GATE 2017 Electronics & Communication

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmi...

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $$V(l) = {e^{ - \gamma l\, + \,j\,\omega \,t}}$$ Volts, where $$l$$ i...

I ___________ made arrangements had I ___________informed earlier.

A three dimensional region $$R$$ of finite volume is described by $$\,\,{x^2} + {y^2} \le {z^3},\,\,\,0 \le z \le 1$$ Where $$x, y, z$$ are real. The volume of $$R$$ correct to two...

The rank of the matrix $$M = \left[ {\matrix{ 5 & {10} & {10} \cr 1 & 0 & 2 \cr 3 & 6 & 6 \cr } } \right]$$ is

Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left( {x + y - 1} \right)^2}$$ , where $$x,$$ $$y$$ are real ?

Which one of the following options correctly describes the locations of the roots of the equation s 4 + s 2 + 1 = 0 on the complex plane?

40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is

In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer household consumption decreases by 20%, while other consumpti...

Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusions can be deduced from the preceding sentences? (i) At least one bench is...

Consider a stable system with transfer function $$$G\left(s\right)=\frac{s^p+b_1s^{p-1}+....+b_p}{s^q+a_1s^{q-1}+....+a_q}$$$ Where $$b_1,.......,b_p$$ and $$a_1,.......,a_q$$ are...

Consider the $$5 \times 5$$ matrix $$A = \left[ {\matrix{ 1 & 2 & 3 & 4 & 5 \cr 5 & 1 & 2 & 3 & 4 \cr 4 & 5 & 1 & 2 & 3 \cr 3 & 4 & 5 & 1 & 2 \cr 2 & 3 & 4 & 5 & 1 \cr } } \right]$...

The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$ does not encircle the point (-1+j0) for K = 10 but does encir...

Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars...

Let $$\,\,f\left( x \right) = {e^{x + {x^2}}}\,\,$$ for real $$x.$$ From among the following. Choose the Taylor series approximation of $$f$$ $$(x)$$ around $$x=0,$$ which includes...

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?

Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

Which one of the following gives the simplified sum of products expression for the Boolean function $$F = {m_0} + {m_2} + {m_3} + {m_5},$$ where $$F = {m_0} + {m_2} + {m_3} + {m_5}...

“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antag...

In binary frequency shift keying (FSK), the given signal wave forms are $$\,{u_o}(t) = 5\,\cos \,(20000\,\pi \,t);\,0 \le \,\,t\, \le \,T,$$ and $${u_o}(t) = 5\,\cos \,(22000\,\pi...

The expression for an electric field in free space is $$E = {E_0}\left( {\widehat x + \widehat y + j2\widehat z} \right){e^{ - j\left( {\omega t - kx + ky} \right)}},$$ where $$x,{...

In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 200...

Let $$\left( {{X_1},\,{X_2}} \right)$$ be independent random variables, $${X_1}$$ has mean 0 and variance 1, while $${X_2}$$ has mean 1 and variance 4. The mutual information I $$\...

The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 $$\mu $$s, then the number of T-states needed for executing the instru...

Which one of the following statements about differential pulse code modulation (DPCM) is true?

A half wavelength dipole is kept in the x-y plane and oriented along $${45^ \circ }$$ from the x-axis. Determine the direction of null in the radiation pattern for $$0 \le \phi \le...

The following five instructions were executed on an 8085 microprocessor. MVI A, 33H MVI B, 78H ADD B CMA ANI 32H The Accumulator value immediately after the execution of the fifth...

Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) _________...

If the vector function $$\,\,\overrightarrow F = \widehat a{}_x\left( {3y - k{}_1z} \right) + \widehat a{}_y\left( {k{}_2x - 2z} \right) - \widehat a{}_z\left( {k{}_3y + z} \right)...

She has a sharp tongue and it can occasionally turn

Let $$\,\,\,{\rm I} = \int_c {\left( {2z\,dx + 2y\,dy + 2x\,dz} \right)} \,\,\,\,$$ where $$x, y, z$$ are real, and let $$C$$ be the straight line segment from point $$A: (0, 2, 1)...

The Miller effect in the context of a Common Emitter amplifier explains

Starting with $$x=1,$$ the solution of the equation $$\,{x^3} + x = 1,\,\,$$ after two iterations of Newton-Raphson's method (up to two decimal places) is ______________

Consider the following statements about the linear dependence of the real valued functions $${y_1} = 1,\,\,{y_2} = x$$ and $${y_3} = {x^2}$$. Over the field of real numbers. $${\rm...

S, T, U, V, W, X, Y and Z are seated around a circular table. T's neighbors are Y and V. Z is seated third to the left of T and second to the right of S. U's neighbors are S and Y:...

A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statement is tru...

A periodic signal x(t) has a trigonometric Fourier series expansion $$$x\left(t\right)=a_0\;+\;\sum_{n=1}^\infty\left(a_n\cos\;n\omega_0t\;+\;b_n\sin\;n\omega_0t\right)$$$ If $$x\l...

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a k } be the complex Fourier series coefficients of x(t), where k is integer valued. Consi...

Consider the following statements for continuous-time linear time invariant (LTI) system. I. There is no bounded input bounded output (BIBO) stable system with a pole in the right...

Two discrete-time signals x [n] and h [n] are both non-zero only for n = 0, 1, 2 and are zero otherwise. It is given that x(0)=1, x[1] = 2, x [2] =1, h[0] = 1, let y [n] be the lin...

A continuous time signal x(t) = $$4\cos (200\pi t)$$ + $$8\cos(400\pi t)$$, where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $$...

Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as $$y\left[ n \ri...

Let h[n] be the impulse response of a discrete time linear time invariant (LTI) filter. The impulse response is given by h(0)= $${1 \over 3};h\left[ 1 \right] = {1 \over 3};h\left[...

An optical fiber is kept along the$$\widehat Z$$ direction. The refractive indices for the electric fields along $$\widehat X$$ and $$\widehat Y$$ directions in the fiber are $${n_...

The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = $$\left[ {\sin (t)/\pi t} \right]u(t);$$ where u(t) is a unit step function. The sy...

In a DRAM,

1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?

Consider the state space realization $$$\left[ {\matrix{ {\mathop x\limits^ \bullet } & {\left( t \right)} \cr {\mathop x\limits^ \bullet } & {\left( t \right)} \cr } } \right] = \...

A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10 Ω, 5 Ω, 2 Ω are provided. Consider all pos...

A unity feedback control system is characterized by the open-loop transfer function $$$G\left(s\right)\;=\;\frac{2\left(s+1\right)}{s^3+ks^2+2s+1}$$$ The value of k for which the s...

A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinki...

Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6...

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), M...

The values of the integrals $$\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dy} } \right)} dx\,\,$$ and $$\,\,\int\limits_0^1 {\left( {\in...

The ninth and the tenth of this month are Monday and Tuesday _______.

“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antag...

The minimum value of the function $$f\left( x \right) = {1 \over 3}x\left( {{x^2} - 3} \right)\,\,$$ in the interval $$ - 100 \le x \le $$ $$100$$ occurs at $$x=$$ __________.

An integral $${\rm I}$$ over a counter clock wise circle $$C$$ is given by $${\rm I} = \oint\limits_c {{{{z^2} - 1} \over {{z^2} + 1}}} \,\,{e^z}\,dz$$ If $$C$$ is defined as $$\le...

It is ____ to read this year’s textbook _____ the last year’s.

Which of the following statement is incorrect?

The residues of a function $$f\left( z \right) = {1 \over {\left( {z - 4} \right){{\left( {z + 1} \right)}^3}}}$$ are

A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal to quantization noise ratio (SQNR) at the output of the quantizer is 40dB. T...

Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover probability P?

Consider the random process x(t) = U + Vt. Where U is a zero mean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are...

A two wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is

Standard air filled rectangular waveguides of dimensions a = 2.29cm and b = 1.02cm are designed for radar applications. It is desired that these waveguides operate only in the domi...

$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate course enrolment as follows: chemistry $$(329)$$, physics $...

The number of 3 digit numbers such that the digit 1 is never to the immediate right of 2 is

Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y married and have two children P and Q, Z is grandfather of the daughter ‘S’ of P. Further Z and W married a...

The rank of the matrix $$\left[ {\matrix{ 1 & { - 1} & 0 & 0 & 0 \cr 0 & 0 & 1 & { - 1} & 0 \cr 0 & 1 & { - 1} & 0 & 0 \cr { - 1} & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 & 1 & { - 1} \cr } }...

The general solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} + 2{{dy} \over {dx}} - 5y = 0\,\,\,$$ in terms of arbitrary constants $${K_1}$$ and $${K_2}$$ is

A second order LTI system is described by the following state equation. $$$\eqalign{ & {d \over {dt}}{x_1}\left( t \right) - {x_2}\left( t \right) = 0 \cr & {d \over {dt}}{x_2}\lef...

Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $$40$$% chance of getting reservation in any at...

The smaller angle (in degrees) between the planes $$x+y+z=1$$ and $$2x-y+2z=0$$ is ________.

The signal x(t) = $$\sin \,(14000\,\pi t)$$, where t is in seconds, is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal lowpass filter with...

The input x(t) and the output y(t) of a continuous time system are related as $$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du.} $$. The system is

An npn bipolar junction transistor (BJT) is operating in the active region. If the reverse bias across the base-collector junction is increased, then

An n-channel enhancement mode MOSFET is biased at V GS > V TH and V DS > (V GS - V TH ), where V GS is the gate-to-source voltage, V DS is the drain-to-source voltage and V TH is t...

Consider an n-channel MOSFET having width W, length L, electron mobility in the channel $$\mu_n$$ and oxide capacitance per unit area $$C_{ox}$$. If gate-to-source voltage V GS =0....

Consider an LTI system with magnitude response $$$\left| {H(f)} \right| = \left\{ {\matrix{ {1 - \,{{\left| f \right|} \over {20}},} & {\left| f \right| \le 20} \cr {0,} & {\left|...

Two n-channel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double of T1. Both the transistor are biased in the saturation region of operation, b...

For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (J L ) is 2.5 mA/cm 2 and the open-circuit voltage (V$$_{oc}$$) is 0.451...

An LTI system with unit sample response $$h\left( n \right) = 5\delta \left[ n \right] - 7\delta \left[ {n - 1} \right] + 7\delta \left[ {n - 3} \right] - 5\delta \left[ {n - 4} \r...

A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV, E c - E F = 0.9 eV; where E c and E F are conduc...

The un-modulated carrier power in an AM transmitter is 5kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is 50%. If it is reduc...

A modulating signal given By $$x\left(t\right)=5\sin\left(4\mathrm\pi10^3\mathrm t\;-\;10\mathrm{πcos}2\mathrm\pi10^3\mathrm t\right)$$ V is fed to a phase modulator with phase dev...

An electron (q 1 ) is moving in free space with velocity 10 5 m/s towards a stationary electron (q 2 ) far away. The closest distance that this moving electron gets to the stationa...