Electronics And Communication - ECE 2013 GATE Paper (Practice Test)

Complete the sentence:
Dare ____________ mistakes.

They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?

Q. No. 6 – 10 Carry Two Marks Each

Q.

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16km in the third quarter. The average speed of the car in km per hour over the entire journey is

Find the sum to n terms of the series 10 + 84 + 734 + …

Statement: There were different streams of freedom movements in colonial India
carried out by the moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?

The set of values of p for which the roots of the equation  3x² + 2x + p( p − 1) = 0
are of opposite sign is

What is the chance that a leap year, selected at random, will contain 53
Sundays?

Q. No. 11 – 35 Carry One Mark Each

Q.

A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles

Consider a vector field  The closed loop line integral  
can be expressed as

In a forward biased pn junction diode, the sequence of events that best describes
the mechanism of current flow is

Two systems with impulse responses  h₁(t) and h₂(t) are connected in cascade.
Then the overall impulse response of the cascaded system is given by

In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces

The maximum value of q until which the approximation sinθ ≈ θ holds to within 10%
error is

The divergence of the vector field 

The impulse response of a system is h(t) = tu(t). For an input u(t − 1) , the output is

The Bode plot of a transfer function G (s) is shown in the figure below

The gain (20 log |G(s)| ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively.
The phase is negative for all ω. The G(s) is

In the circuit shown below what is the output voltage ( ) out V if a silicon transistor
Q and an ideal op-amp are used?

Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of

For 8085 microprocessor, the following program is executed
MVI A, 05H;
MVIB, 05H;
PTR: ADD B;
DCR B;
JNZ PTR;
ADI 03H;
HLT;
At the end of program, accumulator contains

The bit rate of a digital communication system is R kbits/s. The modulation used is
32-QAM. The minimum bandwidth required for ISI free transmission is

For a periodic signal v (t) = 30sin100t + 10cos300t + 6 sin(500t + π / 4) , the
fundamental frequency in rad/s

In a voltage-voltage feedback as shown below, which one of the following
statements is TRUE if the gain k is increased?

A band-limited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the sampling frequency which is not valid is

In a MOSFET operating in the saturation region, the channel length modulation
effect causes

Which one of the following statements is NOT TRUE for a continuous time causal
and stable LTI system?

The minimum Eigen value of the following matrix is

A polynomial  f( x) = a₄ x⁴ + a₃ x³ + a₂ x² + a₁ x − a₀ with all coefficients positive has

Assuming zero initial condition, the response y(t) of the system given below to a
unit step input u(t) is

The transfer function V₂(s) / V₁(s) of the circuit shown below is

A source V_s (t) = V cos100πt has an internal impedance of (4 + j3)? . If a purely
resistive load connected to this source has to extract the maximum power out of the
source, its value in ? should be

The return loss of a device is found to be 20 dB. The voltage standing wave ratio
(VSWR) and magnitude of reflection coefficient are respectively

Let , and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t),
then the Fourier transform of the output is

Q. No. 36 – 65 Carry Two Marks Each

Q

Let U and V be two independent zero mean Gaussian random variables of variances1/4 and 1/9 respectively,. The probability P (3V 2U) is

Let A be an m x n matrix and B an n x m matrix. It is given that determinant
 ( I_m + AB) = determinant (I_n + BA) , where I_k is the k × k identity matrix. Using the
above property, the determinant of the matrix given below is

In the circuit shown below, if the source voltage V_s =10053.13^o V then the
Thevenin’s equivalent voltage in Volts as seen by the load resistance  R_L is

The open-loop transfer function of a dc motor is given as when
connected in feedback as shown below, the approximate value of a K that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

In the circuit shown below, the knee current of the ideal Zener diode is 10mA. To
maintain 5V across R_L , the minimum value of  R_L in ? and the minimum power
rating of the Zener diode in mW, respectively, are

The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8 An ac voltage V_wx1 = 100V is applied across WX to get an open circuit voltage V_YZ1 across YZ. Next, an ac voltage V_YZ2 =100V is applied across YZ to get an open circuit voltage V_WX2 across WX.
Then, V_YZ1 / V_WX1 , V_WX2 / V_YZ2 are respectively.

Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective Q factor at the same operating frequency is

The impulse response of a continuous time system is given by
h(t) = δ (t − 1) + δ (t − 3) . The value of the step response at t = 2 is

The small-signal resistance (  i.e dV_B/dI_D) in k? offered by the n-channel MOSFET M shown in the figure below, at a bias point of V_B = 2 V is (device data for M: device Transconductance parameter  k_N = μ C_ox (W / L0 = 40μA / V² threshold voltage V_TN = 1V, and neglect body effect and channel length
modulation effects)

The ac schematic of an NMOS common-source stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the nchannel MOSFET M, the Transconductance g_m = 1mA / V, and body effect and channel length modulation effect are to be neglected. The lower cutoff frequency
in Hz of the circuit is approximately at

A system is described by the differential equation 

Let x(t) be a rectangular pulse given by

Assuming that y(0)=0 and dy/dt =0 at t = 0, the Laplace transform of y(t) is

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes -2y(t) for t>0, we need to

Consider two identically distributed zero-mean random variables U and V. Let the
cumulative distribution functions of U and 2V be F(x) and G(x) respectively.
Then, for all values of x

The DFT of vector  [ a b c d]  is the vector[ α β γ δ]  . Consider the product

The DFT of the vector [ p q r s] is a scaled version of

The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is

In the circuit shown below the op-amps are ideal. The V_out in Volts is

In the circuit shown below,  Q₁ has negligible collector-to-emitter saturation
voltage and the diode drops negligible voltage across it under forward bias. If
V_cc is + 5V,X and Y are digital signals with 0 V as logic 0 and V_CC as logic 1,
then the Boolean expression for Z is

A voltage 1000sin ωt Volts is applied across YZ. Assuming ideal diodes, the
voltage measured across WX in Volts, is

Three capacitors  C₁ ,C₂ and C₃ whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively.

There are four chips each of 1024 bytes connected to a 16 bit address bus as
shown in the figure below. RAMs 1,2,3 and 4 respectively are mapped to
addresses

In the circuit shown below, the silicon npn transistor Q has a very high value of
b . The required value of R₂ in k? to produce I_C = 1mA is

Let U and V be two independent and identically distributed random variables such
that P(U= 1+) = P(U= -1)=1/2 The entropy H(U + V) in bits is

Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the
respective received signals for both bits are as shown below.

Q.

If the detection threshold is 1, the BER will be

Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the
respective received signals for both bits are as shown below.

Q.

The optimum threshold to achieve minimum bit error rate (BER) is

Consider the following figure

The current I_S in Amps in the voltage source, and voltage V_S in Volts across the
current source respectively, are

Consider the following figure

Q.

The current in the 1? resistor in Amps is

A monochromatic plane wave of wavelength λ = 600μm is propagating in the direction as shown in the figure below.  denote incident, reflected, and transmitted electric field vectors associated with the wave.

The angle of incidence θ₁ and the expression for  are

A monochromatic plane wave of wavelength l = 600μm is propagating in the  direction as shown in the figure below.  denote incident, reflected, and transmitted electric field vectors associated with the wave.

Q.

The expression for  is

The state diagram of a system is shown below. A system is described by the state-variable equations

Q. The state-variable equations of the system shown in the figure above are

The state diagram of a system is shown below. A system is described by the
state-variable equations

Q.

The state transition matrix e^At of the system shown in the figure above is