Gate 2011 EC Question paper

Consider the following statements regarding the complex Poynting vector for the power radiated by a point source in an infinite homogeneous and lossless medium. Re denotes the real part of . S denotes a spherical surface whose

centre is at the point source, and denotes the unit surface normal on S. Which of the following statements is TRUE?

A transmission line of characteristic impedance 50W is terminated by a 50 load. When excited by a sinusoidal voltage source at 10GHz, the phase difference
between two points spaced 2mm apart on the line is found to be radians. The phase velocity of the wave along the line is

An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is _____ bits / second.

The root locus plot for a system is given below. The open loop transfer function corresponding to this plot is given by

A system is defined by its impulse response h (n) = u (n – 2) . The system is

If the unit step response of a network is , then its unit impulse response is

The output Y in the circuit below is always ‘1’ when

In the circuit shown below, capacitors are very large and are shorts at the input frequency. is a small signal input. The gain magnitude at 10M rad/s is

Drift current in the semiconductors depends upon

A Zener diode, when used in voltage stabilization circuits, is biased in

The circuit shown below is driven by a sinusoidal input cos (t / RC) . The steady state output is

Consider a closed surface S surrounding volume V. If is the position vector of a point inside S, with the unit normal on S, the value of the integral is

The modes in a rectangular waveguide are denoted by where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?

The solution of the differential equation = ky, y(0) = c is

The Column-I lists the attributes and the Column-II lists the modulation systems. Match the attribute to the modulation system that best meets it

Column-I	Column-II
P Power efficient transmission of signals	1 Conventional AM
Q Most bandwidth efficient transmission of voice signals	2 FM
R Simplest receiver structure	3 VSB
S Bandwidth efficient transmission of signals with Significant dc component	4 SSB-SC

The differential equation 100 + y = x (t) describes a system with an input x(t) and an output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

For the transfer function G (j ) = 5 + j , the corresponding Nyquist plot for positive frequency has the form

The trigonometric Fourier series of an even function does not have the

When the output Y in the circuit below is ‘1’, it implies that data has

The logic function implemented by the circuit below is (ground implies logic 0)

The circuit below implements a filter between the input current and the output voltage . Assume that the opamp is ideal. The filter implemented is a

A silicon PN junction is forward biased with a constant current at room temperature. When the temperature is increased by the forward bias voltage across the PN junction

In the circuit shown below, the Norton equivalent current in amperes with respect to the terminals P and Q is

In the circuit shown below, the value of such that the power transferred to is maximum is

The value of the integral dz where c is the circle |z| = 1 is given by

A transmission line of characteristic impedance 50W is terminated in a load impedance The VSWR of the line is measured as 5 and the first of the voltage maxima in the line is observed at a distance of from the load. The value of is

X(t) is a stationary random process with autocorrelation function (t) = exp This process is passed through the system shown below. The power spectral density of the output process Y(t) is

The output of a 3-stage Johnson (twisted ring) counter is fed to a digital-toanalog (D/A) converter as shown in the figure below. Assume all the states of the counter to be unset initially. The waveform which represents the D/A converter output is

Two D flip-flops are connected as a synchronous counter that goes through the following sequence The combination to the inputs and are

In the circuit shown below, for the MOS transistors, and the threshold voltage The voltage at the source of the upper transistor is

An input x (t) = exp (- 2t) u (t) + (t – 6) is applied to an LTI system with impulse response h (t) = u (t) . The output is is

For a BJT the common base current gain = 0.98 and the collector base junction reverse bias saturation current This BJT is connected in the common emitter mode and operated in the active region with a base drive current The collector current for this mode of operation is

If F (s) = L [ f (t) ] = then the initial and final values of f(t) are respectively

In the circuit shown below, the current I is equal to

A numerical solution of the equation f (x) = x + = 0 can be obtained using Newton- Raphson method. If the starting value is x = 2 for the iteration, the value of x that is to be used in the next step is

The electric and magnetic fields for a TEM wave of frequency 14 GHz in a homogeneous medium of relative permittivity and relative permeability are given by


Assuming the speed of light in free space to be m/s, the intrinsic impedance of free space to be , the relative permittivity of the medium and the electric field amplitude are

A message signal m(t) = cos200 modulates the carrier (t ) = cos 2t where = 1 MHZto produce an AM signal. For demodulating the generated AM signal using an envelope detector, the time constant RC of the detector circuit should satisfy

The block diagram of a system with one input it and two outputs is given below.

A state space model of the above system in terms of the state vector the output vector = is

Two systems (z) and (z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system (z) is

An 8085 assembly language program is given below. Assume that the carry flag is initially unset. The content of the accumulator after the execution of the program is

The first six points of the 8-point DFT of a real valued sequence are5, 1 – j3,0,3 – j4, 0 and 3 + j4. . The last two points of the DFT are respectively

For the BJT in the circuit shown below, = 0.7V The switch is initially closed. At time t = 0, the switch is opened. The time t at which leaves the active region is

In the circuit shown below, the network N is described by the following Y matrix:

In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t=0. The current i(t) at a time t after the switch is closed is

The system of equations

x + y + z = 6
x + 4y + 6z = 20
x + 4y +

has NO solution for values of given by

A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is

Directions for next two questions: The channel resistance of an N-channel JFET shown in the figure below is 600 when the full channel thickness 10?mis available for conduction. The built-in voltage of the gate N junction is -1 V. When the gate to source voltage is 0 V, the channel is depleted by 1?m on each side due to the builtin voltage and hence the thickness available for conduction is only m

The channel resistance when = -3 V is

The channel resistance when = 0 V is

Directions for next two questions: The input-output transfer function of a plant H (s) = . The plant is placed in a unity negative feedback configuration as shown in the figure below.

The gain margin of the system under closed loop unity negative feedback is

The signal flow graph that DOES NOT model the plant transfer function H(s) is

Directions for next two questions: In the circuit shown below, assume that the voltage drop across a forward biased diode is 0.7 V. The thermal voltage = kT / q = 25mV. The small signal input



The bias current through the diodes is

The ac output voltage is

Directions for next two questions: A four-phase and an eight-phase signal constellation are shown in the figure below.

For the constraint that the minimum distance between pairs of signal points be d for both constellations, the radii of the circles are

Assuming high SNR and that all signals are equally probable, the additional average transmitted signal energy required by the 8-PSK signal to achieve the same error probability as the 4-PSK signal is

There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?

Choose the most appropriate word from the options given below to complete the following sentence:

It was her view that the country’s problems had been_____ by foreign technocrats, so that to invite them to come back would be counter-productive.

Choose the word from the options given below that is most nearly opposite in meaning to the given word:

Frequency

Choose the most appropriate word from the options given below to complete the following sentence:

Under ethical guidelines recently adopted by the Indian Medical Association, human genes are to be manipulated only to correct diseases for which_____ treatments are unsatisfactory.

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

Gladiator : Arena

The fuel consumed by a motorcycle during a journey while traveling at various speeds is indicated in the graph below.

The distances covered during four laps of the journey are listed in the table below


From the given data, we can conclude that the fuel consumed per kilometre was least during the lap

Three friends, R, S and T shared toffee from a bowl. R took of the toffees, but returned four to the bowl. S took of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees-were originally there in the bowl?

Given that f(y) = | y | / y, and q is any non-zero real number, the value of

| f(q) – f(-q) | is

The sum of n terms of the series 4+44+444+.... is

The horse has played a little known but very important role in the field of medicine. Horses were injected with toxins of diseases until their blood built up immunities. Then a serum was made from their blood. Serums to fight with diphtheria and tetanus were developed this way.

It can be inferred from the passage that horses were