Electronics And Communication (Set 2) - ECE 2017 GATE Paper (Practice Test)

In a DRAM,

Consider an n-channel MOSFET having width W, length L, electron mobility in the channel μ_n and oxide capacitance per unit area C_ox. If gate-to-source voltage V_GS = 0.7V, drain-tosource voltage V_DS = 0.1V, (μ_n C_ox) = 100μA / V² , threshold voltage V_TH = 0.3 V and (W/L) = 50, then the transconductance g_m (in mA/V) is ___________.

Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.

For some charge placed on this structure, the potential and surface electric field on S1 are V_a and E_a, and that on S2 are V_b and E_b, respectively, which of the following is CORRECT? 

For the circuit shown in the figure, P and Q are the inputs and Y is the output.

The logic implemented by the circuit is

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 the threshold voltage. Considering channel length modulation effect to be significant, the MOSFET behaves as a

A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10Ω, 5Ω, 2Ω are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) 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

Consider the state space realization
, with the initial condition
where u(t) denotes the unit step function. The value of 

The rank of the matrix 

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 ______________

The input x(t) and the output y(t) of a continuous-time system are related as 

Which of the following statements is incorrect?

The residues of a function 

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. The minimum number of bits per sample needed to achieve the desired SQNR is _______

The general solution of the differential equation  in terms of arbitrary 
constants K₁ and K₂ is

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?

The output V₀ of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the diode, is ____________.

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 statistically independent. The mean value of the random process at t = 2 is ____________

For the system shown in the figure, Y(s) / X(s) = __________.

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

Consider the circuit shown in the figure. Assume base-to- emitter voltage V_BE = 0.8 V and common base current gain (α) of the transistor is unity.

The value of the collector- to – emitter voltage V_CE (in volt) is _______. 

In the figure, D1 is a real silicon pn junction diode with a drop of 0.7V under forward bias condition and D2 is a zener diode with breakdown voltage of -6.8 V. The input V_in(t) is a periodic square wave of period T, whose one period is shown in the figure.

Assuming 10t << T. where t is the time constant of the circuit, the maximum and minimum values of the output waveform are respectively,

If the vector function is irrotational, then the values of the constants k₁, k₂ and k₃ respectively, are

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 reduced to 40%, then the maximum un-modulated carrier power (in kW) that can be used without overloading the transmitter is ___________

Consider an LTI system with magnitude response 

And phase response Arg {H (f)} = -2f.
If the input to the system is

Then the average power of the output signal y (t) is _________.

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-F_F = 0.9 eV, where E_C and E_F are the conduction band minimum and the Fermi energy levels of Si, respectively. Oxide  F / cm. oxide thickness t_ox = 0.1 μm and electronic charge q = 1.6 ×10^-19 C. If the measured flat band voltage of the capacitor is -1V, then the magnitude of the fixed charge at the oxidesemiconductor interface, in nC/cm², is __________.

An electron (q₁) is moving in free space with velocity 10⁵ m/s towards a stationary electron (q₂) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is ___________ ×10^-8m.

[Given, mass of electron m = 9.11×10^-31kg, charge of electron e = -1.6×10^-19C , and permittivity  

The values of the integrals

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 attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is _________.

Figure I shows a 4-bits ripple carry adder realized using full adders and Figure II shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and OR gates in Figure II are 20 ns, 15 ns and 10 ns respectively. Assume all the inputs to the 4-bit adder are initially reset to 0.

At t = 0, the inputs to the 4-bit adder are changed to

The output of the ripple carry adder will be stable at t (in ns) = ___________

The permittivity of water at optical frequencies is 1.75 ε₀ . It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5m, as shown in the figure. The critical angle is θ_c.

The value of d (in meter) is _____________

A unity feedback control system is characterized by the open-loop transfer function

The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below.

If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right – half of the s-plane is

The signal x (t) = sin (14000πt) , where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows :

What is the number of sinusoids in the output and their frequencies in kHz?

A unity feedback control system is characterized by the open-loop transfer function 

The value of k for which the system oscillates at 2 rad/s is ________.

Consider the circuit shown in the figure.

The Thevenin equivalent resistance (in Ω) across P – Q is _________.

The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = [sin(t) / π]u(t), where u(t) is a unit step function, the system output y(t) as t → ∞ is ______.

An integral I over a counter clock wise circle C is given by 
If C is defined as |z| = 3, then the value of I is

Consider a binary memory less channel characterized by the transition probability diagram shown in the figure.

An abrupt pn junction (located at x = 0) is uniformly doped on both p and n sides. The width of the depletion region is W and the electric field variation in the x-direction is E(x). Which of the following figures represents the electric field profile near the pn junction?

A second – order LTI system is described by the following state equations,

Where x₁ (t) and x₂ (t) are the two state variables and r(t) denotes the input. The output c(t) = x₁(t). The system is. 

Consider the parallel combination of two LTI systems shown in the figure.

The impulse responses of the systems are

If the input x(t) is a unit step signal, then the energy of y(t) is ____________.
 

Assuming that transistors M₁ and M₂ are identical and have a threshold voltage of 1V, the state of transistors M₁ and M₂ are respectively

A programmable logic array (PLA) is shown in the figure.

The Boolean function F implemented is

A modulating signal given By x(t) = 5 sin (4π10³ t - 10π cos2π10³ t) V is fed to a phase modulator with phase deviation constant k_p = 0.5rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is __________

The minimum value of the function   in the int erval occurs at x = 
________.

The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0.
The current i(t) (in ampere) at t = 0.5 seconds is ________

In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors Q₁ Q₂….., Q₃₂ are identical in all respects and have infinitely large values of common – emitter current the relation I_C = I_S exp ((V_BE/V_T), where Is is the saturation current. Assume that the voltage V_P shown in the figure is 0.7 V and the thermal voltage V_T = 26mV.

The output voltage V_out(in volts) is __________.

The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input ‘In’ and an output ‘Out’. The initial state of the FSM is S₀.

Standard air – filled rectangular waveguides of dimensions a = 2.29 cm and b = 1.02 cm are designed for radar applications. It is desired that these waveguides operate only in the dominatnt TE₁₀ mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is.

For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (J_L) is 2.5 mA/cm² and the open-circuit voltage (V_oc) is 0.451 V. consider thermal voltage (V_T) to be 25mV. If the intensity of the incident light is increased by 20 times, assuming that the temperature remains unchanged. V_oc (in volts) will be ______.

In the circuit shown, transistors Q₁ and Q₂ are biased at a collector current of 2.6mA. Assuming that transistor current gains are sufficiently large to assume collector current equal to emitter current and thermal voltage of 26 mV, the magnitude of voltage gain V₀/V_s in the mid-band frequency range is _____________ (up to second decimal place).

Two n-channel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double that of T1. Both the transistors are biased in the saturation region of operation, but the gate overdrive voltage (V_GS-V_TH) of T2 is double that of T1, where V_GS and V_TH are the gate – to – source voltage and threshold voltage of the transistors, respectively. If the drain current and transconductance of T1 are I_D1 and g_m1 respectively, the corresponding values of these two parameters for T2 are

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

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). Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

It is _________ to read this year’s textbook __________ the last year’s.

Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?

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 drinking beer. What must be checked to ensure that the rule is being followed?

Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?

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

A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot.

Which of the following is the steepest path leaving from P?

1200 men and 500 women can build a bridge in 2 weeks. 900men 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?

“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 antagonistic parts and the effects this mutilation will have in the respective section, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”

Which of the following statements best reflects the author’s opinion?