GATE ECE 2015 Set 3

## GATE ECE

In the circuit shown, assume that diodes D1 and D2 are ideal. In the steady-state condition the average voltage Vab (in

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In the circuit shown using am ideal opamp, the 3-dB cut-off frequency (in Hz) is _____.

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In the circuit shown, assume that the opamp is ideal. If the gain ($${V_0}/{V_{in}}$$) is -12, the value of R (in K$$\Om

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The modulation scheme commonly used for transmission from GSM mobile terminals is

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A random binary wave $$y(t)$$ is given by
$$$y\left( t \right) = \sum\limits_{n = - \infty }^\infty {{X_n}p\left( {t

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The impulse response of an LTI system can be obtained by

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The characteristic equation of an LTI system is given by F(s) = s5 + 2s4 +3s3 + 6s2 - 4s - 8 = 0.The number of roots tha

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For the system shown in the figure, s = –2.75 lies on the root locus if K is_____.

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Consider the Bode plot shown in the figure. Assume that all the poles and zeroes are real-valued.
The value of fH - fL

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The phase margin (in degrees) of the system
G(s)=$${{10} \over {\left( {s + 10} \right)}}$$ is ___________.

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The transfer function of a first-order controller is given as
$${G_c}(s) = {{K\left( {s + a} \right)} \over {s + b}}$$

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The position control of a DC servo-motor is given in the figure. The values of the parameters are
Kt=1 N-m/A, Ra=$$1\Ome

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A network is described by the state model as
$$$\eqalign{
& {\mathop x\limits^ \bullet _1} = 2{x_1} - {x_2} + 3u,

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In the circuit shown, diodes $${D_1}$$ ,$${D_2}$$ and $${D_3}$$ are ideal, and the inputs $${E_1}$$ , $${E_2}$$ and $

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A universal logic gate can implement any Boolean function by connecting sufficient number of
them appropriately. Three g

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The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset ($$\overline {{R_d}} $$ input).

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A three bit pseudo random number generator is shown. Initially the value of output Y = Y2 Y1 Y0 is set to 111. The value

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An SR latch is implemented using TTL gates as shown in the figure. The set and reset pulse inputs are provided using the

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A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per
unit length of 172 pF/m. If the rat

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A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $$\left( {{\va

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Consider the 3 m long lossless air-filled transmission line shown in the figure. It has a characteristic impedance of $$

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A 200 m long transmission line having parameters shown in the figure is terminated into a load ܴ$$R_L$$. The line is con

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The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements

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The electric field profile in the depletion region of a p-n junction in equilibrium is shown
in the figure. Which one of

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In the circuit shown in the figure, the BJT has a current gain (β) of 50. For an emitter-base
voltage VEB = 600 mV, the

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If the base width in a bipolar junction transistor is doubled, which one of the following
statements will be TRUE?

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An npn BJT having reverse saturation current $$I_s\;=\;10^{-15}\;A$$ is biased in the forward active
region with VBE = 7

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Which one of the following processes is preferred to from the gate dielectric (SiO2) of
MOSFETs?

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In the circuit shown, both the enhancement mode NMOS transistors have the following characteristics: kn = $${\mu _n}{C_{

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The current in an enhancement mode NMOS transistor biased in saturation mode was measured to be 1 mA at a drain-source v

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For $$A = \left[ {\matrix{
1 & {\tan x} \cr
{ - \tan x} & 1 \cr
} } \right],$$ the determinant of $$

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The contour on the $$x-y$$ plane, where the partial derivative of $${x^2} + {y^2}$$ with respect to $$y$$ is equal to th

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The value of $$\sum\limits_{n = 0}^\infty {n{{\left( {{1 \over 2}} \right)}^n}\,\,} $$ is _______.

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A fair die with faces $$\left\{ {1,2,3,4,5,6} \right\}$$ is thrown repeatedly till $$'3'$$ is observed for the first tim

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The variance of the random variable $$X$$ with probability density function $$\,f\left( x \right) = {1 \over 2}\left| x

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Consider the differential equation $${{{d^2}x\left( t \right)} \over {d{t^2}}} + 3{{dx\left( t \right)} \over {dt}} + 2x

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The Newton-Raphson method is used to solve the equation $$f\left( x \right) = {x^3} - 5{x^2} + 6x - 8 = 0.$$ Taking the

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If $$C$$ is a circle of radius $$r$$ with centre $${z_0}$$ in the complex $$z$$-plane and if $$'n'$$ is a non-zero integ

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Consider the function $$g\left( t \right) = {e^{ - t}}\,\sin \left( {2\pi t} \right)u\left( t \right)$$ ,where $$u(t)$$

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Which one of the following 8085 microprocessor programs correctly calculates the product of two 8-bit numbers stored in

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For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a-b is _____.

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In the circuit shown, the voltage Vx (in Volts) is ______.

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At very high frequencies, the peak output voltage V0 (in Volts) is ______.

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In the circuit shown, the current $${\rm I}$$ flowing through the $$50\,\Omega $$ resistor will be zero if the value of

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The ABCD parameters of the following 2-port network are

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The value of $$\sum\limits_{n = 0}^\infty n {\left( {{1 \over 2}} \right)^n}$$ is ________________.

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Let $$\widetilde x\left[ n \right]\, = \,1 + \cos \left[ {{{\pi n} \over 8}} \right]$$ be a periodic signal with period

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A realization of a stable discrete time system is shown in the figure. If the system is excited by a
unit step sequence

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Suppose x $$\left[ n \right]$$ is an absolutely summable discrete-time signal. Its z-transform is a rational function
wi

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The impulse response of an LTI system can be obtained by

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The complex envelope of the bandpass signal $$x(t)\, = \, - \sqrt 2 \left( {{{\sin (\pi t/5)} \over {\pi t/5}}} \right)\

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Two sequence $${x_1}\left[ n \right]$$ and $${x_2}\left[ n \right]$$ have the same energy.
Suppose $${x_1}\left[ n \rig

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Consider a four-point moving average filter defined by the equation $$y[n] = \sum\limits_{i = 0}^3 {{\alpha _i}x[n - i]}

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Consider a continuous-time signal defined as $$x(t) = \left( {{{\sin \,(\pi t/2)} \over {(\pi t/2)}}} \right)*\sum\limit

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Consider the function $$g(t) = {e^{ - t}}\,\,\,\sin (2\pi t)\,u(t)$$ where u(t) is the unit step function. The area unde

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The complex envelope of the bandpass signal $$x(t) = - \sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,\

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## General Aptitude

If x>y>1, which of the following must be true?
$$$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\lef

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Find the missing sequence in the letter series below:
A, CD, GHI, ? , UVWXY

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