GATE EE 2013

## GATE EE

In the circuit shown below, the knee current of the ideal Zener diode is $$10$$ $$mA.$$ To maintain $$5 V$$ across $${R_

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A voltage $$1000\sin \omega t$$ Volts is applied across $$YZ.$$ Assuming ideal diodes, the voltage measured across $$WX$

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In the circuit shown below what is the output voltage $$\left( {{V_{out}}} \right)$$ in Volts If a silicon transfer $$Q$

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In the circuit shown below the op-amps are ideal. Then $${V_{out}}$$ in Volts is

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In the feedback network shown below, if the feedback factor $$k$$ is increased, then the

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The transfer function $${{{V_2}\left( s \right)} \over {{V_1}\left( s \right)}}$$ of the circuit shown below is

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The signal flow graph for a system is given below. The transfer function $${{Y\left( s \right)} \over {U\left( s \right)

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The open-loop transfer function of a $$dc$$ motor is given as $${{\omega \left( s \right)} \over {{V_a}\left( s \right)}

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The Bode plot of a transfer function $$G(s)$$ is shown in the figure below.
The gain is $$\left( {20\log \left| {G\le

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The state variable formulation of a system is given as
$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr

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The state variable formulation of a system is given as
$$\left[ {\matrix{
{\mathop {{x_1}}\limits^ \bullet } \cr

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A bulb in staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bul

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The clock frequency applied to the digital circuit shown in the figure below is $$1$$ $$kHz.$$ If the initial state of t

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Consider a delta connection of resistors and it's equivalent star connection as
shown below. If all elements of the delt

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Three capacitors C1, C2 and C3 whose values are 10μF, 5μF and 2μF
respectively, have breakdown voltages of 10V, 5V and 2

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A source $$v_s\left(t\right)=V\cos100\mathrm{πt}$$ has an internal impedance of (4 + j3) Ω.If a purely
resistive load co

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In the circuit shown below, if the source voltage $$V_s=100\angle53.12^\circ\;V$$ then the Thevenin’s equivalent
voltage

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Two magnetically uncoupled inductive coils have Q factors q1 and q2 at the
chosen operating frequency. Their respective

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The input impedance of the permanent magnet moving coil $$(PMMC)$$ voltmeter is infinite. Assuming that the diode shown

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Three moving iron type voltmeters are connected as shown below. Voltmeter readings are $$V,$$ $${V_1}$$ and $${V_2}$$ ,

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A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance without any load as $$

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A single-phase transformer has no-load loss of 64 W, as obtained from an open circuit
test. When a short-circuit test is

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The following arrangement consists of an ideal transformer and an attenuator
which attenuates by a factor of 0.8. An ac

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Leakage flux in an induction motor is

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A 4-pole induction motor, supplied by a slightly unbalanced three-phase 50Hz
source, is rotating at 1440 rpm. The electr

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A dielectric slab with 500 mm x 500 mm cross-section is 0.4 m long. The slab is
subjected to a uniform electric field of

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The flux density at a point in space is given by
$$\overrightarrow B=\;4x{\widehat a}_x\;+\;2ky{\widehat a}_y\;+\;8{\wid

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The equation $$\left[ {\matrix{
2 & { - 2} \cr
1 & { - 1} \cr
} } \right]\left[ {\matrix{
{{x_1}}

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A matrix has eigen values $$-1$$ and $$-2.$$ The corresponding eigenvectors are $$\left[ {\matrix{
1 \cr
{ - 1}

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A function $$y = 5{x^2} + 10x\,\,$$ is defined over an open interval $$x=(1,2).$$ At least at one point in this interval

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The curl of the gradient of the scalar field defined by $$\,V = 2{x^2}y + 3{y^2}z + 4{z^2}x$$ is

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Given a vector field $$\overrightarrow F = {y^2}x\widehat a{}_x - yz\widehat a{}_y - {x^2}\widehat a{}_z,$$ the line i

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A continuous random variable $$X$$ has a probability density function $$f\left( x \right) = {e^{ - x}},0 < x < \in

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When the Newton-Raphson method is applied to solve the equation $$\,\,f\left( x \right) = {x^3} + 2x - 1 = 0,\,\,$$ the

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Square roots of $$-i,$$ where $$i = \sqrt { - 1} $$ are

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$$\oint {{{{z^2} - 4} \over {{z^2} + 4}}} dz\,\,$$ evaluated anticlockwise around the circular $$\left| {z - i} \right|

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Thyristor $$T$$ in the figure below is initially off and is triggered with a single pulse of width $$10\mu s.$$ It is gi

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In the figure shown below, the chopper feeds a resistive load from a battery source. $$MOSFET$$ $$Q$$ is switched at $$2

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In the figure shown below, the chopper feeds a resistive load from a battery source. $$MOSFET$$ $$Q$$ is switched at $$2

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The Voltage Source Inverter $$(VSI)$$ shown in the figure below is switched to provide a $$50$$ $$Hz,$$ square-wave $$ac

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The Voltage Source Inverter $$(VSI)$$ shown in the figure below is switched to provide a $$50$$ $$Hz,$$ square-wave $$ac

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A single load is supplied by a single voltage source. If the current flowing from the load to the source is $$10\angle

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The angle $$\delta $$ in the swing equation of a synchronous generator is the

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In the following network, the voltage magnitudes at all buses are equal to $$1$$ p.u., the voltage phase angles are very

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For a power system network with $$n$$ nodes, $${Z_{33}}$$ of its bus impedance matrix is $$j0.5$$ per unit. The voltage

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In the following network, the voltage magnitudes at all buses are equal to $$1$$ p.u., the voltage phase angles are very

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For a periodic signal the $$v\left(t\right)=30\sin100t\;+\;10\cos300t\;+\;6\sin\left(500t\;+\;\frac{\mathrm\pi}4\right)

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Assuming zero initial condition, the response y(t) of the system given below to a
unit step input u(t) is

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Two systems with impulse responses h1(t) and h2(t) are connected in cascade.
Then the overall impulse response of the ca

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The impulse response of a system is h(t) = tu(t). For an input u(t − 1), the output
is

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The impulse response of a continuous time system is given by
h(t) = $$\delta$$(t − 1) + $$\delta$$(t − 3). The value of

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A band-limited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the samplin

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Which one of the following statements is NOT TRUE for a continuous time causal
and stable LTI system?

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