GATE ECE 2014 Set 3

## GATE ECE

The figure shows a half-wave rectifier. The diode D is ideal. The average steady-state current
(in Amperes) through the

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In the circuit shown, the PNP transistor has $$\left|{\mathrm V}_\mathrm{BE}\right|=0.7\;\mathrm V$$ and β = 50. Assume

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In the circuit shown, the silicon BJT has $$\beta \,\,\,\,50.\,\,\,\,\,$$ Assume $${V_{BE}}\,\,\, = \,\,\,0.7$$ and $${V

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The desirable characteristics of a transconductance amplifier are

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Assuming that the Op-amp in the circuit shown is ideal, V0 is given by

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Consider an FM signal $$f\left(t\right)\;=\;\cos\left[2{\mathrm{πf}}_\mathrm c\mathrm t\;+\;{\mathrm\beta}_1\sin\;2{\mat

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Let $$X(t)$$ be a wide sense stationary $$(WSS)$$ random procfess with power spectral density $${S_x}\left( f \right)$$.

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A real band-limited random process $$X( t )$$ has two -sided power spectral density
$$${S_x}\left( f \right) = \left\{ {

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Let $${X_1},\,{X_2},$$ and $${X_3}$$ be independent and identically distributed random variables with the uniform distri

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In a PCA system, the signal $$m(t) = \{ \sin (100\,\pi \,t)\, + \cos (100\,\pi \,t\} $$ V is sampled at the Nyquist rate

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A binary random variable X takes the value of 1 with probability 1/3. X is input to a casade of 2 independent identical

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The steady state error of the system shown in the figure for a unit step input is _______.

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Consider the following block diagram in the figure.
The transfer function $$\frac{\mathrm C\left(\mathrm s\right)}{\ma

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The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applie

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In the root locus plot shown in the figure, the pole/zero marks and the arrows have been
removed. Which one of the follo

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The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left(

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In the circuit shown, 𝑊𝑊 and 𝑌𝑌 are MSBs of the control inputs. The output 𝐹𝐹 is given by

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If X and Y are inputs and the Difference (D = X – Y) and the Borrow (B) are the outputs, which one of the following diag

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The circuit shown in the figure is a

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Consider the multiplexer based logic circuit shown in the figure.
Which one of the following Boolean functions is rea

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If WL is the Word Line and BL the Bit Line, an SRAM cell is shown in

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Given the vector $$$\mathrm A=\left(\cos\;\mathrm x\right)\left(\sin\;\mathrm y\right)\;{\widehat{\mathrm a}}_\mathrm x\

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In the following figure, the transmitter Tx sends a wideband modulated RF signal via a coaxial cable to the receiver Rx.

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A region shown below contains a perfect conducting half-space and air. The surface current $${\overrightarrow K _{_s}}$$

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Assume that a plane wave in air with an electric field
$$\overrightarrow E = 10\cos \left( {\omega t - 3x - \sqrt {3z}

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Consider an air filled rectangular waveguide with a cross-section of $$5\,\,cm\,\, \times \,\,3\,cm$$. For this waveguid

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A thin P-type silicon sample is uniformly illuminated with light which generates excess
carriers. The recombination rate

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At T = 300 K, the hole mobility of a semiconductor $$\mu_p\;=500\;cm^2/V-s$$ and $$\frac{kT}q\;=\;26\;mV$$.The hole diff

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In MOSFET fabrication, the channel length is defined during the process of

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The slope of the ID vs. VGS curve of an n-channel MOSFET in linear region is 10-3$${\Omega ^{ - 1}}$$ at VDS = 0.1V. Fo

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An ideal MOS capacitor has boron doping concentration of 1015 cm-3 in the substrate. When a gate voltage is applied, a d

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For the MOSFET M1 shown in the figure, assume W/L =2, VDD = 2.0 V, $$\mu n$$ COX = 100$$\mu {\rm A}/{V^2}$$ and VTH =0.5

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Which one of the following statements is NOT true for a square matrix $$A$$?

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The maximum value of the function $$\,f\left( x \right) = \ln \left( {1 + x} \right) - x$$ (where $$x > - 1$$ ) occu

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If $$z=xy$$ $$ln(xy),$$ then

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The maximum value of $$f\left( x \right) = 2{x^3} - 9{x^2} + 12x - 3$$
in the interval $$\,0 \le x \le 3$$ is _________

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An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss i

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A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is

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Let $${X_1},{X_{2,}}$$ and $${X_{3,}}$$ be independent and identically distributed random variables with the uniform di

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Which ONE of the following is a linear non - homogeneous differential equation , where $$x$$ and $$y$$ are the independe

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Match the application to appropriate numerical method
Applications
$$P1:$$ Numerical integration
$$P2:$$ Solution to a

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In the figure shown, the value of the current I (in Amperes) is __________.

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For the Y-network shown in the figure, the value of R1 (in Ω) in the equivalent ∆ -network is ________.

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In the circuit shown in the figure, the value of node voltage V2 is

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In the circuit shown in the figure, the angular frequency $$\omega$$ (in rad/s), at which the Norton equivalent impedanc

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A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage VS, the r

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Consider the building block called 'Network N' shown in the figure.
Let $$C = 100\,\mu F\,\,$$ and $$R = 10\,k\Omega $$

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The input $$ - 3{e^{2t}}\,\,u\left( t \right)$$, where u(t) is the unit step function$$\, {{s - 2} \over {s + 3}}$$. If

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Let h(t) denote the impulse response of a casual system with transfer function $${1 \over {s + 1}}$$. Consider the follo

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For an all-pass system H(z)= $${{({z^{ - 1}} - b)} \over {(1 - a{z^{ - 1}})}}$$ where $$\left| {H({e^{ - j\omega }})}

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The z-transform of the sequence x$$\left[ n \right]$$ is given by x(z)= $${1 \over {{{(1 - 2{z^{ - 1}})}^2}}}$$ , with t

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Let $${H_1}(z) = {(1 - p{z^{ - 1}})^{ - 1}},{H_2}(z) = {(1 - q{z^{^{ - 1}}})^{ - 1}}$$ , H(z) =$${H_1}(z)$$ +r $${H_2}$$

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Let $$\,x\,\,\left( t \right)\,\,\, = \,\,\,\cos \,\,\,\left( {10\pi t} \right)\,\, + \,\,\cos \,\,\left( {30\pi t} \rig

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A modulated signal is $$y\left( t \right)\, = \,\,\,\,\,\,\,\,\,m\left( t \right)\,\cos \left( {40000\pi t} \right),$$

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The phase response of a passband waveform at receiver is given by $$\varphi \,(f) = - 2\,\pi \,\alpha \,(f - {f_c}) - \

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