GATE EE 2014 Set 1

## GATE EE

The figure shows the circuit of a rectifier fed from a 230 V (rms), 50Hz sinusoidal voltage source. If we want to replac

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The magnitude of the mid-band voltage gain of the circuit shown in figure is (assuming $${h_{fe}}$$ of the transistor to

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Given the Op-amps in the figure of ideal, the output voltage $${V_0}$$ is

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In the figure shown, assume the op-amp to be ideal. Which of the alternatives gives the correct Bode plots for the trans

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In the Wien Bridge oscillator circuit shown in figure, the bridge is balanced when

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

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For the given system, it is desired that the system be stable. The minimum value of $$\alpha $$ for this condition is __

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The root locus of unity feedback system is shown in figure
The closed loop transfer function of the system is

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The Bode magnitude plot of the transfer function $$G\left( s \right) = {{K\left( {1 + 0.5s} \right)\left( {1 + as} \righ

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Which of the following logic circuits is a realization of the function $$F$$ whose karnaugh map is shown in figure

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

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An output device is interfaced with $$8$$ bit microprocessor $$8085$$$$A.$$ The interfacing circuit is shown in figure

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The three circuit elements shown in the figure are part of an electric circuit. The total power
absorbed by the three ci

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C0 is the capacitance of a parallel plate capacitor with air as dielectric (as in figure (a)). If,
half of the entire ga

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

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In the figure, the value of resistor R is $$\left(25+\frac{\mathrm I}2\right)\mathrm\Omega$$, where I is the current in

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A combination of 1μF capacitor with an initial voltage Vc(0) = −2V in series with a 100Ω
resistor is connected to a 20 m

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The reading of voltmeter $$(rms)$$ in volts, for the circuit shown in the figure is ______.

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The dc current flowing in a circuit is measured by two ammeters, one PMMC and another electrodynamometer type, connected

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Power consumed by a balanced $$3$$-phase, $$3$$-wire load is measured by the two wattmeter method. The first wattmeter r

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In an oscilloscope screen, linear sweep is applied at the

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A 15kW, 230V dc shunt motor has armature circuit resistance of 0.4 $$\Omega$$ and field circuit
resistance of 230 $$\Ome

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For a specified input voltage and frequency, if the equivalent radius of the core of a
transformer is reduced by half, t

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

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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

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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 dr

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A star connected 400 V, 50 Hz, 4 pole synchronous machine gave the following open circuit
and short circuit test results

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A three phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figu

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The following four vector fields are given in cartesian coordinate system. The vector field
which does not satisfy the p

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A system matrix is given as follows
$$$A = \left[ {\matrix{
0 & 1 & { - 1} \cr
{ - 6} & { - 11} &am

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

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

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

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

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The solution for the differential equation $$\,\,{{{d^2}x} \over {d{t^2}}} = - 9x,\,\,$$ with initial conditions $$x(0

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

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

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Figure shows four electronic switches $$(i), (ii), (iii)$$ and $$(iv).$$ Which of the switches can block voltages of eit

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The figure shows the circuit diagram of a rectifier. The load consists of a resistance $$10\,\Omega $$ and an inductance

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Figure (i) shows the circuit diagram of a chopper. The switch $$S$$ in the circuit in figure (i) is switched such that t

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In the figure shows on period of the output voltage of an inverter. $$\alpha $$ should be chosen such that $${60^0} <

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The undesirable property of an electrical insulating material is

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A two bus power system shown in figure supplies load of $$1.0+j0.5$$ $$p.u$$
The value of $${V_1}$$ in $$p.u$$ and $${

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A distribution feeder of $$1$$ $$km$$ length having resistance, but negligible reactance, is fed from both the ends by $

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Three phase to ground fault takes place at locations $${F_1}$$ and $${F_2}$$ in the system shown in the figure.
If the

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A 2-bus system and corresponding zero sequence network are shown in the figure.
The transformers T1 and T2 are connec

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In an unbalanced three phase system phase current $${{\rm I}_a} = 1\angle \left( { - {{90}^0}} \right)\,\,pu,\,\,$$ nega

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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}:\,{

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The over current relays for the line protection and loads connected at the buses are shown in the figure.
The relays a

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x(t) is nonzero only for $$T_x\;<\;t\;<\;T_x^1$$ , and similarly, y(t) is nonzero only for $$T_y\;<\;t\;<\;T

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The function shown in the figure can be represented as

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

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Let f(t) be a continuous time signal and let F($$\omega$$) be its Fourier Transform defined by $$F\left(\omega\right)=\i

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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] a

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