $$0.2$$ is having three voltage settings $$300V,$$ $$150V$$ and $$75V,$$ and two current settings $$5 A$$ and $$10A.$$ The full scale reading i...