GATE 2005 Electrical Engineering
49 questions across 1 session
The output voltage waveform of a three - phase square-wave inverter contains
A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance...
The $$8085$$ assembly language instruction that stores the content of $$H$$ and $$L$$ registers into the memory locations $$2050H$$ and $$2051H,$$ respectively, is
A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven (i) at half the rated speed by armature voltage control and (ii) at 1.5 times the ra...
In relation to DC machines, match the following and choose the correct combination. Group-I(Performance variables) (P) Armature emf (E) (Q) Developed torque (T) (R) Developed power...
Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input line voltages
For an induction motor, operating at a slip 's', the ratio of gross power output to air gap power is equal to:
Under no load condition, if the applied voltage to an induction motor is reduced from the rated voltage to half the rated value,
A three-phase cage induction motor is started by direct-on-line (DOL) switching at the rated voltage. If the starting current drawn is 6 times the full load current, and the full l...
In a single phase induction motor driving a fan load, the reason for having a high resistance rotor is to achieve
Assertion [a]: Under V/f control of induction motor, the maximum value of the developed torque remains constant over a wide range of speed in the subsynchronous region. Reason [r]:...
In relation to the synchronous machines, which one of the following statements is false?
The p.u. parameters for a $$500$$ MVA machine on its own base are: Inertia, M = $$20$$ p.u.; reactance X = $$2$$ p.u. The p.u. values of inertia and reactance on $$100$$ MVA common...
For the function $$f\left( x \right) = {x^2}{e^{ - x}},$$ the maximum occurs when $$x$$ is equal to
The insulation strength of an EHV transmission line is mainly governed by
The conduction loss versus device current characteristic of a power $$MOSFET$$ is best approximated by
At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the res...
A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is
A digital-to-analog converter with a full -scale output voltage of $$3.5$$ $$V$$ has a resolution close to $$14$$ $$m$$ $$V.$$ Its bit size is
for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1,3)$$ is
A state variable system $$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \ri...
A coil of inductance $$10$$ $$H$$ resistance $$40\,\,\Omega $$ is connected as shown in Fig. After the switch $$S$$ has been in connection with point $$1$$ for a very long time, it...
High Voltage DC (HVDC) transmission is mainly used for
If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value
A system with zero initial conditions has the closed loop transfer function $$T\left( s \right) = {{{s^2} + 4} \over {\left( {s + 1} \right)\left( {s + 4} \right)}}.$$ The system o...
The typical frequency response of a two-stage direct coupled voltage amplifier is as shown in figure
The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \right),\,x\left( 0 \right) = {x_0}\,\,\,\,$$ is
In the $$GH(s)$$ plane, the Nyquist plot of the loop transfer function $$G\left( s \right)\,H\left( s \right) = {{\pi {e^{ - 0.25s}}} \over s}$$ passes through the negative real ax...
At a $$220$$ kV substation of a power system, it is given that the three-phase fault level is $$4000$$ MVA and single-line to ground fault level is $$5000$$ MVA. Neglecting the res...
The parameters of transposed overhead transmission line are given as: self reactance $${X_s} = 0.4\,\,\Omega /km$$ and Mutual reactance $$\,{X_m} = 0.1\,\,\Omega /km.\,\,$$ The pos...
If $$P$$ and $$Q$$ are two random events, then which of the following is true?
For the matrix $$P = \left[ {\matrix{ 3 & { - 2} & 2 \cr 0 & { - 2} & 1 \cr 0 & 0 & 1 \cr } } \right],$$ one of the eigen values is $$-2.$$ Which of the following is an eigen vecto...
A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance...
At an industrial sub-station with a $$4$$ $$MW$$ load, a capacitor of $$2$$ MVAR is installed to maintain the load power factor at $$0.97$$ lagging. If the capacitor goes out of se...
For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \right) + 2x\left( t \right) = 5,\,\,\,$$ the solution $$x(t)$$ a...
A state variable system $$\mathop X\limits^ \bullet \left( t \right) = \left( {\matrix{ 0 & 1 \cr 0 & { - 3} \cr } } \right)X\left( t \right) + \left( {\matrix{ 1 \cr 0 \cr } } \ri...
If $$R = \left[ {\matrix{ 1 & 0 & { - 1} \cr 2 & 1 & { - 1} \cr 2 & 3 & 2 \cr } } \right]$$ then the top row of $${R^{ - 1}}$$ is
The gain margin of a unity feedback control system with the open loop transfer function $$G\left( s \right) = {{\left( {s + 1} \right)} \over {{s^2}}}$$ is
In the matrix equation $$PX=Q$$ which of the following is a necessary condition for the existence of atleast one solution for the unknown vector $$X.$$
A three - phase diode bridge rectifier is fed from a $$400$$ $$V$$ $$RMS$$. $$50$$ $$Hz$$, three $$-$$ phase $$AC$$ source. If the load is purely resistive, then peak instantaneous...
The RMS value of the voltage v(t) = 3 + 4cos(3t) is
The Fourier series for the function f(x) = sin 2 x is
The Laplace transform of a function f(t) is F(s) = $$\frac{5s^2+23s+6}{s\left(s^2+2s+2\right)}$$. As $$t\rightarrow\infty$$, f(t) approaches
For the equation $$\ddot x\left(t\right)+3\dot x\left(t\right)+2x\left(t\right)=5$$, the solution x(t) approaches which of the following values as t$$\rightarrow\infty$$ ?
If u(k) is the unit step and $$\delta\left(k\right)$$ is the unit impulse function, the inverse z-transform of $$F\left(z\right)=\frac1{z+1}$$ for k>0 is:
A DC ammeter has a resistance of $$0.1$$$$\Omega $$ and its current range is $$0$$ – $$100A.$$ If the range is to be extended to $$0$$ –$$500A,$$ the meter requires the following s...
The simultaneous application of signals $$x(t)$$ and $$y(t)$$ to the horizontal and vertical plates, respectively, of an oscilloscope, produces a vertical figure-of-$$8$$ display....
A digital-to-analog converter with a full scale output voltage of $$3.5V$$ has resolution close to $$14mV.$$ It's bit size is _____.
Two wattmeter's, which are connected to measure the total power on a three-phase system supplying a balanced load, read $$10.5$$ $$kW$$ and $$–2.5$$ $$kW$$ respectively. The total...