2007|Electronics and Comm (GATE Exam)-Previous Question Paper Solution
| Description: GATE Exam Previous Year Question Paper Solution Electronics and Communication (ECE) - 2007 | |
| Number of Questions: 84 | |
| Created by: Yashbeer Singh | |
| Tags: Communications Electronics and Communication Engineering - EC Electronic Devices Analog Circuits Differential Calculus Matrices and Determinants Vector Calculus |
The Boolean function Y = AB + CD is to be realized using only 2-input NAND gates. The minimum number of gates required is
An 8085 assembly language program is given below. Line 1: MVI A, B5H 2: MVI B, 0EH 3: XRI 69H 4: ADD B 5: ANI 9BH 6: CPI 9FH 7: STA 3010H 8: HLT
The contents of the accumulator just after execution of the ADD instruction in line 4 will be
An 8085 assembly language program is given below. Line 1: MVI A, B5H 2: MVI B, 0EH 3: XRI 69H 4: ADD B 5: ANI 9BH 6: CPI 9FH 7: STA 3010H 8: HLT
After execution of line 7 of the program, the status of the CY and Z flags will be
The circuit diagram of a standard TTL NOT gate is shown in the figure. When Vi = 2.5 V, the modes of operation of the transistors will be
Two 5-bit binary numbers, i.e. X = 01110 and Y = 11001 are represented in two’s complement format. The sum of X and Y represented in two’s complement format using 6 bits is
The boolean expression Y = $\bar A \bar B \bar C D + \bar ABC\bar D + A\bar B \bar C D + AB\bar C \bar D$ can be minimized to
In the digital -to- Analog converter circuit shown in the figure below, VR = 10 V and R = 10 k$\Omega$.
The Voltage V0 is
An 8255 chip is interfaced to an 8085 microprocessor system as an I/O mapped I/O as shown in the figure. The address lines A0 and A1 of the 8085 are used by the 8255 chip to decode internally its three ports and the Control register. The address lines A3 to A7 as well as the IO$\sqrt M$signal are used for address decoding. The range of addresses for which the 8255 chip would get selected is
The following binary values were applied to the X and Y inputs of the NAND latch shown in the figure in the sequence indicated below: X = 0, Y = 1; X = 0, Y = 0; X = 1, Y = 1. The corresponding stable P, Q outputs will be
For the circuit shown below, the counter state (Q1, Q0) follows the sequence
In the following circuit, X is given by
The $\vec E$ field in a rectangular waveguide of inner dimensions a$\times$b is given by
$\vec E$= $\dfrac{\omega \mu}{h^2} \left( \dfrac{\pi}{a} \right)$H0 sin $\left( \dfrac{2\pi x}{a} \right)^2$sin ($\omega t - \beta z$$\widehat y$
Where H0 is a constant, and a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is
A load of 50$\Omega$is connected in shunt in a 2-wire transmission line of Z0 = 50 $\Omega$as shown in the figure. The 2-port scattering parameter matrix (S-matrix) of the shunt element is
In a p+n junction diode under reverse bias, the magnitude of electric field is maximum at
Group I lists four types of p-n junction diodes. Match each device in Group I with one of the option in Group II to indicate the bias condition of that device in its normal mode of operation.||| |---|---| | Group I| Group II| | (P) Zener Diode| (1) Forward bias| | (Q) Solar cell| (2) Reverse bias| | (R) LASER diode| | | (S) Avalanche Photodiode| |
The parallel branches of a 2-wire transmission line are terminated in 100 $\Omega$ and 200 $\Omega$ resistors as shown in the figure. The characteristic impedance of the line is Z0 = 50 $\Omega$ and each section has a length of $\dfrac{\lambda}{4}$. The voltage reflection coefficient 
at the input is
A plane wave of wavelength $\lambda$ is travelling in a direction making an angle 30° with positive x-axis and 90° with positive y-axis. The $\vec E$ field of the plane wave can be represented as (E0 is constant)
A $\dfrac{\lambda}{2}$ dipole is kept horizontally at a height of $\dfrac{\lambda_0}{2}$ above a perfectly conducting infinite ground plane. The radiation pattern in the plane of the dipole ($\vec E$ plane) looks approximately as
A right circularly polarised (RCP) plane wave is incident at an angle of 60° to the normal, on an air-dielectric interface. If the reflected wave is linearly polarised, the relative dielectric constant $\epsilon_{r2}$ is
The DC current gain ($\beta$)of a BJT is 50. Assuming that the emitter injection efficiency is 0.995, the base transport factor is
The electron and hole concentrations in an intrinsic semiconductor are ni per cm3 at 300 K. Now, if acceptor impurities are introduced with a concentration of NA per cm3 where (where NA >> ni), the electron concentration per cm3 at 300 K will be
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a Metal/SiO2 /silicon (MOS) capacitor having an area of 1 $\times$10-4 cm2. Assume that the permittivities ($\epsilon_0 \epsilon_r$) of silicon and SiO2 are 1 $\times$ 10-12 F / cm and 3.5 $\times$10-13 F / cm respectively.
The gate oxide thickness in the MOS capacitor is
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a Metal/SiO2 /silicon (MOS) capacitor having an area of 1 $\times$10-4 cm2. Assume that the permittivities ($\epsilon_0 \epsilon_r$) of silicon and SiO2 are 1 $\times$ 10-12 F / cm and 3.5 $\times$10-13 F / cm respectively.
Consider the following statements about the C-V characteristics plot: S1: The MOS capacitor has an n-type substrate. S2: If positive charges are introduced in the oxide, the C-V plot will shift to the left. Which of the following is true?
The figure shows the high-frequency capacitance-voltage (C-V) characteristics of a Metal/SiO2 /silicon (MOS) capacitor having an area of 1 $\times$10-4 cm2. Assume that the permittivities ($\epsilon_0 \epsilon_r$) of silicon and SiO2 are 1 $\times$ 10-12 F / cm and 3.5 $\times$10-13 F / cm respectively.
The maximum depletion layer width in silicon is
A p +n junction has a built-in potential of 0.8 V. The depletion layer width at a reverse bias of 1.2V is 2 $\mu$m. For a reverse bias of 7.2 V, the depletion layer width will be
The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll - off factor is given by p(t) =$\dfrac{sin \ 4\pi Wt}{4\pi Wt(1 - 16 w^2t^2)}$ The value of p(t) at t = $\dfrac{1}{4W}$is
In a GSM system, 8 channels can co-exist in 200 KHz bandwidth using TDMA. A GSM based cellular operator is allocated 5 MHz bandwidth. Assuming a frequency reuse factor of $\dfrac{1}{5}$ i.e a five-cell repeat pattern, the maximum number of simultaneous channels that can exist in one cell is
If R($\tau$) is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is NOT true?
In delta modulation, the slope overload distortion can be reduced by
If S(f) is the power spectral density of a real, wide-sense, stationary random process, then which of the following relations is true?
Two 4-ray signal constellations are shown. It is given that $\phi_1$ and $\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let $\dfrac{N_0}{2}$ denote the power spectral density of white Gaussian noise.
If these constellations are used for digital communications over an AWGN channel, then which of the following statements is true?
Two 4-ray signal constellations are shown. It is given that $\phi_1$ and $\phi_2$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let $\dfrac{N_0}{2}$ denote the power spectral density of white Gaussian noise.
The ratio of the average energy of constellation 1 to the average energy of constellation 2 is
In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be
If E denotes expectation, then the variance of a random variable X is given by
During transmission over a certain binary communication channel, bit errors occur independently with probability p. The probability of AT MOST one bit in error in a block of n bits is given by
A Hilbert transformer is a
In a Direct Sequence CDMA System, the chip rate is 1.2288 $\times$ 106 chips per second. If the processing gain is desired to be at least 100, then the data rate
An input to a 6-level quantizer has the probability density function f(x) as shown in the figure. Decision boundaries of the quantizer are chosen so as t maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are -1, 0 and 1.
Assuming that the reconstruction levels of the quantizer are the mid-points of the decision boundaries, the ratio of signal power to quantization noise power is
An input to a 6-level quantizer has the probability density function f(x) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are -1, 0 and 1.
The values of a and b are
The z-transform X [z] of a sequence x[n] is given by x[z] =$\dfrac{0.5}{1-2z^{-1}}$. It is given that the region of convergence of X[z] includes the unit circle. The value of x[0] is
The 3-dB bandwidth of the low-pass signal e-t u(t), where u(t) is the unit step function, is given by
A 5-point sequence x (n) is given as X [–3] = 1, x [–2] = 1, x [–1] = 0, x [0] = 5, x [1] = 1. If x($e^{j\omega}$) denotes the discrete – time fourier transform of x [n], what is the value of $\displaystyle \int_{-\pi}^\pi x(e^{j\omega})$$d\omega$?
If the Laplace transform of a signal y (t) is y(s) = $\dfrac{1}{s(s-1)}$, its final value is
The frequency response of a linear, time-invariant system is given by H(f) = $\dfrac{5}{1 + j10\pi f}$ The step response of the system is
The RC circuit shown in the figure is
For the circuit shown in the figure, the Thevenin voltage and resistance looking into X - Y are
In the AC network shown in the figure, the phasor voltage VAB (in Volts) is
An independent voltage source in series with an impedance ZS = RS + jXS delivers a maximum average power to a load impedance ZL when
In the circuit shown, VC is 0 volts at t = 0 sec. For t > 0, the capacitor current ic (t) where t is in seconds, is given by
Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of Filter 1 be B1 and that of Filter 2 be B2. The value of $\dfrac{B_1}{B_2}$ is
For |x| << 1, coth (x) can be approximated as
$lim_{\theta \rightarrow 0} \frac{sin(\theta / 2)}{\theta}$ is
The following plot shows a function y which varies linearly with x. The value of the integral I = $\int\limits_1^2 y \hspace{0.2cm}dx$is
Which one of the following functions is strictly bounded?
For the function e-x, the linear approximation around x = 2 is
The correct full wave rectifier circuit is
In a transconductance amplifier, it is desirable to have
It is given that X1, X2, …..XM are M non-zero orthogonal vectors. The dimension of the vector space spanned by the 2M vectors X1, X2, …XM , - XM is
Consider the function f(x) = x2 -x -2. The maximum value of f (x) in the closed interval [-4, 4] is
An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is
The equation x3 -x2 + 4x - 4 = 0 is to be solved using the Newton-Raphson method. If x = 2 is taken as the initial approximation of the solution, the next approximation using this method will be
Three functions f1 (t), f2 (t) and f3 (t) which are zero outside the interval [0, T] are shown in the figure. Which of the following statements is correct?
If C is a closed curve enclosing a surface S, the magnetic field intensity $\overrightarrow{H}$, the current density $\overrightarrow{j}$and the electric flux density $\overrightarrow{D}$ are related by
The solution of the differential equation K2 $\frac{d^2y}{dx^2}$ = y – y2 under the boundary conditions (i) y = y1 at x = 0 and (ii) y = y2 at x = $\infty$, where k, y1 and y2 are constants, is
If a semi-circular contour D of radius 2 is as shown in the figure given below, the value of the integral $\int_D N \frac{1}{(S^2 -1)}ds$ is
For the BJT circuit shown, assume that the $\beta$ of the transistor is very large and VBE = 0.7 V. The mode of operation of the BJT is
For the op-amp circuit shown in the figure, V0 is
For the Zener diode shown in the figure, the Zener voltage at the knee is 7 V. The knee current is negligible and the Zener dynamic resistance is 10 $\Omega$. If the input voltage (Vi) ranges from 10 V to 16 V, what will be the range of out put voltage (V0)?
In the Op-Amp circuit shown, assume that the diode current follows the equation I = Is exp (V/VT). For Vi = 2V, V0 = V01, and for Vi = 4 V, V0 = V02. The relationship between V01 and V02 is
Group I lists four different semiconductor devices. Match each device in Group I with its characteristic property in Group II
| Group I | Group II |
| (P) BJT | (1) Population inversion |
| (Q) MOS capacitor | (2) Pinch-off voltage |
| (R) LASER diode | (3) Early effect |
| (S) JFET | (4) Flat-band voltage |
If the closed-loop transfer function of a control system is given as T(s) = $$\dfrac{s-5}{(s+2)(s+3)}$$, then it is
In the CMOS inverter circuit shown, if the transconductance parameters of the NMOS and PMOS transistor are kn = kp = $\mu$nC0x $\frac{W_n}{L_n}$=$\mu$p Cox $\frac{W_p}{L_p}$= 40 $\mu$A/ V2 and their threshold voltage are VTHn = |VTHp| = 1V, the current I is
The open loop transfer function of a plant is given as G(s) = $\dfrac{1}{s^2-1}$. If the plant is operated in a unity feedback configuration, the lead compensator that an stabilize this control system is
The asymptotic Bode plot of a transfer function is as shown in the figure. The transfer function G(s) corresponding to this Bode plot is
A control system with a PD controller is shown in the figure. If the velocity error constant KV = 1000 and the damping ratio $\xi$= 0.5, the values of KP and KD are
A transmission line of characteristic impedance 50 Ω is terminated by a 50 Ωload. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm apart on the line is found to be $\frac{2 \pi}{\lambda}$ radians. The phase velocity of the wave along the line is
An air-filled rectangular waveguide has inner dimensions of 3 cm X 2 cm. The wave impedance of the TE20 mode of propagation in the waveguide at a frequency of 30 GHz is (free space impedance $\eta_0$= 377$\Omega$)
The transfer function of a plant is T (s) = $ \dfrac{5}{(s+5)(s^2+s+1)} $. The second - order approximation of T(s) using dominate pole concept is
Consider the Op-Amp circuit shown in the figure.
The transfer function V0 (s) / Vi (s) is
The state space representation of a separately excited DC servo motor dynamics is given as $ \left[ \begin{array} \dfrac{d \omega }{ dt } \\ \dfrac{di_s}{dt} \end{array} \right] = \left[ \begin{array} \ -1 & 1 \\ -1 & -10 \end{array} \right] \left[ \begin{array} \ \omega \\ i_s \end{array} \right] $ + $ \left[ \begin{array} \ 0 \\ 10 \end{array} \right] u $
Consider the Op-Amp circuit shown in the figure.
If Vi = V1 sin ($\omega t$) and V0 = V2 sin ($\omega t$+ $\phi$), the minimum and maximum values of $\phi$(in radians) are respectively
Consider a linear system whose state space representation is x and (t) = Ax (t). If the initial state vector of the system is x (0) =$ \left[ \begin{array} \ 1 \\ -2 \end{array} \right] $, the system response is x (t) = $ \left( \begin{array} \ e^{-2t} \\ -2 e^{-2t} \end{array} \right) $. If the initial state vector of the system changes, the system response becomes x(t) = $ \left[ \begin{array} \ e^{-t} \\ -e^{-6} \end{array} \right] $.
The system matrix A is
Consider a linear system with state space representation is x and (t) = Ax (t). If the initial state vector of the system is x (0) = $ \left[ \begin{array} \ 1 \\ -2 \end{array} \right] $, the system response is x (t) = $ \left( \begin{array} \ e^{-2t} \\ -2 e^{-2t} \end{array} \right) $ . If the initial state vector of the system changes, the system response becomes x(t) = $ \left[ \begin{array} e^{-t} \\ -e^{-6} \end{array} \right] $ .
The eigen value and eigen vector pairs ($\lambda_i, V_i$) for the system are
