GATE 2010 Electronics & Communication Question Paper with Answers

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Question

The eigen values of a skew-symmetric matrix are

Possible Answers

Selected	Possible Answer
	always zero
	always pure imaginary
	either zero or pure imaginary
	always real

Question

The trigonometric Fourier series for the waveform f(t) shown below contains

Possible Answers

Selected	Possible Answer
	only cosine terms and zero value for the dc component
	only cosine terms and a positive value for the dc component
	only cosine terms and a negative value for the dc component
	only sine terms and a negative value for the dc component

Question

A function n(x) satisfies the differential equation $\cfrac{d^2n (x)}{dx^2} - \cfrac{n (x)}{L^2}$ = 0 where L is a constant. The boundary conditions are : n(0) = K and $n ( \infty ) = 0$ . The solution to this equation is :

Possible Answers

Selected	Possible Answer
	n(x) = Kexp(x / L)
	n(x) = Kexp $(x / \sqrt{L})$
	n(x) = exp(-x / L)
	n(x) = Kexp(-x / L)

Question

For the two-port network shown below, the short-circuit admittance parameter matrix is :

Possible Answers

Selected	Possible Answer
	$\bigg[ \overset{4}{-2}$ $\overset{-2}{4} \bigg] S$
	$\bigg[ \overset{1}{-0.5}$ $\overset{-0.5}{1} \bigg] S$
	$\bigg[ \overset{1}{0.5}$ $\overset{0.5}{1} \bigg] S$
	$\bigg[ \overset{4}{2}$ $\overset{2}{4} \bigg] S$

Question

For a parallel RLC circuit, which one of the following statements is NOT correct ?

Possible Answers

Selected	Possible Answer
	The bandwidth of the circuit decreases if R is increased
	The bandwidth of the circuit remains same if L is increased
	At resonance, input impedance is a real quantity
	At resonance, the magnitude of input impedance attains its minimum value

Question

At room temperature, a possible value for the mobility of electrons in the inversion layer of a silicon nchannel MOSFET is :

Possible Answers

Selected	Possible Answer
	450 / V – s
	1350 / V – s
	1800 / V – s
	3600 / V – s

Question

Thin gate oxide in a CMOS process is preferably grown using

Possible Answers

Selected	Possible Answer
	wet oxidation
	dry oxidation
	epitaxial deposition
	ion implantation

Question

In the silicon BJT circuit shown below, assume that the emitter area of transistor Q1 is half that of transistor Q2.

The value of current I_0

is approximately

Possible Answers

Selected	Possible Answer
	0.5 mA
	2 mA
	9.3 mA
	15 mA

Question

The amplifier circuit shown below uses a silicon transistor. The capacitance $C_C\ and\ E_C$ can be assumed to be short at signal frequency and the effect of output resistance r_0 can be ignored. If C_E is disconnected from the circuit, which one of the following statements is TRUE ?

Possible Answers

Selected	Possible Answer
	The input resistance increases and the magnitude of voltage gain decreases
	The input resistance decreases and the magnitude of voltage gain increases
	Both input resistance and the magnitude of voltage gain decrease
	Both input resistance and the magnitude of voltage gain increase

Question

Assuming the OP-AMP to be ideal, the voltage gain of the amplifier shown below is :

Possible Answers

Selected	Possible Answer
	$- \cfrac{R_2}{R_1}$
	$- \cfrac{R_3}{R_1}$
	$-\bigg( \cfrac{R_2 \|\| R_3}{R_1} \bigg)$
	$-\bigg( \cfrac{R_2+ R_3}{R_1} \bigg)$

Question

Match the logic gates in Column A with their equivalents in Column B.

Possible Answers

Selected	Possible Answer
	2 4 1 3
	4 2 1 3
	2 4 3 1
	4 2 3 1

Question

For the output F to be 1 in the logic circuit shown, the input combination should be

Possible Answers

Selected	Possible Answer
	A = 1, B = 1, C = 0
	A = 1, B = 0, C = 0
	A = 0, B = 1, C = 0
	A = 0, B = 0, C = 1

Question

In the circuit shown, the device connected to Y5 can have address in the range

Possible Answers

Selected	Possible Answer
	2000 – 20FF
	2D00 – 2DFF
	2E00 – 2EFF
	FD00 – FDFF

Question

Consider the z-transform X(z) = $5z^2 + 4z^{-1} + 3; 0 < |z| < \infty$ . The inverse z-transform x[n] is :

Possible Answers

Selected	Possible Answer
	$5 \delta [n+2]+ \delta [n]+4 \delta [n-1]$
	$5 \delta [n-2]+ \delta [n]+4 \delta [n+1]$

Question

Two discrete time systems with impulse responses $h_1[n] = \delta [n-1]$ and $h_2 [n] = \delta [n-2]$ are connected in cascade. The overall impulse response of the cascaded system is :

Possible Answers

Selected	Possible Answer
	$\delta [n - 1] + \delta [n - 2]$
	$\delta [n - 4]$
	$\delta [n - 3]$
	$\delta [n - 1] \delta [n - 2]$

Question

For an N-point FFT algorithm with N = 2^m , which one of the following statements is TRUE ?

Possible Answers

Selected	Possible Answer
	It is not possible to construct a signal flow graph with both input and output in normal order
	The number of butterflies in the $m^{th}$ stage is N/m
	In-place computation requires storage of only 2N node data
	Computation of a butterfly requires only one complex multiplication

Question

The transfer function Y(s)/R(s) of the system shown is :

Possible Answers

Selected	Possible Answer

	$\cfrac{1}{s + 1}$
	$\cfrac{2}{s + 1}$
	$\cfrac{2}{s + 3}$

Question

A system with the transfer function $\cfrac{Y (s)}{X (s)} = \cfrac{s}{s+p}$ has an output y(t) = cos $\bigg(2t - \cfrac{\pi}{3} \bigg)$ for the input signal x(t) = p cos $\bigg(2t - \cfrac{\pi}{2} \bigg)$ . Then, the system parameter ‘p’ is :

Possible Answers

Selected	Possible Answer
	$\sqrt{3}$
	$\cfrac{2}{\sqrt{3}}$

	$\cfrac{\sqrt{3}}{2}$

Question

For the asymptotic Bode magnitude plot shown below, the system transfer function can be

Possible Answers

Selected	Possible Answer
	$\cfrac{10s + 1}{0.1s + 1}$
	$\cfrac{100s + 1}{0.1s + 1}$
	$\cfrac{100s}{10s + 1}$
	$\cfrac{0.1s + 1}{10s + 1}$

Question

Suppose that the modulating signal is m(t) = 2cos $(2 \pi f_m t)$ and the carrier signal is $X_c (t) = A_c cos(2 \pi f_c t)$ . Which one of the following is a conventional AM signal without over-modulation ?

Possible Answers

Selected	Possible Answer
	$X (t) = A_c m(t)\ cos(2 \pi f_ct)$
	$X (t) = A_c[1+m(t)]\ cos(2 \pi f_ct)$
	$X (t) = A_c\ cos(2 \pi f_ct) +$ $\cfrac{A_c}{4} m(t)\ cos(2 \pi f_c t)$
	$X (t) = A_c\ cos(2 \pi f_m t) cos(2 \pi f_ct)$ $+ A_c sin(2 \pi f_m t) sin(2 \pi f_c t)$

Question

Consider an angle modulated signal $x(t) = 6 cos[2 \pi X 10^6 t+2 sin$ $(8000 \pi t) +4 cos(8000 \pi t)]$ V. The average power of x(t) is :

Possible Answers

Selected	Possible Answer
	10W
	18W
	20W
	28W

Question

If the scattering matrix [S] of a two port network is

then the network is :

Possible Answers

Selected	Possible Answer
	lossless and reciprocal
	lossless but not reciprocal
	not lossless but reciprocal
	neither lossless nor reciprocal

Question

A transmission line has a characteristic impedance of $50 \Omega$ and a resistance of $0.1 \Omega$ / m . If the line is distortionless, the attenuation constant (in Np/m) is :

Possible Answers

Selected	Possible Answer
	500
	5
	0.014
	0.002

Question

Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is :

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Selected	Possible Answer

Question

The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector $(in\ W / m^2)$ is:

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{30\ \pi}$
	$\cfrac{1}{60\ \pi}$
	$\cfrac{1}{120\ \pi}$
	$\cfrac{1}{240\ \pi}$

Question

If $e^y = X^{\frac{1}{x}}$ , then y has a

Possible Answers

Selected	Possible Answer
	maximum at x = e
	minimum at x = e
	maximum at $X = e^{-1}$
	minimum at $X = e^{-1}$

Question

A fair coin is tossed independently four times. The probability of the event “the number of time heads shown up is more than the number of times tails show up” is :

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{16}$
	$\cfrac{1}{8}$
	$\cfrac{1}{4}$
	$\cfrac{5}{16}$

Question

If $\vec A = xy\ \hat a_x+x\ {}^2 \hat a_y$ , then $\overset{\int}{C}$ $\vec A \ d \vec I$ over the path shown in the figure is :

Possible Answers

Selected	Possible Answer

	$\cfrac{2}{\sqrt{3}}$

	$2 \sqrt{3}$

Question

The residues of a complex function X (z) = $\cfrac{1-2z}{z(z-1) (z-2)}$ at its poles are

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{2}\ , - \cfrac{1}{2}\ and\ 1$
	$\cfrac{1}{2}\ , \cfrac{1}{2}\ and - 1$
	$\cfrac{1}{2}\ , 1\ and\ - \cfrac{3}{2}$
	$\cfrac{1}{2}\ , -1\ and\ \cfrac{3}{2}$

Question

Consider a differential equation $\cfrac{dy(x)}{dx} - y (x) = x$ with the initial condition y(0) = 0 . Using Euler’s first order method with a step size of 0.1, the value of y (0.3) is :

Possible Answers

Selected	Possible Answer
	0.01
	0.031
	0.0631
	0.1

Question

Given $f (t) = L^{-1}$ $\bigg[$ $\cfrac{3s+1}{s^3+4s^2+(K-3)s}$ $\bigg]$ . if $\overset{lim}{t \rightarrow \infty}$ f (t) = 1 , then the value of K is :

Possible Answers

Selected	Possible Answer
	1
	2
	3
	4

Question

In the circuit shown, the switch S is open for a long time and is closed at t = 0. The current i(t) for $t \ge 0^+$ is :

Possible Answers

Selected	Possible Answer
	i(t) = 0.5 – 0.125 $e^{-1000t}$ A
	i(t) = 1.5 – 0.125 $e^{-1000t}$ A
	i(t) = 0.5 – 0.5 $e^{-1000t}$ A
	i(t) = 0.375 $e^{-1000t}$ A

Question

The current I in the circuit shown is :

Possible Answers

Selected	Possible Answer
	- j1 A
	j1 A
	0 A
	20 A

Question

In the circuit shown, the power supplied by the voltage source is :

Possible Answers

Selected	Possible Answer
	0 W
	5 W
	10 W
	100 W

Question

In a uniformly doped BJT, assume that $N_E , N_B\ and\ N_C$ are the emitter, base and collector dopings in atoms/ cm^3 , respectively. If the emitter injection efficiency of the BJT is close to unity, which one of the following conditions is TRUE ?

Possible Answers

Selected	Possible Answer

	$N_E >> N_B\ and\ N_B > N_C$
	$N_E = N_B\ and\ N_B < N_C$

Question

Compared to p-n junction with $N_A = N_D = 10^{14} / cm^3$ , which one of the following statements is TRUE for a p-n junction with $N_A = N_D = 10^{20} / cm^3$ ?

Possible Answers

Selected	Possible Answer
	Reverse breakdown voltage is lower and depletion capacitance is lower
	Reverse breakdown voltage is higher and depletion capacitance is lower
	Reverse breakdown voltage is lower and depletion capacitance is higher
	Reverse breakdown voltage is higher and depletion capacitance is higher

Question

Assuming that all flip-flops are in reset condition initially, the count sequence observed at Q_a in the circuit shown is :

Possible Answers

Selected	Possible Answer
	0010111…
	0001011…
	0101111…
	0110100…

Question

The transfer characteristic for the precision rectifier circuit shown below is (assume ideal OP-AMP and practical diodes)

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Selected	Possible Answer

Question

The Boolean function realized by the logic circuit shown is :

Possible Answers

Selected	Possible Answer
	F = $\Sigma$ m(0,1,3,5,9,10,14)
	F = $\Sigma$ m(2,3,5,7,8,12,13)
	F = $\Sigma$ m(1, 2,4,5,11,14,15)
	F = $\Sigma$ m(2,3,5,7,8,9,12)

Question

For the 8085 assembly language program given below, the content of the accumulator after the execution of the program is :

Possible Answers

Selected	Possible Answer
	00H
	45H
	67H
	E7H

Question

A continuous time LTI system is described by

$\cfrac{d^2y(t)}{dt^2} + 4$ $\cfrac{dy(t)}{dt} + 3y(t) = 2$ $\cfrac{dx(t)}{dt} + 4x (t)$
Assuming zero initial conditions, the response y(t) of the above system for the input $x (t) = e^{-2t} u (t)$ is given by

Possible Answers

Selected	Possible Answer
	$(e^t - e^{3t}) \ u (t)$
	$(e^{-t} - e^{-3t}) \ u (t)$
	$(e^{-t} + e^{-3t}) \ u (t)$
	$(e^t + e^{3t}) \ u (t)$

Question

The transfer function of a discrete time LTI system is given by

Consider the following statements :

S1 : The system is stable and causal for ROC : |z| > $\cfrac{1}{2}$

S2 : The system is stable but not causal for ROC : |z| < $\cfrac{1}{4}$

S3 : The system is neither stable nor causal for ROC : $\cfrac{1}{4}$ < |z| < $\cfrac{1}{2}$

Which one of the following statements is valid ?

Possible Answers

Selected	Possible Answer
	Both S1 and S2 are true
	Both S2 and S3 are true
	Both S1 and S3 are true
	S1, S2 and S3 are all true

Question

The Nyquist sampling rate for the signal $s(t) = \cfrac{sin(500 \pi t)}{\pi t}\ X$ $\cfrac{sin(700 \pi t)}{\pi t}$ is given by

Possible Answers

Selected	Possible Answer
	400 Hz
	600 Hz
	1200 Hz
	1400 Hz

Question

A unity negative feedback closed loop system has a plant with the transfer function $G(s) = \cfrac{1}{s^2 + 2s + 2}$ and a controller G_c (s) in the feedforward path. For a unit step input, the transfer function of the controller that gives minimum steady error is :

Possible Answers

Selected	Possible Answer
	$G_c (s) = \cfrac{s+1}{s+2}$
	$G_c (s) = \cfrac{s+2}{s+1}$
	$G_c (s) = \cfrac{(s+1) (s+4)}{(s+2) (s+3)}$
	$G_c (s) = 1+ \cfrac{2}{s} + 3s$

Question

X(t) is a stationary process with the power spectral density S_x (f) > 0 for all f. The process is passed through a system shown below.

Let

be the power spectral density of Y(t). Which one of the following statements is correct ?

Possible Answers

Selected	Possible Answer
	$S_Y (f) > 0\ for\ all\ f$
	$S_Y (f) > 0\ for\ \| f \| > 1kHz$
	$S_Y (f) > 0\ for\ f = n f_0 , f_0 = 2kHz,$ n any integer
	$S_Y (f) = 0 \ for \ f = (2n+1)$ $f_0, \ f_0 = 1kHz ,$ n any integer

Question

A plane wave having the electric field component $\vec E i = 24\ cos$ $(3\ X\ 10^8\ t- \beta y) \hat a {}_z$ V/m and travelling in free space is incident normally on a lossless medium with $\mu = \mu_0 \ and\ \in = 9 \in_0$ which occupies the region $y \ge 0$ . The reflected magnetic field component is given by

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{10 \pi}$ $cos(3\ X\ 10^8 t+y) \hat a_x\ A/m$
	$\cfrac{1}{5 \pi}$ $cos(3\ X\ 10^8 t+y) \hat a_x\ A/m$
	$\cfrac{1}{20 \pi}$ $cos(3\ X\ 10^8 t+y) \hat a_x\ A/m$
	$\cfrac{1}{30 \pi}$ $cos(3\ X\ 10^8 t+y) \hat a_x\ A/m$

Question

In the circuit shown, all the transmission line sections are lossless. The Voltage Standing Wave Ratio (VSWR) on the $60 \Omega$ line is :

Possible Answers

Selected	Possible Answer
	1.00
	1.64
	2.50
	3.00

Question

Directions for next two questions: Consider the common emitter amplifier shown below with the following circuit parameters :

$\beta = 100, g_m$ $0.3861 A / V , r_0 = \infty ,$ $r_\pi = 259 \Omega$ , $R_s = 1k \Omega$ , $R_B = 93k \Omega$ , $R_C = 250 \Omega$ , $R_L = 1k \Omega , C_1 = \infty$ $and\ C_2 = 4.7 \mu F$ .

The resistance seen by the source V_S

is :

Possible Answers

Selected	Possible Answer
	$258 \Omega$
	$1258 \Omega$
	$93k \Omega$
	$\infty$

Question

The lower cut-off frequency due to C_2 is :

Possible Answers

Selected	Possible Answer
	33.9 Hz
	27.1 Hz
	13.6 Hz
	16.9 Hz

Question

Directions for next two questions: The signal flow graph of a system is shown below

The state variable representation of the system can be

Possible Answers

Selected	Possible Answer

Question

The transfer function of the system is :

Possible Answers

Selected	Possible Answer
	$\cfrac{s + 1}{s^2 + 1}$
	$\cfrac{s - 1}{s^2 + 1}$
	$\cfrac{s + 1}{s^2 + s + 1}$
	$\cfrac{s - 1}{s^2 + s + 1}$

Question

Directions for next two questions: The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T=300K, electronic charge $= 1.6 X 10^{-19} C ,$ thermal voltage = 26 mV and electron mobility = 1350cm^2 / V - s .

The magnitude of the electric field at $x = 0.5 \ \mu m$ is :

Possible Answers

Selected	Possible Answer
	1 kV/cm
	5 kV/cm
	10 kV/cm
	26 kV/cm

Question

The magnitude of the electron drift current density at $x = 0.5\ \mu m$ is :

Possible Answers

Selected	Possible Answer
	$2.16 X 10^4 \ A / cm^2$
	$1.08 X 10^4 \ A / cm^2$
	$4.32 X 10^3 \ A / cm^2$
	$6.48 X 10^2 \ A / cm^2$

Question

Directions for next two questions: Consider a baseband binary PAM receiver shown below. The additive channel noise n(t) is whit with power spectral density $S_N\ (f) = N_0\ / 2 = 10^{-20}$ W / Hz. The low-pass filter is ideal with unity gain and cutoff frequency 1MHz. Let Y_k represent the random variable y (t_k) .

	if transmitted bit
	if transmitted bit

where N_k represents the noise sample value. The noise sample has a probability density function, $P_{N_k} \ (n) = 0.5 \alpha\ e^{- \alpha InI}$ (This has mean zero and variance $2 / \alpha^2$ ). Assume transmitted bits to be equiprobable and threshold z is set to $a / 2 = 10^{-6}$ V.

The value of the parameter $\alpha \ (in\ V^{-1} )$ is :

Possible Answers

Selected	Possible Answer
	$10^{10}$

	$1.414 X 10^{-10}$
	$2 X 10^{-20}$

Question

The probability of bit error is :

Possible Answers

Selected	Possible Answer
	$0.5 X \ e^{-3.5}$
	$0.5 X \ e^{-5}$
	$0.5 X \ e^{-7}$
	$0.5 X \ e^{-10}$

Question

Which of the following options is the closest in meaning to the world below:

Circuitous

Possible Answers

Selected	Possible Answer
	cyclic
	indirect
	confusing
	crooked

Question

The question below consists of a pair of related of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.

Unemployed: Worker

Possible Answers

Selected	Possible Answer
	fallow : land
	unaware : sleeper
	wit : jester
	renovated : house

Question

Choose the most appropriate word from the options given below to complete the following sentence :
If we manage to ________ our natural resources, we would leave a better planet for our children.

Possible Answers

Selected	Possible Answer
	uphold
	restrain
	cherish
	conserve

Question

Choose the most appropriate word from the options given below to complete the following sentence :
His rather casual remarks on politics ______ his lack of seriousness about the subject.

Possible Answers

Selected	Possible Answer
	masked
	belied
	betrayed
	suppressed

Question

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is :

Possible Answers

Selected	Possible Answer
	2
	17
	13
	3

Question

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.

Which of the following statements best sums up the meaning of the above passage :

Possible Answers

Selected	Possible Answer
	Modern warfare has resulted in civil strife.
	Chemical agents are useful in modern warfare.
	Use of chemical agents in warfare would be undesirable.
	People in military establishments like to use chemical agents in war.

Question

If 137 + 276 = 435 how much is 731 + 672 ?

Possible Answers

Selected	Possible Answer
	534
	1403
	1623
	1513

Question

skilled workers can build a wall in 20 days; 8 semi-skilled worker can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall ?

Possible Answers

Selected	Possible Answer
	20 days
	18 days
	16 days
	15 days

Question

Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed ?

Possible Answers

Selected	Possible Answer
	50
	51
	52
	54

Question

Hari (H), Gita (G), Irfan (I) and Saira (S) are sibiligs (i.e. brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than3 years. Given the following facts :

i. Hair’s age + Gita’s age > Irfan’s age + Saira’s age.
ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest.
iii. There are not twins.

In what order were they born (oldest first) ?

Possible Answers

Selected	Possible Answer
	HSIG
	SGHI
	IGSH
	IHSG

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GATE 2010 Electronics & Communication Question Paper with Answers

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