GATE ECE 2016 Set 3

## GATE ECE

The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is very
large compared to

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Consider the circuit shown in the figure. Assuming VBE1 = VEB2 = 0.7 volt, value of the dc voltage Vc2 (in volt) is _

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In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the output pin 3 is

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For the circuit shown in the figure, R1 = R2 = R3 = 1 Ω, L = 1 µH and C = 1 µF. If the input Vin = cos(106t) , then the

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For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency
is 3.5 GHz. If t

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A wide sense stationary random process $$X(t)$$ passes through the $$LTI$$ system shown in the figure. If the autocorrel

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The bit error probability of a memoryless binary symmetric channel is $${10^{ - 5}}$$. If $${10^{ - 5}}$$ bits are sent

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An analog baseband signal, band limited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four m

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A binary baseband digital communication system employs the signal
$$$p\left( t \right) = \left\{ {\matrix{
{{1 \ove

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A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise powe

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For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is
given as $$G\left(s\r

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The forward-path transfer function and the feedback-path transfer function of a single loop negative
feedback control sy

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The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is

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The first two rows in the Routh table for the characteristic equation of a certain closed-loop control
system are given

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A second-order linear time-invariant system is described by the following state equations
$$$\eqalign{& {d \over {dt

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Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is

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For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns, 1.5 ns and 1 ns, resp

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The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is

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If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave w

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Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

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Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the

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Consider an air-filled rectangular waveguide with dimensions a = 2.286cm and b = 1.016cm. At 10GHz operating frequency,

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A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is al

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Consider the charge profile shown in the figure. The resultant potential distribution is best
described by

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The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of
power 100 mW/cm2. The

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The injected excess electron concentration profile in the base region of an npn BJT, biased in the
active region, is lin

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The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of
this MOS is in

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Figures $${\rm I}$$ and $${\rm I}{\rm I}$$ show two MOS capacitor of unit area. The capacitor in Figure I has insulator

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In the circuit shown in the figure, the channel length modulation of all transistors is non-zero $$\left( {\lambda \ne

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In the circuit shown in the figure, transistor M1 is in saturation and has transconductance
gm = 0.01 siemens. Ignoring

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Consider a $$2 \times 2$$ square matrix $$A = \left[ {\matrix{
\sigma & x \cr
\omega & \sigma \cr

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If the vectors $${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$ and $${e_3} = \left( { - 2,0,1} \righ

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The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}} $$ is equal ________.

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A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangl

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The probability of getting a ''head'' in a single toss of a biased coin is $$0.3.$$ The coin is tossed repeatedly till a

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The particular solution of the initial value problem given below is $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx}

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Consider the first order initial value problem $$\,y' = y + 2x - {x^2},\,\,y\left( 0 \right) = 1,\,\left( {0 \le x <

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The value of the integral $${1 \over {2\pi j}}\oint\limits_C {{{{e^z}} \over {z - 2}}dz} $$ along a closed contour $$c$$

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For $$f\left( z \right) = {{\sin \left( z \right)} \over {{z^2}}},$$ the residue of the pole at $$z=0$$ ________.

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In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If th

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In the figure shown, the current i (in ampere) is ______.

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The z-parameter matrix $$\begin{bmatrix}z_{11}&z_{12}\\z_{21}&z_{22}\end{bmatrix}$$ for the two-port network sho

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Assume that the circuit in the figure has reached the steady state before time t = 0 when the
3 Ω
resistor suddenly burn

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In the $$RLC$$ circuit shown in the figure, the input voltage is given by vi(t) = 2 cos(200t)+4 sin(500t). The out

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The z-parameter matrix for the two-port network shown is $$$\left[ {\matrix{
{2\,j\,\omega } & {j\,\omega } \cr

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If the signal x(t) = $${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$ with * denoting the convolution operation

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A continuous-time speech signal $${x_a}(t)$$ is sampled at a rate of 8 kHz and the samples are subsequently grouped in

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A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$ has z-t

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The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded
region in the

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Consider the signal $$\,x\left( t \right)$$ $$\,\,\, = \,\,\,\cos \left( {6\pi t} \right)\,\, + \,\,\sin \left( {8\pi t}

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The direct form structure of an FIR (finite impulse response) filter is shown in the figure.
The filter can be used

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## General Aptitude

The number that least fits this set: (324, 441, 97 and 64) is ________.

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It takes 10 s and 15 s, respectively, for two trains traveling at different constant speeds to completely pass
a telegra

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