Electronics And Communication - ECE 2019 GATE Paper (Practice Test) - Electronics and Communication Engineering (ECE)

When he did not come home, she _______ him lying dead on the roadside somewhere.

It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machines work simultaneously at their respective constant rates, the time taken to complete the same order is __________ hours.

The bar graph in Panel (a) shows the proportion of male and female iliterates in 2001 and 2011. The proportions of males and females in 2001 and 2011 are given in Panel (b) and (c), respectively. The total population did not change during this period. The percentage increase in the total number of litertes from 2001 to 2011 is

Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is an engineer, one is a doctor, one a teacher and another a dancer. You are told that :
1. Mathew is not standing next to Seema
2. There are two people standing between Lohit and the engineer
3. Rahul is not a doctor
4. The teacher and the dancer are standing next to each other
5. Seema is turning to her right to speak to the doctor standing next to her
Q. Who among them is an engineer?

“Indian history was written by British historians – extremely well documented and researched, but not always impartial. History had to serve its purpose: Everything was made subservient to the glory of the Union Jack. Latter-day Indian scholars presented a contrary picture.”From the text above, we can infer that :Indian history written by British historians _________

Two design consultants, P and Q started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working when the hour hand moved by 240 degrees. P took two tea breaks of 15 minutes each during her shift, but took no lunch break. Q took only one lunch break for 20 minutes, but no teabreaks. The market rate for consultants isUSD 200 per hour and breaks are not paid.After paying the consultants, the clientshall have USD ________ remaining in thebudget.

Five people P, Q, R, S and T work in a bank. P and Q don’t like each other but have to share an office till T gets a promotion and moves to the big office next to the garden. R, who is currently sharing an office with T wants to move to the adjacent office with S, the handsome new intern. Given the floor plan, what is the current location of Q, R and T? (O = Office, WR = Washroom)

Which one of the following functions is analystic over the entire complex plane?

Which one of the following options describes correctly the equilibrium band diagram at T = 300 K of a Silicon pnn⁺p⁺⁺ configuration shown in the figure?

Consider the two-port resistive network shown in the figure. When an excitation of 5 V is applied across Port 1, and Port 2 is shorted, the current through the short circuit at Port 2 is measured to be 1 A (see (a) in the figure).

Now, if an excitation of 5 V is applied across Port 2, and Port 1 is shorted (see (b) in the figure), what is the current through the short circuit at Port 1?

In the circuit shown, what are the values of F for EN = 0 and EN = 1, respectively?

The number of distinct eigenvalues of the matrix

is equal to __________.

The families of curves represented by the solution of the equation

for n = - 1 and n = + 1, respectively, are

Let H(z) be the z-transform of a realvalued discrete-time signal h[n]. If P(z) = H(z) has a zero at and
P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?

The value of the integral is equal to __________.

Radiation resistance of a small dipole current element of length l at a frequency of 3 GHz is 3 ohms. If the length is changed by 1%, then the percentage change in the radiation resistance, rounded off to two decimal places, is _________%.

Let Y(s) be the unit-step response of a causal system having a transfer function

that is, The forced response of the system is

The correct circuit representation of the structure shown in the figure is

What is the electric flux through a quarter-cylinder of height H (as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of Q?

In the circuit shown, A and B are the inputs and F is the output. What is the functionality of the circuit?

In the circuit shown, Vs is a square wave of period T with maximum and minimum values of 8 V and -10 V, respectively. Assume that the diode is ideal and R₁ = R₂ = 50 Ω.
The average value of VL is _________ volts (rounded off to 1 decimal place).

If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then E[X] + E[Y] = _________.

A standard CMOS inverter is designed with equal rise and fall times (βn = βp). If the width of the pMOS transistor in the inverter is increased, what would be the effect on the LOW noise margin (NML) and the HIGH noise margin NMH?

In the table shown, List I and List II, respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with the corresponding right-hand side.

For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles N_p and the number of system zeros N_z in the frequency range 1 Hz ≤ f ≤ 10⁷ Hz is

The baseband signal m(t) shown in the figure is phase-modulated to generate the PM signal φ(t) = cos (2πf_ct + k m(t)). The time t on the x-axis in the figure is in milliseconds. If the carrier frequency is f_c = 50 kHz and k = 10π, then the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _________ (rounded off to 2 decimal places).

In the circuit shown, the clock frequency, i.e., the frequency of the Clk signal, is 12 kHz. The frequency of the signal at Q2 is __________ kHz.

A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword 0000111, and the message 0011 is mapped to the codeword 100110, then the message 0010 is mapped to

Let Z be an exponential random variable with mean 1. That is, the cumulative distribution function of Z is given by

Then Pr(Z > 2 |Z > 1), rounded off to two decimal places, is equal to __________.

Consider the signal f(t) = 1 + 2cos (πt) + 3 where t is in  seconds. Its fundamental time period, in seconds, is ____________.

The figure shows the high-frequency C-V curve of a MOS capacitor (at T = 300 K) with and no oxide charges. The flat-band, inversion, and accumulation conditions are represented, respectively, by the points

The value of the contour integral

evaluated over the unit circle |z| = 1 is ________.

The state transition diagram for the circuit shown is

In the circuits shown, the threshold voltage of each nMOS transistor is 0.6 V. Ignoring the effect of channel length modulation and body bias, the values of Vout 1 and Vout 2, respectively, in volts, are

The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function

A random variable X takes -1 and +1 with probabilities 0.2 and 0.8, respectively. It is transmitted across a channel which adds noise N, so that the random variable at the channel output is Y = X + N. The noise n is independent of X, and is uniformly distributed over the interval [-2, 2]. The receiver makes a decision

Where the threshold θ ∈ [-1, 1] is chosen so as to minimize the probability of error Pr The minimum probability of error, rounded off to 1 decimal place, is ______________.

A germanium sample of dimensions 1 cm × 1 cm is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dixodieGermanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at 600 nm is 3 × 104 cm^-1 and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is _________ μm.

In the circuit shown, the threshold voltages of the pMOS (|V_tp|) and nMOS (V_tn) transistors are both equal to 1 V. All the transistors have the same output resistance r_ds of 6 MΩ. The other parameters are listed below.

Μ_n and μ_p are the carrier mobilites, and C_ox is the oxide capacitance per unit area. Ignoring the effect of channel length modulation and body bias, the gain of the circuit is ____________(rounded off to 1 decimal place).

It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form

where c₁ and c₂ are arbitrary real numbers.

The desired three-tap filter is given by

h[0] = 1, h[1] = a, h[2] = b and h[n] = 0 for n < 0 or n > 2.

What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above?

Consider a long-channel MOSFET with a channel length 1 μm and width 10 μm. The device parameters are acceptor concentration NA = 5 × 10¹⁶ cm^-3, electron mobility μ_n = 800 cm²/V-s, oxide capacitance/area C_ox = 3.45 × 10^-7 F/cm2, threshold voltage V_T = 0.7 V. The drain saturation current (I_Dsat) for a gate voltage of 5 V is ____________ mA (rouonded off to two decimal places).

In the circuit shown, V₁ = 0 and V₂ = V_dd. The other relevant parameters are mentioned in the figure. Ignoring the effect of channel length modulation and the body effect, the value of I_out is ___________ mA (rounded off to 1 decimal place).

The quantum efficiency (η) and responsivity (R) at  wavelength λ (in μm) in a p-i-n photodetector are related by

In the circuit shown, if v(t) = 2 sin (1000 t) volts, R = 1 kΩ and C = 1 μF, then the steady-state current i(t), in milliamperes (mA), is

In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are 20 V and 60 mA, respectively. The values of R1 and RL are 200 Ω and 1 kΩ, respectively. What is the range of Vi that will maintain the Zener diode in the ‘on’ state?

Consider a differentiable function f(x) on the set of real numbers such that f(-1) = 0 and |f’(x)| ≤ 2. Given these conditions, which one of the following inequalities is necessarily true for all x ∈ [-2, 2]?

Two identical copper wires W1 and W2, placed in parallel as shown in the figure, carry currents I and 2I, respectively, in opposite directions. If the two wires are separated by a distance of 4r, then the magnitude of the magnetic field B between the wires at a distance r from W1 is

The dispersion equation of a waveguide, which relates the wavenumber k to the frequency ω, is

where the speed of light c = 3 × 10⁸ m/s, and ω_o is a constant. If the group velocity is 2 × 10⁸ m/s, then the phase velocity is

Consider a causal second-order system with the transfer function with a unit-step as an input. Let C(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value rounded off to two decimal places, is

Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[1] is shown in the figure. Let In the figure, what should be the values of the coefficients a₁, a₂, a₃ in terms of W6 so that X[1] is obtained correctly?