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

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

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

View Question The desirable characteristics of a transconductance amplifier are

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

View Question The circuit shown in the figure is a

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

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

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

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

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

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

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

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

View Question 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

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

View Question 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

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

View Question 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

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

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

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

View Question 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 _________

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question