Electronics And Communication (Set 1) - ECE 2017 GATE Paper (Practice Test)

Consider the 5 × 5 matrix

It is given that A has only one real eigen value. Then the real eigen value of A is

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance isvolts, Where ℓ is the distance along the length of the cable in meters. γ = (0.1 + j40)m^-1 is the complex propagation constant, and rad s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.

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 true?

The rank of the matrix 

For a narrow base PNP BJT, the excess minority carrier concentration (Δn_E for emitter, Δp_B for base.Δn_C for collector) normalized to equilibrium minority carrier concentration (n_E0 for emitter, p_B0 for base, n_C0 for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in?

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

Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1. The duty cycle at the output latch in percentage is ___________.

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

In the latch circuit shown, the NAND gates have non-zero, but unequal propagation delays. The present input condition is: P = Q = ‘0’. If the input condition is changed simultaneously to P = Q = ‘1’, the outputs X and Y are

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) __________.

A periodic signal x(t) has a trigonometric Fourier series expansion

 we can conclude that

The open loop transfer function 
Where p is an integer, is connected in unity feedback configuration as shown in figure.

Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________.

An n⁺ - n Silicon device is fabricated with uniform and non-degenerate donor doping concentrations ofcorresponding to the n + and n regions respectively. At the operational temperature T, assume complete impurity ionization, kT/q = 25 mV, and intrinsic carrier concentration to be . What is the 
magnitude of the built-in potential of this device?

For the operational amplifier circuit shown, the output saturation voltages are ±15V. The upper and lower threshold voltages for the circuit are, respectively.

In the circuit shown, the positive angular frequency ω (in radians per second) at which magnitude of the phase difference between the voltages V1 and V2 equals  is 
__________.

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 2000 symbols per second, for which of the following cases is inter symbol interference zero?

Consider a stable system with transfer function

Where are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to -60 dB decade as A possible pair of values for p and q is

A good transconductance amplifier should have

Let (X₁ , X₂) be independent random variables. X₁ has mean 0 and variance 1, while X₂ has mean 1 and variance 4. The mutual information I (X₁; X₂) between X₁ and X₂ in bits is 

Consider the following statements for continuous-time linear time invariant (LTI) systems.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.

Which one among the following is correct?

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

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 transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link

Starting with x = 1, the solution of the equation x³ + x = 1, after two iterations of NewtonRaphson’s method (up to two decimal places) is _________.

In binary frequency shift keying (FSK), the given signal waveform are

Where T is the bit-duration interval and t is in seconds. Both u₀ (t) and u₁ (t) are zero outside the interval . With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u₀ (t) and u₁ (t) uncorrelated is

For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector current are equal. Given that V_T = 25mV, V_BE = 0.7V, and the BJT output resistance r₀ is practically infinite. Under these conditions, the midband voltage gain magnitude. , is _________.

The figure shows an RLC circuit exited by the sinusoidal voltage 100 cos (3t) volts, where t is in seconds. 

Which one of the following is the general solution of the first order differential equation   = (x + y - 1)², where x, y are real?

A linear time invariant (LTI) system with the transfer function

is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < ∞ intersects the imaginary axis for K = 1.5. The closed loop system is stable for

 where x, y, z are real, and let C be the straight line segment from point A : (0, 2,1) to point B : (4,1, -1) . The value of I is _________.

As shown, two Silicon (Si) abrupt p-n junction diodes are fabricated with uniform donor doping concentration of N_D1 = 10¹⁴ cm^-3 and N_D2 = 10¹⁶ cm^-3 in the n-regions of the diodes, and uniform acceptor doping concentration of N_A1 = 10¹⁴ cm^-3 and N_A2 = 10¹⁶ cm^-3 in the pregions of the diodes, respectively. Assuming that the reverse bias voltage is >> built-in potentials of the diodes, the ratio C₂/C₁ of their reverse bias capacitances for the same applied reverse bias, is __________.

An optical fiber is kept along direction. The refractive indices for the electric fields along directions in the fiber are n_x = 1.5000 and n_y = 1.5001, respectively (n_x ≠ n_y) due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5 μm. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeter, is ___________.

Two discrete-time signals x[n] and h[n] are both non-zero 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 linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.

Which one of the following options correctly describes the locations of the roots of the equation s⁴ + s² + 1 = 0 on the complex plane?

The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of and electronic charge . If a bias of 5V is applied across a 1 mm region of this semiconductor, the resulting current density in this region, in kA/cm², is _________.

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage 
V_tn = 1V and its transconductance parameter . Neglect channel length modulation and body bias effects. Under these conditions, the drain current I_D in mA is ___________. 

Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response

As shown in Figure (b). The output of the lowpass filter is Y(t).

Let E be the expectation operator and consider the following statements.

I. E (X(t)) = E(Y(t))
II. E(X²(t)) = E(Y²(t))
III. E(Y²(t)) = 2

Select the correct option:

As shown a uniformly doped Silicon (Si) bar of length L = 0.1 mm with a donor concentration N_D = 10¹⁶ cm^-3 is illuminated at x = 0 such that electron and hole pairs are generated at the 
rate of  where  Hole lifetime is 10^-4 s, electronic charge  hole diffusion coefficient D_p = 100 cm²/s and low level injection condition prevails. Assuming a linearly decaying steady state excess hole concentration that goes to 0 at x = L, the magnitude of the diffusion current density at x = L/2, in A/cm², is _________.

The Nyquist plot of the transfer function

does not encircle the point (1 + j0) for K = 10 but does encircle the point (-1+ j0) for K = 100. Then the closed loop system (having unity gain feedback) is 

In the figure shown, the npn transistor acts as a switch

For the input V_in (t) as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage saturation V_CE(sat) = 0.2V and base-to-emitter voltage V_BE = 0.7V. The minimum value of the common-base current gain (α) of the transistor for the switching should be _________.

A three dimensional region R of finite volume is described by , Where x, y, z are real. The volume of R (up to two decimal places) is ___________.

The expression for an electric field in free space is  , where x, y, z represent the spatial coordinates, t represents time, and ω,k are constants. This electric field 

A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are Q_AQ_B = 00, 01,10 and 11.

Assume that X_1N is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state Q_AQ_B = 00 and clocked, after a few clock cycles, it starts cycling through

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. Consider the following statements about x(3t):

I. The complex Fourier series coefficients of x(3t) are {a_k} where k is integer valued
II. The complex Fourier series coefficients of x(3t) are {3a_k} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6π rad/s

For the three statements above, which one of the following is correct?

A 4-bit shift register circuit configured for right-shift operation, i.e, D_in → A, A → B, B → C, C → D, is shown. If the present state of the shift register is ABCD = 1101, the number of clock cycles required to reach the state ABCD = 1111 is _________.

Let for real x. From among the following, choose the Taylor series approximation of f(x) around x = 0, which included all powers of x less than or equal to 3.

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 instruction is

In the circuit shown, the voltage V_1N (t) is described by:

Where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is ___________.

A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x-axis. Determine the direction of null in the radiation pattern for . Here the angle  is measured from the z-axis, and the angle is measured from the x-axis in the x-y plane.

The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, A_o = 10⁵ V/V and an open-loop cut-off frequency f_c = 8Hz. The voltage gain of the amplifier at 15 kHz, in V/V is __________.

Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by

Let H (ω) be the discrete-time Fourier system transform (DTFT) of h[n], where ω is the normalized angular frequency in radians. Given that H (ω₀) = 0 and 0 < ω₀ < π, the value of ω₀ (in radians) is equal to __________.

Which one of the following gives the simplified sum of products expression for the Boolean function F = m₀ + m₂ + m₃ + m₅ , where m₀ , m₂ , m₃ and m₅ are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

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

Let y(t) be the output of this filter. The maximum value of

She has a sharp tongue and it can occasionally turn _______.

Some table are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences?

(i) At least one bench is a table
(ii) At least one shelf is a bench
(iii) At least one chair is a table
(iv) All benches are chairs

40% of deaths on city roads may be attributed to drunken driving. The number of degree 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 consumption increases by 70%.

Which of the following statement is correct?

I ________ made arrangements had I _________informed earlier.

“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”.

Here, the word ‘antagonistic’ is closest in meaning to

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?

A contour line joints 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 25 m intervals in this plot. The path from P to Q is best described by

Trucks (10m long) and cars (5 m long) go on a single lane bridge. There must be a gap of atleast 20 m after each truck and a gap of atleast 15m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternatively, what is the maximum number of vehicles that can use the bridge in one hour?

S, T, U, V, W, X, Y and Z are seated around a circular table. T’s neighbours are Y and V. Z is seated third to the left of T and second to the right of S.U‟s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?