The Boolean function realised by the logic circuit shown below is ![](https://i.imgur.com/aLXEkZk.png)

F = $\sum$ m(2, 3, 5, 7, 8, 9, 12)

Compared to a p-n junction with NA=ND=10 14 /cm 3 , which one of the following statements is TRUE for a p-n junction with N A =N D =10 20 /cm 3 ?

Reverse breakdown voltage is lower and depletion capacitance is higher.

Consider the z-transform X(z) = 5z 2 + 4z -1 + 3; 0<|z| < $\infty$. The inverse z-transform x[n] is

5$\delta$[n + 2] + 3$\delta$[n] + 4$\delta$[n - 1]

The amplifier circuit shown below uses a silicon transistor. The capacitors C C and C E can be assumed to be short at signal frequency and the effect of output resistance R 0 can be ignored. If C E is disconnected from the circuit, which one of the following statements is TRUE? ![](https://i.imgur.com/s9OWtKy.png)

The input resistance Ri increases and the magnitude of voltage gain A V decreases.

The signal flow graph of a system is shown below. ![](https://i.imgur.com/xDwDamH.png) Which of the following is the state variable representation of the system?

$ x = \left[ \begin{array} \ -1 & 1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0.5 & 0.5] x

2010|Electronics and Comm (GATE Exam)-Previous Question Paper Solution

Question 1 Multiple Choice (Single Answer)

Assuming that flip-flops are in reset condition initially, the count sequence observed at Q_Ain the circuit shown is

0010111…
0001011…
0101111…
01101..........…

Question 2 Multiple Choice (Single Answer)

Match the logic gates in Column A with their equivalents in Column B.

P-2, Q-4, R-1, S-3
P-4, Q-2, R-1, S-3
P-2, Q-4, R-3, S-1
P-4, Q-2, R-3, S-1

Question 3 Multiple Choice (Single Answer)

For the 8085 assembly language program given below, the content of the accumulator after the execution of the program is

00H
45H
67H
E7H

Question 4 Multiple Choice (Single Answer)

The Boolean function realised by the logic circuit shown below is

F =^$\sum$m(0, 1, 3, 5, 9, 10, 14)
F =^$\sum$m(2, 3, 5, 7, 8, 12, 13)
F =^$\sum$m(1, 2, 4, 5, 11, 14, 15)
F =^$\sum$m(2, 3, 5, 7, 8, 9, 12)

Question 5 Multiple Choice (Single Answer)

For the output F to be 1 in the logic circuit shown, the input combination should be

A = 1, B = 1, C = 0
A = 1, B = 0, C = 0
A = 0, B = 1, C = 0
A = 0, B = 0, C = 1

Question 6 Multiple Choice (Single Answer)

In the circuit shown, the device connected to Y5 can have address in the range.

2000 - 20FF
2D00 - 2DFF
2E00 - 2EFF
FD00 - FDFF

Question 7 Multiple Choice (Single Answer)

If the scattering matrix [S] of a two port network is [S] = $
\left[
\begin{array}
\ 0.2\angle0^\circ & 0.9 \angle90^\circ \\
0.9\angle90^\circ & 0.1 \angle 90^\circ
\end{array}
\right]
$ then the network is

lossless and reciprocal
lossless but not reciprocal
not lossless but reciprocal
neither lossless nor reciprocal

Question 8 Multiple Choice (Single Answer)

A transmission line has a characteristic impedance of 50$\Omega$ and a resistance of 0.1$\Omega$ /m. if the line is distortion less, the attenuation constant (in Np/m) is

500
5
0.014
0.002

Question 9 Multiple Choice (Single Answer)

Thick oxide in a CMOS process is preferably grown using

wet oxidation
dry oxidation
epitaxial deposition
ion implantation

Question 10 Multiple Choice (Single Answer)

Compared to a p-n junction with NA=ND=10¹⁴/cm³, which one of the following statements is TRUE for a p-n junction with N_A=N_D=10²⁰/cm³?

Reverse breakdown voltage is lower and depletion capacitance is lower.
Reverse breakdown voltage is higher and depletion capacitance is lower.
Reverse breakdown voltage is lower and depletion capacitance is higher.
Reverse breakdown voltage is higher and depletion capacitance is higher.

Question 11 Multiple Choice (Single Answer)

A plane wave having the electric field component $E_1$ = 24 cos(3$\times$10⁸t -$\beta$y)$\widehat a_z$V/m and traveling in free space is incident normally on a lossless medium with m = m₀ and e = 9e0 which occupies the region y ≥ 0. The reflected magnetic field component is given by

$\dfrac{1}{10\pi} cos(3 \times 10^8 t + y) a_x \ A/m $
$\dfrac{1}{20\pi}$cos (3$\times$10⁸t + y)$\widehat a_x$ A/m
-$\dfrac{1}{20\pi}$cos (3$\times$10⁸t + y)$\widehat a_x$ A/m
- $\dfrac{1}{10\pi}$cos (3$\times$10⁸t + y)$\widehat a_x$ A/m

Question 12 Multiple Choice (Single Answer)

In the circuit shown, all the transmission line sections are lossless. The Voltage Standing Wave Ration (VSWR) on the 60W line is

1.00
1.64
2.50
3.00

Question 13 Multiple Choice (Single Answer)

At room temperature, a possible value for the mobility of electrons in the inversion layer of a silicon n-channel MOSFET is

450 cm²/ VS
1350 cm²/ VS
1800 cm²/ VS
3600 cm²/ VS

Question 14 Multiple Choice (Single Answer)

The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T=300K, electronic charge=1.6x10^-19C, thermal voltage=26mV and electron mobility = 1350cm²/V-s

The magnitude of the electric field at x = 0.5 $\mu$m is

1kV/cm
5kV/cm
10 kV/cm
26kV/cm

Question 15 Multiple Choice (Single Answer)

The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The following information is given: T=300K, electronic charge=1.6x10^-19C, thermal voltage=26mV and electron mobility = 1350cm²/V-s

The magnitude of the electron drift current density at x = 0.5 $\mu$m is

2.16$\times$10⁴ A/cm²
1.08$\times$10⁴ A/cm²
4.32$\times$10³ A/cm²
.48$\times$10² A/cm²

Question 16 Multiple Choice (Single Answer)

Suppose that the modulating signal is m(t) = 2cos (2$\pi$f_mt) and the carrier signal is x_C(t) = A_C cos(2$\pi$f_Ct), which one of the following is a conventional AM signal without over-modulation?

x(t) = A_cm(t) cos(2$\pi$f_ct)
x(t) = A_c[1 + m(t)]cos(2$\pi$f_ct)
x(t) = A_c cos(2$\pi$f_ct) + $\dfrac{A_0}{4}$m(t) cos (2$\pi$f_Ct)
x(t) = A_c cos(2$\pi$f_mt) cos(2$\pi$f_ct) + A_c sin(2$\pi$f_mt) sin(2$\pi$f_ct)

Question 17 Multiple Choice (Single Answer)

Consider a baseband binary PAM receiver shown below. The additive channel noise n(t) is whit with power spectral density S_N(f)=N₀/2=10^-20 W/Hz. The low-pass filter is ideal with unity gain and cutoff frequency 1MHz. Let Y_k represent the random variable y(t_k).
Y_k=N_k if transmitted bit bk=0
Y_k=a+N_k if transmitted bit bk=1
Where N_k represents the noise sample value. The noise sample has a probability density function, P_Nk(n)=0.5لe^-^ل^|n| (This has mean zero and variance 2/ل²). Assume transmitted bits to be equiprobable and threshold z is set to a/2=10^-6V.

The probability of bit error is

0.5xe^-3.5
0.5xe^-5
0.5xe^-7
0.5xe^-10

Question 18 Multiple Choice (Single Answer)

Consider a baseband binary PAM receiver shown below. The additive channel noise n(t) is whit with power spectral density S_N(f)=N₀/2=10^-20 W/Hz. The low-pass filter is ideal with unity gain and cutoff frequency 1MHz. Let Y_k represent the random variable y(t_k).
Y_k=N_k if transmitted bit bk=0
Y_k=a+N_k if transmitted bit bk=1
Where N_k represents the noise sample value. The noise sample has a probability density function, P_Nk(n)=0.5لe^-^ل^|n| (This has mean zero and variance 2/ل²). Assume transmitted bits to be equiprobable and threshold z is set to a/2=10^-6V.

The value of the parameter ل (in V-1) is

10¹⁰
10⁷
1.414$\times$10^-10
2$\times$10^-20

Question 19 Multiple Choice (Single Answer)

Consider an angle modulated signal x(t) = 6cos[2π x 10⁶t + 2sin(8000πt) + 4cos(8000pt)] V. The average power of x(t)

10W
18W
20W
28W

Question 20 Multiple Choice (Single Answer)

Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

Question 21 Multiple Choice (Single Answer)

The Nyquist sampling rate for the signal s(t) = ^{$\dfrac{sin(500 \pi t)}{\pi t}$_$\times$ $\dfrac{sin(700 \pi t)}{\pi t}$} is given by

400 Hz
600 Hz
1200Hz
1400 Hz

Question 22 Multiple Choice (Single Answer)

X(t) is a stationary process with the power spectral density Sx(f)>0 for all f. The process is passed through a system shown below. Let Sy(f) be the power spectral density of Y(t). Which one of the following statements is correct?

Let S_y(f) be the power spectral density of Y(t). Which one of the following statements is correct?

S_y(f)>0 for all f
S_y(f)=0 for |f|>1kHz
S_y(f)=0 for f=nf₀, f₀=2kHz, n any integer
S_y(f)=0 for f=(2n+1)f₀=1kHz, n any integer

Question 23 Multiple Choice (Single Answer)

The transfer function of a discrete time LTI system is given by
H(z) = $\dfrac{ 2-\dfrac{3}{4}z^{-1} }{ 1 - \dfrac{3}{4}z^{-t} + \dfrac{1}{8}z^{-2} }$
Consider the following statements:
S1: The system is stable and causal for ROC:|z|>½
S2: The system is stable but not causal for ROC:|z|<¼
S3: The system is neither stable nor causal for ROC: ¼<|z|<½

Which one of the following statements is valid?

Both S1 and S2 are true.
Both S2 and S3 are true.
Both S1 and S3 are true.
S1, S2 and S3 are all true.

Question 24 Multiple Choice (Single Answer)

Consider the z-transform X(z) = 5z² + 4z^-1 + 3; 0<|z| < $\infty$. The inverse z-transform x[n] is

5$\delta$[n + 2] + 3$\delta$[n] + 4$\delta$[n - 1]
5$\delta$[n - 2] + 3$\delta$[n] + 4$\delta$[n + 1]
5 u[n + 2] + 3 u[n] + 4 u[n - 1]
5 u[n - 2] + 3 u[n] + 4 u[n + 1]

Question 25 Multiple Choice (Single Answer)

A continuous time LTI system is described by ^{$\dfrac{d^2 y(t)}{dt^2} + 4 \dfrac{dy(t)}{dt} 3 y(t) = 2 \dfrac{dx(t)}{dt} + 4 \times (t)$}. Assuming zero initial condition, the response y(t) of the above system for the input x(t) = e^-2tu(t) is given by

(e^t-e^3t)u(t)
(e^-t-3^-3t)u(t)
(e^-t+e^-3t)u(t)
(e^t+e^3t)u(t)

Question 26 Multiple Choice (Single Answer)

For an N-point FFT algorithm with N = 2m which one of the following statements is TRUE?

It is not possible to construct a signal flow graph with both input and output in normal order.
The number of butterflies in the m^th stage is N/m.
In-place computation requires storage of only 2N node data.
Computation of a butterfly requires only one complex multiplication.

Question 27 Multiple Choice (Single Answer)

Two discrete time systems with impulse responses h₁[n] = $\delta$[n -1] and h₂[n] = $\delta$[n - 2] are connected in cascade. The overall impulse response of the cascaded system is

$\delta$[n - 1] + $\delta$[n - 2]
$\delta$[n - 4]
$\delta$[n - 3]
$\delta$[n - 1] $\delta$[n - 2]

Question 28 Multiple Choice (Single Answer)

The trigonometric Fourier series for the waveform f(t) shown below contains

only cosine terms and zero value for the dc component
only cosine terms and a positive value for the dc component
only cosine terms and a negative value for the dc component
only sine terms and a negative for the dc component

Question 29 Multiple Choice (Single Answer)

Given f(t) = L^–1 ^{$\left[ \dfrac{3s+1}{s3 + 4s2 + (K-3)s} \right]$}. If ^{$\displaystyle lim_{x \rightarrow \theta}$}f(t) = 1, then the value of K is

1
2
3
4

Question 30 Multiple Choice (Single Answer)

A circuit consists of a resistor, an inductor and a capacitor connected in series to a 150 V AC mains. For the circuit, R = 9 Ohms, X_L = 28 Ohms and X_C = 16 Ohms. What is the value of the current in the circuit?

10 A
15 A
<font size="2"><font face="Arial">20 A</font></font>
25 A

Question 31 Multiple Choice (Single Answer)

For parallel RLC circuit, which one of the following statements is NOT correct?

The bandwidth of the circuit deceases if R is increased.
The bandwidth of the circuit remains same if L is increased.
At resonance, input impedance is a real quantity.
At resonance, the magnitude of input impedance attains its minimum value.

Question 32 Multiple Choice (Single Answer)

In the circuit shown, the power supplied by the voltage source is

0W
5W
10W
100W

Question 33 Multiple Choice (Single Answer)

In the circuit shown, the switch S is open for a long time and is closed at t = 0. The current i(t) for t$\ge$ 0⁺ is

i(t)=0.5-0.125e-¹⁰⁰⁰tA
i(t)=1.5-0.125e^-1000tA
i(t)=0.5-0.5e^-1000tA
i(t)=0.375e^-1000tA

Question 34 Multiple Choice (Single Answer)

For the two-port network shown below, the short circuit admittance parameter matrix is

^{$\left[
\begin{array}
\ 4 & -2 \\\\
-2 & 4
\end{array}
\right]
$}S
^{$\left[
\begin{array}
\ 1 & -0.5 \\\\
-0.5 & 1
\end{array}
\right]
$}S
^{$\left[
\begin{array}
\ 1 & 0.5 \\\\
0.5 & 1
\end{array}
\right]
$}S
^{$\left[
\begin{array}
\ 4 & 2 \\\\
2 & 4
\end{array}
\right]
$}S

Question 35 Multiple Choice (Single Answer)

The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector (in W/m2) is

$\frac{1}{30 \pi}$
$\frac{1}{60 \pi}$
$\frac{1}{120 \pi}$
$\frac{1}{240 \pi}$

Question 36 Multiple Choice (Single Answer)

In a uniformly doped BJT, assume that NE, NB and NC are the emitter, base and collector dopings in atoms/cm3, respectively. If the emitter injection efficiency of the BJT is close unity, which one of the following conditions is TRUE?

N_E= N_B = N_C
N_E >>N_B and N_B > N_C
N_E = N_B and N_B< N_C
N_E < N_B < N_C

Question 37 Multiple Choice (Single Answer)

A function n(x) satisfied the differential equation $\frac{d^2 n(x)}{dx^2} - \frac{n(x)}{L^2}$ = 0 where L is a constant. The boundary conditions are: n(0) = K and n (∞) = 0. The solution to this equation is

n(x) = K exp(x/L)
n(x) = K exp(-x/$\sqrt{5}$)
n(x) = K² exp(-x/L)
n(x) = K exp(-x/L)

Question 38 Multiple Choice (Single Answer)

If ^{$A^.$} = xy + x²^$\hat{a}_y$ then ^{_{$\oint_c A^. dl^.$}}over the path shown in the figure is

0
$\frac{2}{\sqrt{3}}$
1
2^$\sqrt{3}$

Question 39 Multiple Choice (Single Answer)

The eigen values of a skew-symmetric matrix are

always zero
always purely imaginary
either zero or purely imaginary
always real

Question 40 Multiple Choice (Single Answer)

Consider differential equation ^{$\frac{dy(x)}{dx} - y$}(x) = x with the initial condition y(0) = 0. Using Euler’s first order method with a step size of 0.1, the value of y (0.3) is

0.01
0.031
0.0631
0.1

Question 41 Multiple Choice (Single Answer)

If e^y = $X^{\frac{1}{x}}$, then y has a

maximum at x = e
minimum at x = e
maximum at x = e^-1
minimum at x = e^-1

Question 42 Multiple Choice (Single Answer)

The residues of a complex function X(z) = $\frac{1 - 12z}{z(z - 1)(z - 2)}$at its poles are

$\frac{1}{2}$, $\frac{1}{2}$ and 1
$\frac{1}{2}$, $\frac{1}{2}$and – 1
$\frac{1}{2}$, 1 and –3/2
$\frac{1}{2}$, – 1 and $\frac{2}{3}$

Question 43 Multiple Choice (Single Answer)

In the silicon BJT circuit shown below, assume that the emitter area of transistor Q1 is half that of transistor Q2.

The value of current I₀ is approximately

0.5 mA
2 mA
9.3 mA
15 mA

Question 44 Multiple Choice (Single Answer)

Consider the common emitter amplifier shown below with the following circuit parameters.

B = 100, g_m = 0.3861 A/V, r₀= ^_$\infty$, r_p = 259 W, R_S = 1 kW, R_B = 93 kW, R_C = 250 W, R_L = 1 kW, C₁= ^_$\infty$ and C₂ = 4.7 mF.

The lower cut-off frequency due to C₂ is

33.9 Hz
27.1 Hz
13.6 Hz
16.9 Hz

Question 45 Multiple Choice (Single Answer)

Consider the common emitter amplifier shown below with the following circuit parameters.

B = 100, g_m = 0.3861 A/V, r₀= ^_$\infty$, r_p = 259 W, R_S = 1k W, R_B = 93kW, R_C = 250 W, R_L = 1k W, C₁= ^_$\infty$and C₂ = 4.7mF.

The resistance seen by the source Vs is

258^$\Omega$
1252^$\Omega$
93 K^$\Omega$
$\infty$

Question 46 Multiple Choice (Single Answer)

The amplifier circuit shown below uses a silicon transistor. The capacitors C_C and C_E can be assumed to be short at signal frequency and the effect of output resistance R₀ can be ignored. If C_E is disconnected from the circuit, which one of the following statements is TRUE?

The input resistance Ri increases and the magnitude of voltage gain A_V decreases.
The input resistance R_idecreases and the magnitude of voltage gain A_V decreases.
Both input resistance R_iand the magnitude of voltage gain A_V decrease.
Both input resistance R_iand the magnitude of voltage gain A_V increase.

Question 47 Multiple Choice (Single Answer)

Assuming the OP-AMP to be ideal, the voltage gain of the amplifier shown below is

$ - \dfrac{R_2}{R_1}$
$ - \dfrac{R_3}{R_1}$
$ - \dfrac{R_2 || R_3}{R_1}$
$ - \dfrac{R_2 || R_3}{R_1}$

Question 48 Multiple Choice (Single Answer)

The transfer characteristic for the precision rectifier circuit shown below is
(assume ideal OP-AMP and practical diodes)

Question 49 Multiple Choice (Single Answer)

For the asymptotic Bode magnitude plot shown below, the system transfer function can be

$$ \dfrac{10s+1}{0.1s + 1} $$
$$ \dfrac{100s+1}{0.1s + 1} $$
$$ \dfrac{100s}{10s + 1} $$
$$ \dfrac{0.1s+1}{10s + 1} $$

Question 50 Multiple Choice (Single Answer)

The transfer function Y(s)/R(s) of the system shown is

0
$\dfrac{1}{s+1}$
$\dfrac{2}{s+1}$
$\dfrac{2}{s+3}$

Question 51 Multiple Choice (Single Answer)

The signal flow graph of a system is shown below.

Which of the following is the state variable representation of the system?

$ x = \left[ \begin{array} \ 1 & 1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0 & 0.5] x
$ x = \left[ \begin{array} \ -1 & 1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0 & 0.5] x
$ x = \left[ \begin{array} \ 1 & -1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0.5 & 0.5] x
$ x = \left[ \begin{array} \ -1 & 1 \\\\ -1 & 0 \end{array} \right] x + \left[ \begin{array} \ 0 \\\\ 2 \end{array} \right] u $ y = [0.5 & 0.5] x

Question 52 Multiple Choice (Single Answer)

The signal flow graph of a system is shown below.

The transfer function of the system is

$ \dfrac{s+1}{(s^2+1)} $
$ \dfrac{s-1}{(s^2+1)} $
$ \dfrac{s+1}{(s^2+s+1)} $
$ \dfrac{s-1}{(s^2+s+1)} $

Question 53 Multiple Choice (Single Answer)

A system with transfer function ^{$
\left[
\begin{array}
\ Y(s) \\
X(s)
\end{array}
\right]
$} = ^{$\dfrac{s}{s+p}$}has an output y(t) = cos ^{$
\left(
\begin{array}
\ 2t - \dfrac{\pi}{3}
\end{array}
\right)
$}for the input signal x(t) = p cos ^{$
\left(
\begin{array}
\ 2t - \dfrac{\pi}{2}
\end{array}
\right)
$}. Then, the system parameter ‘p’ is

$\sqrt3$
$\dfrac{2}{\sqrt3}$
1
$\dfrac{\sqrt3}{2}$

Question 54 Multiple Choice (Single Answer)

A unity negative feedback closed loop system has a plant with the transfer function G(s) = ^{$\dfrac{1}{s^2 + 2s +2}$} and a controller G_c(S) in the feed forward path. For a unit set input, the transfer function of the controller that gives minimum steady state error is

G_C(s) = ^{$\dfrac{s+1}{s+2}$}
G_C(s) = ^{$\dfrac{s+2}{s+1}$}
G_C(s) = ^{$\dfrac{(s+1)(s+4)}{(s+2)(s+3)}$}
G_C(s) = 1 + ^{$\dfrac{2}{s}$}+ 3s

2010|Electronics and Comm (GATE Exam)-Previous Question Paper Solution

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