GATE ECE 2016 Set 3
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## 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 $$p\left( t \right) = \left\{ {\matrix{ {{1 \ove View Question A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise powe View Question For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as$$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{&amp; {d \over {dt View Question Following is the k-map of a Boolean function of five variable P, Q, R, S and X. The minimum for the function is View Question The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is View Question 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 View Question If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave w View Question Faraday's law of electromagnetic induction is mathematically described by which one of the following equations? View Question Consider an air-filled rectangular waveguide with dimensions a = 2.286cm and b = 1.016cm. At 10GHz operating frequency, View Question Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the View Question A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is al View Question Consider the charge profile shown in the figure. The resultant potential distribution is best described by View Question The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of power 100 mW/cm2. The View Question The injected excess electron concentration profile in the base region of an npn BJT, biased in the active region, is lin View Question The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in View Question Figures{\rm I}$$and$${\rm I}{\rm I}$$show two MOS capacitor of unit area. The capacitor in Figure I has insulator View Question In the circuit shown in the figure, transistor M1 is in saturation and has transconductance gm = 0.01 siemens. Ignoring View Question In the circuit shown in the figure, the channel length modulation of all transistors is non-zero$$\left( {\lambda \ne
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If the vectors $${e_1} = \left( {1,0,2} \right),\,{e_2} = \left( {0,1,0} \right)$$ and $${e_3} = \left( { - 2,0,1} \righ View Question Consider a$$2 \times 2$$square matrix$$A = \left[ {\matrix{ \sigma &amp; x \cr \omega &amp; \sigma \cr
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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 integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}}$$ is equal ________.
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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 $$\,\,{{{d^2}y} \over {d{x^2}}} + 12{{dy} \over {dx} View Question Consider the first order initial value problem$$\,y' = y + 2x - {x^2},\,\,y\left( 0 \right) = 1,\,\left( {0 \le x &lt;
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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 $$\begin{bmatrix}z_{11}&amp;z_{12}\\z_{21}&amp;z_{22}\end{bmatrix}$$ 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 $$\left[ {\matrix{ {2\,j\,\omega } &amp; {j\,\omega } \cr View Question If the signal x(t) =$${{\sin (t)} \over {\pi t}}*{{\sin (t)} \over {\pi t}}$$with * denoting the convolution operation View Question A continuous-time speech signal$${x_a}(t)$$is sampled at a rate of 8 kHz and the samples are subsequently grouped in View Question A discrete-time signal$$x\left[ n \right]\, = \delta \left[ {n - 3} \right]\, + 2\delta \left[ {n - 5} \right]$$has z-t View Question The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the View Question Consider the signal$$\,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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