GATE ECE 2004

## GATE ECE

Assuming VCesat=0.2V and β = 50, the minimum base current (IB) required to drive the transistor in the figure to saturat

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A bipolar transistor is operating in the active region with a collector current of
1mA. Assuming that the 'β' of the tra

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The value of 'C' required for a sinusoidal oscillation of frequency 1 KHz in the circuit of the figure is

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An ideal Op-Amp is an ideal

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The circuit in the figure is a

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Voltage series feedback (also called series-shunt feedback) results in

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In the op-amp circuit given in the figure, the load current iL is

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An AM signal is detected using an envelope detector. The carrier frequency and
modulating signal frequency are 1 MHz and

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An AM signal and a narrow-band FM signal with identical carriers, modulating
signals and modulation indices of 0.1 are a

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Two sinusoidal signals of same amplitude and frequencies 10 kHz and 10.1 kHz
are added together. The combined signal is

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In a PCM system, if the code word length is increased from 6 to 8 bits, the signal to quantization noise ratio improves

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In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval t1 $$ \le $$

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A 1 mW video signal having a bandwidth of 100 MHz is transmitted to a receiver through a cable that has 40 dB loss. If t

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Three analog signals, having bandwidths 1200 Hz, 600 Hz and 600 Hz are sampled at their respective Nyquist rates, enocod

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A source produces binary data at the rate of 10 kbps. The binary symbols are represented as shown in fig.
The source

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Choose the correct one from among the alternatives A, B, C, D after matching an item from Group 1 with the most appropri

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Consider a binary digital communication system with equally likely $$0’s$$ and $$1’s$$.
When binary $$0$$ is transmitted

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A causal system having the transfer function $$G\left(s\right)\;=\;\frac1{s\;+\;2}$$
is excited with 10u(t).
The time at

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For the polynomial P(s) = s5 + s4 + 2s3 + 2s2 + 3s + 15 ,the number of roots which
lie in the right half of the s-plane

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Consider the signal flow graph shown in Figure. The gain $$\frac{x_5}{x_1}$$ is

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A system described by the following differential equation
$$$\frac{d^2y}{dt^2}+3\frac{dy}{dt}+2y=x\left(t\right)$$$ is i

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Consider the Bode magnitude plot shown in figure. The transfer function H(s) is

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A system has poles at 0.01 Hz, 1Hz and 80 Hz; zeroes at 5hz, 100 Hz and 200 Hz. The approximate phase of the system resp

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The state variable equations of a system are:
$$${\mathop {{x_1} = - 3{x_1} - x}\limits^ \bullet _2} + u$$$
$$${\matho

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Given A $$ = \left[ {\matrix{
1 & 0 \cr
0 & 1 \cr
} } \right],$$ the state transition ma

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If A = $$\left[ {\matrix{
{ - 2} & 2 \cr
1 & { - 3} \cr
} } \right],$$ then sin At is

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The range of signed decimal numbers that can be represented by 6-bite 1’s
complement number is

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11001, 1001 and 111001 correspond to the 2’s complement representation of
which one of the following sets of number?

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The Boolean expression AC + B$$\overline C $$ is equivalent to

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A Boolean function 'f' of two variables x and y is defined as follows:
f(0,0)=f(0,1)=f(1,1)=1;f(1,0)=0
Assuming compleme

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The minimum number of 2 to 1 multiplexers required to realize a 4 to 1 mutliplexer is

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A master slave flip-flop has the characteristic that

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Choose the correct one from among the alternatives A, B, C, D after matching an
item from Group 1 with the most appropri

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In the modulo-6 ripple counter shown in the figure, the output of the 2-input gate is
used to clear the J-K flip-flops.

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Figure shows the internal schematic of a TTL AND-OR-Invert (AOI) gate. For the inputs shown in Figure, the output Y is

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Consider a 300$$\Omega $$, quarter-wave long (at 1 GHz) transmission line as shown in Fig. It is connected to a 10V, 50$

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Consider an impedance Z = R + jX marked with point P in an impedance Smith chart as shown in Fig. The movement from poin

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A lossless transmission line is terminated in a load which reflects a part of the incident power. The measured VSWR is 2

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A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non-magnetic,

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The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $$T{E_{10}}$

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Consider a lossless antenna with a directive gain of + 6 dB. If 1 m W of power is fed to it the total power radiated by

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The impurity commonly used for realizing the base region of a silicon n-p-n
transistor is

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Consider the following statements S1 and S2.
S1: The threshold voltage (VT) of a MOS capacitor decreases with increase i

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The drain of an n-channel MOSFET is shorted to the gate so that VGS = VDS. The
threshold voltage (VT) of MOSFET is 1 V.

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The 8255 Programmable Peripheral Interface is used as described below.
I. An A/D converter is interfaced to a microproce

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The number of memory cycles required to execute the following 8085 instructions
(I.) LDA 3000H
(II.) LXI D, FOF 1H
W

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It is desired to multiply the numbers 0AH by 0BH and store the result in the accumulator. The numbers are available in r

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Consider the sequence of 8085 instructions given below.
LXI H, 9258
MOV A, M
CMA
MOV M, A
Which one of the follo

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The equivalent inductance measured between the terminals 1 and 2 for the
circuit shown in figure, is

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For the R-L circuit shown in Fig, the input voltage. vi(t) = u (t) The current
i(t) is

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The circuit shown in Fig, has initial current $${\mathrm i}_\mathrm L\left(0^-\right)\;=\;1\;\mathrm A$$ through the ind

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Consider the following statements S1 and S2.
S1: The $$\beta$$ of a bipolar transistor reduces if the base width is incr

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The circuit shown in figure, with $$R = 1/3\Omega $$, $$L = 1/4H$$, $$C = 3F$$ has input voltage $$v\left( t \right) = \

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For the circuit shown in figure, the time constant $$RC = 1$$ $$ms$$. The input voltage is $${v_i}\left( t \right) = \sq

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The transfer function $$H\left( s \right) = {{{V_0}\left( s \right)} \over {{V_i}\left( s \right)}}$$ of an R-L-C circui

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For the lattice circuit shown in Fig., $${Z_a} = j\,2\,\Omega \,\,and\,\,{Z_b} = \,\,2\Omega $$. The values of the open

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For the circuit shown in Figure, the initial conditions are zeros. Its transfer function
$$H(s) = {{{V_c}\,(s)} \over {

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The Fourier transform of a conjugate symmetric function is always

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The z transform of a system is
H(z) = $${z \over {z - 0.2}}$$ .
If the ROC is $$\left| {z\,} \right|$$ < 0.2, then

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A system described by the differential equation: $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dt}} + 2y = x(t)$$ is initi

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A rectangular pulse train s(t) as shown in Fig.1 is convolved with the signal $${\cos ^2}$$ ($$4\pi \,{10^{3\,}}$$t). Th

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A causal system having the transfer function H(s) = $${1 \over {s + 2}}$$, is excited with 10 u(t). The time at which th

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Let x(t) and y(t) (with Fourier transforms X(f) and Y(f) respectively) be related as shown in Fig.(1) & (2).
Then Y

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The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$ = u\le

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A causal LTI system is described by the difference equation $$2y\left[ n \right] = ay\left[ {n - 2} \right] - 2x\left[ n

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The impulse response $$h\left[ n \right]$$ of a linear time invariant system is given as
$$h\left[ n \right] = \left\{

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A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system res

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Consider the signal x(t) shown in Fig. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) bei

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A 1 kHz sinusoidal signal is ideally sampled at 1500 samples /sec and the sampled signal is passed through an ideal low-

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Consider the sequence
$$x[n] = [ - \,4 - \,j5,\,\mathop {1 + j2}\limits_ \uparrow ,\,\,4]$$
The conjugate anti-symm

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