GATE 2008 Electronics & Communication
44 questions across 1 session
For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is
For real values of $$x,$$ the minimum value of function $$f\left( x \right) = {e^x} + {e^{ - x}}\,\,$$ is
The equation sin(z) = 10 has
The number of open right half plane poles of $$$G\left(s\right)\;=\;\frac{10}{s^5\;+2s^4\;+3s^3\;+6s^2\;+5s\;+3}\;is$$$
Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit step u(t) is applie...
The magnitude of frequency response of an underdamped second order system is 5 at 0 rad/sec and peaks to $${{10} \over {\sqrt 3 }}$$ at 5 $$\sqrt 2 $$ rad/sec. The transfer functio...
Which of the following is a solution to the differential equation $${d \over {dt}}x\left( t \right) + 3x\left( t \right) = 0,\,\,x\left( 0 \right) = 2?$$
Consider points $$P$$ and $$Q$$ in $$xy-$$plane with $$P=(1,0)$$ and $$Q=(0,1).$$ The line integral $$2\int\limits_P^Q {\left( {x\,dx + y\,dy} \right)\,\,} $$ along the semicircle...
Which of the following function would have only odd powers of $$x$$ in its Taylor series expansion about the point $$x=0$$ ?
The system of linear equations $$\left. {\matrix{ {4x + 2y = 7} \cr {2x + y = 6} \cr } } \right\}$$ has
The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function. The frequency response H(ω) of the sy...
In the Taylor series expansion of $${e^x} + \sin x$$ about the point $$x = \pi ,$$ the coefficient of $${\left( {x = \pi } \right)^2}$$ is
A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. If the bit...
An 8085 executes the following instructions 2710 LXI H, 30A0H DAD H PCHL All addresses and constants are in Hex. Let PC be the contents of the program counter and HL be the content...
The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is
A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $${\varepsilon _r} = 9$$ ). The magnitude of the reflection...
A speech signal, band limited to 4 kHz and peak voltage varying between + 5V and - 5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. Assuming t...
A speech signal, band limited to 4kHz and peak voltage varying between +5V and -5V is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. The number of...
Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3-dB cut-off frequency of f c . The noise power at the filter o...
A rectangular waveguide of internal dimensions (a = 4 cm and b = 3 cm ) is to be operated in $$T{E_{11}}$$ mode. The minimum operating frequency is
Consider a Binary Symmetric Channel (BSC) with probability of error being 'p'. To transit a bit, say 1, we transmit a sequence of three 1s. The receiver will interpret the received...
A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n
At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is
One end of loss-less transmission line having the characteristic impedance of 75 $$\Omega $$ and length of 1 cm is short-ciruited. At 3 GHz, the input impedance at the other end of...
Four messages band limited to W, W, 2 W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth required for transmission of this T...
The value of the integral of the function $$\,\,g\left( {x,y} \right) = 4{x^3} + 10{y^4}\,\,$$ along the straight line segment from the point $$(0,0)$$ to the point $$(1,2)$$ in th...
Which of the following is NOT associated with a P-N junction?
The residue of the function $$f(z) = {1 \over {{{\left( {z + 2} \right)}^2}{{\left( {z - 2} \right)}^2}}}$$ at z = 2 is
The impulse response h(t) of a linear time invariant system is given by h(t) = $${e^{ - 2t}}u(t),$$ where u(t) denotes the unit step function. The output of this system to the sinu...
All the four entries of $$2$$ $$x$$ $$2$$ matrix $$P = \left[ {\matrix{ {{p_{11}}} & {{p_{12}}} \cr {{p_{21}}} & {{p_{22}}} \cr } } \right]$$ are non-zero and one of the eigen valu...
The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is
A silicon wafer has 100 mm of oxide on it and is inserted in a furnace at a temperature above 1000ºC for further oxidation in dry oxygen. The oxidation rate
{x(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point. Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence y (n) = $${1 \over N}\,\...
Which of the following is true?
The measured transconductance g m of an NMOS transistor operating in the linear region is plotted against the gate voltage V G at constant drain voltage V D . Which of the followin...
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = - 2 and s = - 4, and one simple zero at s = - 1. A unit step u(t)...
A discrete time linear shift - invariant system has an impulse response $$h\left[ n \right]$$ with $$h\left[ 0 \right]$$ $$ = 1,\,\,h\left[ 1 \right]\,\, = - 1,\,\,h\left[ 2 \right...
Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4. Properties P1 : Linear but...
The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?
The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\left( t \right)\,\,\, + \,\,\e...
The signal x(t) is described by $$x\left( t \right) = \left\{ {\matrix{ {1\,\,\,for\,\, - 1 \le t \le + 1} \cr {0\,\,\,\,\,\,\,\,\,\,\,\,\,\,otherwise} \cr } } \right.$$ Two of the...
Consider the amplitude modulated (AM) signal $$A_c\cos\omega_ct\;+\;2\cos\omega_mt\;\cos\omega_ct$$. For demodulating the signal using envelope detector, the minimum value of A c s...
The value of the integral of the function $$\mathrm g\left(\mathrm x,\mathrm y\right)=4\mathrm x^3\;+\;10\mathrm y^4$$ along the straight line segment from the point (0, 0) to the...