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2009|Electronics and Comm (GATE Exam)-Previous Question Paper Solution

GATE Exam Previous Year Question Paper Solution Electronics and Communication (ECE) - 2009

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Question 1 Multiple Choice (Single Answer)

Directions : Two products are sold from a vending machine, which has two push buttons P1 and P2.
When a button is pressed, the price of the corresponding product is displayed in a 7 - segment display. If no
buttons are pressed, '0' is displayed signifying 'Rs 0'.
If only P1 is pressed, '2' is displayed, signifying 'Rs. 2'.
If only P2 is pressed, '5' is displayed, signifying 'Rs. 5'.
If both P1 and P2 are pressed, 'E' is displayed, signifying 'Error'
The names of the segments in the 7 - segment display, and the glow of the display for '0', '2', '5' and 'E' are shown below.

Consider
(1) push buttons pressed/not pressed in equivalent to logic 1/0 respectively.
(2) a segment glowing/not glowing in the display is equivalent to logic 1/0 respectively.

What are the minimum numbers of NOT gates and 2 - input OR gates required to design the logic of the driver for this 7 - Segment display?

  1. 3 NOT and 4 OR
  2. 2 NOT and 4 OR
  3. 1 NOT and 3 OR
  4. 2 NOT and 3 OR
Question 2 Multiple Choice (Single Answer)

If X = 1 in logic equation $[X+Z{\bar Y+(\bar Z + X \bar Y ) }] \ [\bar X + \bar Z(X+Y)]$ = 1 then

  1. Y = Z
  2. Y = $\bar Z$
  3. Z = 1
  4. Z = 0
Question 3 Multiple Choice (Single Answer)

Directions : Two products are sold from a vending machine, which has two push buttons P1 and P2.
When a button is pressed, the price of the corresponding product is displayed in a 7 - segment display. If no
buttons are pressed, '0' is displayed signifying 'Rs 0'.
If only P1 is pressed, '2' is displayed, signifying 'Rs. 2'
If only P2 is pressed '5' is displayed, signifying 'Rs. 5'
If both P1 and P2 are pressed, 'E' is displayed, signifying 'Error'
The names of the segments in the 7 - segment display, and the glow of the display
for '0', '2', '5' and 'E' are shown below.

Consider
(1) push buttons pressed/not pressed in equivalent to logic 1/0 respectively.
(2) a segment glowing/not glowing in the display is equivalent to logic 1/0 respectively.

If segments a to g are considered as functions of P1 and P2, which of the following is correct?

  1. g = $\overline P_1$+ P2, d = c + e
  2. g = P1+ P2, d = c + e
  3. g = $\overline P_1$+ P2, e = b + c
  4. g = P1+ P2, e = b + c
Question 4 Multiple Choice (Single Answer)

In a microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed or rejected. Such an interrupt is

  1. non-maskable and non-vectored
  2. maskable and non-vectored
  3. non-maskable and vectored
  4. maskable and vectored
Question 5 Multiple Choice (Single Answer)

What are the counting states (Q1 Q 2) for the counter shown in the figure below?

  1. 11 10 00 11 10....
  2. 01 10 11 00 01...
  3. 00 11 01 10 00...
  4. 01 10 00 01......
Question 6 Multiple Choice (Single Answer)

The full form of the abbreviations TTL and CMOS in reference to logic families are

  1. Triple Transistor Logic and Chip Metal Oxide Semiconductor
  2. Tristate Transistor Logic and Chip Metal Oxide Semiconductor
  3. Transistor Transistor Logic and Complementary Metal Oxide Semiconductor
  4. Tristate Transistor Logic and Complementary Metal Oxide Silicon
Question 7 Multiple Choice (Single Answer)

What are the minimum number of 2 to 1 multiplexers required to generate a 2 input AND gate and a 2 input EX-OR gate?

  1. 1 and 2
  2. 1 and 3
  3. 1 and 1
  4. 2 and 2
Question 8 Multiple Choice (Single Answer)

Refer to the NAND and NOR latches shown in the figures. The inputs (P1, P2) for both latches are first made (0, 1) and then, after a few seconds, made (1, 1). The corresponding stable outputs (Q1, Q2) are

  1. NAND : first (0, 1) then (0, 1) NOR : first (1, 0) then (0, 0)
  2. NAND : first (1, 0) then (1, 0) NOR : first (1, 0) then (1, 0)
  3. NAND : first (1, 0) then (1, 0) NOR : first (0, 1) then race around
  4. NAND : first (1, 0) then (1, 1) NOR : first (0, 1) then (0, 1)
Question 9 Multiple Choice (Single Answer)

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y−axis. The other wire is in the x-y plane and parallel to the x−axis. Which components of the resulting magnetic field are non-zero at the origin?

  1. x, y, z components
  2. x, y components
  3. y, z components
  4. x, z components
Question 10 Multiple Choice (Single Answer)

In an n-type silicon crystal at room temperature, which of the following can have a concentration of 4 x1019 cm-3?

  1. Silicon atoms
  2. Holes
  3. Dopant atoms
  4. Valence electrons
Question 11 Multiple Choice (Single Answer)

Consider the following two statements about the internal conditions in a n − channel MOSFET operating in the active region.
S1 : The inversion charge decreases from source to drain.
S2 : The channel potential increases from source to drain.
Which of the following is correct?

  1. Only S2 is true.
  2. Both S1 and S2 are false.
  3. Both S1 and S2 are true, but S2 is not a reason for S1.
  4. Both S1 and S2 are true, and S2 is a reason for S1.
Question 12 Multiple Choice (Single Answer)

A transmission line terminates in two branches, each of length $\dfrac{\lambda}{4}$, as shown.
The branches are terminated by 50 $\Omega$ loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Zi as seen by the source.

  1. 200 $\Omega$
  2. 100 $\Omega$
  3. 50 $\Omega$
  4. 25 $\Omega$
Question 13 Multiple Choice (Single Answer)

Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?

  1. Only P has no cutoff-frequency
  2. Only Q has no cutoff-frequency
  3. Only R has no cutoff-frequency
  4. All three have cutoff-frequencies
Question 14 Multiple Choice (Single Answer)

If a vector field $\vec V$is related to another vector field $\vec A$through $\vec V$= $\nabla$x $\vec A$, which of the following is true? (Note : C and Sc refer to any closed contour and any surface whose boundary is C.)

  1. $\oint_0 \vec V. \vec{dl} = \int_z \int \vec A. \vec d S$
  2. $\oint_0 \vec A. \vec{dl} = \int_z \int \vec V. \vec d S$
  3. $\oint_0 \vec V. \vec{dl} = \int_z \int \Delta x \vec A. \vec d S$
  4. $\oint_0 \Delta x \vec V. \vec{dl} = \int_z \int \vec V. \vec d S$
Question 15 Multiple Choice (Single Answer)

The ratio of the mobility to the diffusion coefficient in a semiconductor has the units

  1. V-1
  2. V1 .cm
  3. V. cm-1
  4. V. s
Question 16 Multiple Choice (Single Answer)

Directions: Consider a silicon p - n junction at room temperature having the following parameters:
Doping on the n-side = 1 x 1017 cm-3
Depletion width on the n-side = 0.1 $\mu$m

The built-in potential of the junction
Depletion width on the p −side = 1.0 $\mu$m
Intrinsic carrier concentration = 1.4 x 1010 cm-3
Thermal voltage = 26 mV
Permittivity of free space = 8.85 x 10-14 F cm-1
Dielectric constant of silicon = 12
The built-in potential of the junction

  1. is 0.70 V
  2. is 0.76 V
  3. is 0.82 V
  4. Cannot be estimated from the data given
Question 17 Multiple Choice (Single Answer)

Directions : Consider a silicon p - n junction at room temperature having the following parameters:
Doping on the n-side = 1 x 1017 cm-3
Depletion width on the n-side = 0.1 $\mu$m
Depletion width on the p −side = 1.0 $\mu$m
Intrinsic carrier concentration = 1.4 x 1010 cm-3
Thermal voltage = 26 mV
Permittivity of free space = 8.85 x 10-14 F cm-1
Dielectric constant of silicon = 12

The peak electric field in the device is

  1. 0.15 MV. cm-1, directed from p −region to n −region
  2. 0.15 MV. cm-1, directed from n −region to p −region
  3. 1 80 MV. cm-1, directed from p-region to n −region
  4. 1.80 MV. cm-1, directed from n −region to p −region
Question 18 Multiple Choice (Single Answer)

Consider two independent random variables X and Y with identical distributions. The variables X and Y take values 0, 1 and 2 with probabilities $\dfrac{1}{2}. \dfrac{1}{4}$ and $\dfrac{1}{4}$ respectively. What is the conditional probability P (X + Y = 2, X - Y = 0)?

  1. 0
  2. 1/16
  3. 1/6
  4. 1
Question 19 Multiple Choice (Single Answer)

For a message signal m(t) = cos $2\pi f_m t$ and carrier of frequency fc, which of the following represents a single side band (SSB) signal?

  1. cos $2\pi f_m t$ cos $2\pi f_o t$
  2. cos $2\pi f_o t$
  3. cos $[ (2\pi (f_o + f_m) ) t]$
  4. [1 + cos $2\pi f_m t$ cos $2\pi f_o t$ ]
Question 20 Multiple Choice (Single Answer)

A message signal is given by m (t) = $\dfrac{1}{2} cos\omega_1 t - \dfrac{1}{2} sin\omega_2 t$cos sin amplitude-modulated with a carrier of frequency $\omega_0$to generator s (t) + m (t) [1 + m (t)] cos$\omega_0$t. What is the power efficiency achieved by this modulation scheme?

  1. 8.33%
  2. 11.11%
  3. 20%
  4. 2%
Question 21 Multiple Choice (Single Answer)

Directions :The amplitude of a random signal is uniformly distributed between - 5 V and 5 V.

If the signal to quantization noise ratio required in uniformly quantizing the signal is 43.5 dB, the step of the quantization is approximately

  1. 0.033 V
  2. 0.05 V
  3. 0.0667 V
  4. 0.10 V
Question 22 Multiple Choice (Single Answer)

Directions :The amplitude of a random signal is uniformly distributed between - 5 V and 5 V.

If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the negative values are uniformly quantized with a step size of 0.1 V, the resulting signal to quantization noise ration is approximately

  1. 46 dB
  2. 43.8 dB
  3. 42 dB
  4. 40 dB
Question 23 Multiple Choice (Single Answer)

A communication channel with AWGN operating at a signal to noise ration SNR >> 1 and bandwidth B has capacity C1. If the SNR is doubled keeping constant, the resulting capacity C2 is given by

  1. C2 $\approx$ 2C1
  2. C2 $\approx$ C1 + B
  3. C2 $\approx$ C1 + 2B
  4. C2 $\approx$ C1 + 0.3 B
Question 24 Multiple Choice (Single Answer)

A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean X as 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true?

  1. Both the student and the teacher are right.
  2. Both the student and the teacher are wrong.
  3. The student is wrong but the teacher is right.
  4. The student is right but the teacher is wrong.
Question 25 Multiple Choice (Single Answer)

The ROC of z -transform of the discrete time sequence x (n) = $\left( \dfrac{1}{3} \right)^n u(n) - \left( \dfrac{1}{2} \right)^n$u (- n - 1) is

  1. $\dfrac{1}{3} \lt \left| z \right| \lt \dfrac{1}{2}$
  2. |z| > $\dfrac{1}{2}$
  3. |z| < $\dfrac{1}{3}$
  4. 2 < |z| < 3
Question 26 Multiple Choice (Single Answer)

The Fourier series of a real periodic function has only
(P) cosine terms if it is even
(Q) sine terms if it is even
(R) cosine terms if it is odd
(S) sine terms if it is odd
Which of the above statements are correct?

  1. P and S
  2. P and R
  3. Q and S
  4. Q and R
Question 27 Multiple Choice (Single Answer)

A system with transfer function H(z) has impulse response h(.), defined as h(2) = 1, h(3) = - 1 and h(k) = 0 otherwise. Consider the following statements.

S1 : H(z) is a low-pass filter.
S2 : H(z) is an FIR filter.

Which of the following is correct?

  1. Only S2 is true
  2. Both S1 and S2 are false
  3. Both S1 and S2 are true, and S2 is a reason for S1
  4. Both S1 and S2 are true, but S2 is not a reason for S1
Question 28 Multiple Choice (Single Answer)

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence {1, 0, 2, 3} is

  1. [0, -2 + 2j, 2, - 2 - 2j]
  2. [2, 2 + 2j, 6, 2 - 2j]
  3. [6, 1 - 3j, 2, 1 + 3j]
  4. [6, - 1 + 3j, 0, - 1 - 3j]
Question 29 Multiple Choice (Single Answer)

A function is given by f (t) = sin2 t + cos 2t. Which of the following is true?

  1. f has frequency components at 0 and $\dfrac{1}{2\pi}$Hz.
  2. f has frequency components at 0 and $\dfrac{1}{\pi}$Hz.
  3. f has frequency components at $\dfrac{1}{2\pi}$ and $\dfrac{1}{\pi}$Hz.
  4. f has frequency components at $\dfrac{0.1}{2\pi}$ and $\dfrac{1}{\pi}$Hz.
Question 30 Multiple Choice (Single Answer)

Given that F (s) is the one-sided Laplace transform of f (t). What is the Laplace transform of $\int_0^t f(\tau) d\tau$?

  1. F (s) - f (0)
  2. $\dfrac{1}{s}$F (s)
  3. $\displaystyle \int_0^s F(\tau) d\tau$
  4. $\dfrac{1}{s}$[F (s) - f (0)]
Question 31 Multiple Choice (Single Answer)

Consider a system whose input x and output y are related by the equation y (t) = $\displaystyle \int_{-\infty} ^\infty x(t - \tau) g(2\tau) d\tau$, where h (t) is shown in the graph.

Which of the following four properties are possessed by the system?
BIBO : Bounded input gives a bounded output.
Causal : The system is causal.
LP : The system is low pass.
LTI : The system is linear and time-invariant.

  1. Causal, LP
  2. BIBO, LTI
  3. BIBO, Causal, LTI
  4. LP, LTI
Question 32 Multiple Choice (Single Answer)

An LTI system having transfer function $\dfrac{s^2 +1}{s^2 +2s + 1}$ and input x (t) = sin (t + 1) is in steady state. The output is sampled at a rate $\omega_s$rad/s to obtain the final output {x (k)}. Which of the following is true?

  1. y (.) is zero for all sampling frequencies $\omega_s$.
  2. y (.) is nonzero for all sampling frequencies $\omega_s$.
  3. y (.) is nonzero for $\omega_s$> 2, but zero for $\omega_s$< 2.
  4. y (.) is zero for$\omega_s$ > 2, but nonzero for $\omega_s$< 2.
Question 33 Multiple Choice (Single Answer)

In the interconnection of ideal sources shown in the figure, it is known that the 60 V source is absorbing power.

Which of the following can be the value of the current source I?

  1. 10 A
  2. 13 A
  3. 15 A
  4. 18 A
Question 34 Multiple Choice (Single Answer)

The time domain behaviour of an RL circuit is represented by

L$\dfrac{d_i}{d_t} + R_i = V_0 (1 + Be^{-RT/L} sint ) \ u(t)$

For an initial current of i (0) = $\dfrac{V_0}{R}$, the steady state value of the current is given by

  1. i (t) $\rightarrow \dfrac{V_0}{R}$
  2. i (t) $\rightarrow \dfrac{2V_0}{R}$
  3. i (t) $\rightarrow \dfrac{V_0}{R}$(1 + B)
  4. i (t) $\rightarrow \dfrac{2V_0}{R}$(1 + B)
Question 35 Multiple Choice (Single Answer)

The switch in the circuit shown was on position for a long time, and is move to position b at time t = 0. The current i (t) for t > 0 is given by

  1. 0.2 $e^{-125t}$u (t) mA
  2. 20$e^{-1250t}$u (t) mA
  3. 0.2$e^{-1250t}$u (t) mA
  4. 20$e^{-1000t}$u (t) mA
Question 36 Multiple Choice (Single Answer)

A fully charged mobile phone with a 12 V battery is good for a 10 minute talk-time. Assume that during the talk-time, the battery delivers a constant current of 2 A and its voltage drops linearly from 12 V to 10 V as shown in the figure. How much energy does the battery deliver during this talk-time?

  1. 220 J
  2. 12 kJ
  3. 13.2 kJ
  4. 14.4 J
Question 37 Multiple Choice (Single Answer)

An AC source of RMS voltage 20 V with internal impedance Zs = (1 + 2j) $\Omega$ feeds a load of impedance ZL = (7 + 4j) $\Omega$ in the figure below. The reactive power consumed by the load is

  1. 8 VAR
  2. 16 VAR
  3. 28 VAR
  4. 32 VAR
Question 38 Multiple Choice (Single Answer)

If the transfer function of the following network is

The value of the load resistance RL is

  1. $\dfrac{R}{4}$
  2. $\dfrac{R}{2}$
  3. R
  4. 2R
Question 39 Multiple Choice (Single Answer)

In the circuit given below, what value of RL maximizes the power delivered to RL?

  1. 2.4 $\Omega$
  2. $\dfrac{8}{3}$$\Omega$
  3. 4$\Omega$
  4. 6$\Omega$
Question 40 Multiple Choice (Single Answer)

The order of the differential equation $\frac{d^2y}{dt^2}+\Big(\frac{dy}{dt}\Big)^3$+ y4 = e-t is

  1. 1
  2. 2
  3. 3
  4. 4
Question 41 Multiple Choice (Single Answer)

A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield heads?

  1. $\Big(\frac{1}{2}\Big)^2$
  2. $^{10} C_2$$\Big(\frac{1}{2}\Big)^2$
  3. $\Big(\frac{1}{2}\Big)^{10}$
  4. $^{10} C_2$$\Big(\frac{1}{2}\Big)^{10}$
Question 42 Multiple Choice (Single Answer)

A white noise process X (t) with two-sided power spectral density 1 x 10-10 W / Hz is input to a filter whose magnitude squared response is shown below.

The power of the output process Y (t) is given by

  1. 5 x 10-7 W
  2. 1 x 10-6 W
  3. 2 x 10-6 W
  4. 1 x 10-5 W
Question 43 Multiple Choice (Single Answer)

If the power spectral density of stationary random process is a sine-squared function of frequency, the shape of its autocorrelation is

Question 44 Multiple Choice (Single Answer)

The Eigen values of following matrix are
$\begin{bmatrix}
\ -1 & 3 & 5 \
\ -3 & -1 & 6 \
\ 0 & 0 & 3 \
\end{bmatrix}$

  1. 3, 3 + 5j, 6 - j
  2. - 6 + 5j, 3 + j, 3 - j
  3. 3 + j, 3 - j, 5 + j
  4. 3, - 1 + 3j, - 1 - 3j
Question 45 Multiple Choice (Single Answer)

The Taylor series expansion of $\frac{sin x}{x - \pi}$ at x = $\pi$ is given by

  1. 1 + $\frac{(x - \pi)^2}{3!} + ...$
  2. - 1 - $\frac{(x - \pi)^2}{3!} + ...$
  3. 1 - $\frac{(x - \pi)^2}{3!} + ...$
  4. - 1 + $\frac{(x - \pi)^2}{3!} + ...$
Question 46 Multiple Choice (Single Answer)

Match each differential equation in Group I to its family of solution curves in Group II:

  1. A - 2, B - 3, C - 3, D - 1
  2. A - 1, B - 3, C - 2, D - 1
  3. A - 2, B - 1, C - 3, D - 3
  4. A - 3, B - 2, C - 1, D - 2
Question 47 Multiple Choice (Single Answer)

A magnetic field in air is measured to be
$\overrightarrow{B} = B_0 \bigg(\frac{x}{x^2 + y^2} \hat{y} - \frac{y}{x^2 + y^2} \hat{x}\bigg)$

What current distribution leads to this field? [Hint : The algebra is trivial in cylindrical coordinates.]

  1. $\overrightarrow{J} = \frac{B_0 \hat{z}}{\mu_0} \bigg(\frac{1}{x^2 + y^2}\bigg), r \neq 0$
  2. $\overrightarrow{J} = \frac{B_0 \hat{z}}{\mu_0} \bigg(\frac{2}{x^2 + y^2}\bigg), r \neq 0$
  3. $\overrightarrow{J} = 0\hspace{0.2cm}, r \neq 0$
  4. $\overrightarrow{J} = \frac{B_0 \hat{z}}{\mu_0} \bigg(\frac{1}{x^2 + y^2}\bigg), r \neq 0$
Question 48 Multiple Choice (Single Answer)

Directions: Consider the CMOS circuit shown below, where the gate voltage v0 of the n-MOSFET is increased from zero, while the gate voltage of the p −MOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the trans-conductance parameter is 1 mAV-2.

For small increase in VG beyond 1 V, which of the following gives the correct description of the region of operation of each MOSFET?

  1. Both the MOSFETs are in saturation region.
  2. Both the MOSFETs are in triode region.
  3. n -MOSFET is in triode and p −MOSFET is in saturation region.
  4. n -MOSFET is in saturation and p −MOSFET is in triode region.
Question 49 Multiple Choice (Single Answer)

Directions: Consider the CMOS circuit shown, where the gate voltage v0 of the n-MOSFET is increased from zero, while the gate voltage of the p−MOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the trans-conductance parameter is 1 mA V-2.

Estimate the output voltage V0 for VG = 15 V.

  1. 4 - $\dfrac{1}{\sqrt2}$
  2. 4 + $\dfrac{1}{\sqrt2}$
  3. 4 - $\dfrac{\sqrt3}{2}$
  4. 4 + $\dfrac{\sqrt3}{2}$
Question 50 Multiple Choice (Single Answer)

In the following a stable multivibrator circuit, which properties of v0 (t) depend on R2?

  1. Only the frequency
  2. Only the amplitude
  3. Both the amplitude and the frequency
  4. Neither the amplitude nor the frequency
Question 51 Multiple Choice (Single Answer)

In the circuit below, the diode is ideal. The voltage V is given by

  1. min (Vi, 1)
  2. max (Vi, 1)
  3. min (-Vi, 1)
  4. max (-Vi, 1)
Question 52 Multiple Choice (Single Answer)

A small signal source Vi = A cos 20 t + B sin 106 t is applied to a transistor amplifier as shown below. The transistor has $\beta$= 150 and hie = 3 $\Omega$. Which expression best approximate V0 (t)?

  1. V0 (t) = - 1500 (A cos 20 t + B sin 106 t)
  2. V0 (t) = - 150 (A cos 20 t + B sin 106 t)
  3. V0 (t) = - 1500 B sin 106 t
  4. V0 (t) = - 150 B sin 106 t
Question 53 Multiple Choice (Single Answer)

In the circuit shown below, the op-amp is ideal, the transistor has VBE = 0.6 and $\beta$ = 150. Decide whether the feedback in the circuit is positive or negative and determine the voltage V at the output of the op-amp.

  1. Positive feedback, V = 10 V
  2. Positive feedback, V = 0 V
  3. Negative feedback, V = 5 V
  4. Negative feedback, V = 2 V
Question 54 Multiple Choice (Single Answer)

The feedback configuration and the pole-zero locations of are shown below. The root locus for negative values of k , i.e. for -$\infty$< k < 0, has breakaway / break-in points and angle of departure at pole P (with respect to the positive real axis) equal to

  1. $\pm \sqrt2 $ and 00
  2. $\pm \sqrt2 $ and 450
  3. $\pm \sqrt3 $ and 00
  4. $\pm \sqrt3 $ and 450
Question 55 Multiple Choice (Single Answer)

Consider the system
$\dfrac{dx}{dt}$= Ax + Bu with A = $$
\left[
\begin{array}
\ 1&0\\
0&1
\end{array}
\right]
$$ and B = $$
\left[
\begin{array}
\ p\\
q
\end{array}
\right]
$$

where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?

  1. The system is completely state controllable for any non-zero values of p and q.
  2. Only p = 0 and q = 0 result in controllability.
  3. The system is uncontrollable for all values of p and q.
  4. We cannot conclude about controllability from the given data.
Question 56 Multiple Choice (Single Answer)

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer functions has theses properties?

  1. $ \dfrac{-2.24}{(s^2+2.59s+1.12)} $
  2. $ \dfrac{-3.82}{(s^2+1.91s+1.91)} $
  3. $ \dfrac{-2.24}{(s^2-2.59s+1.12)} $
  4. $ \dfrac{-3.82}{(s^2-1.91s+1.91)} $
Question 57 Multiple Choice (Single Answer)

The magnitude plot of a rational transfer function G (s) with real coefficients is shown below. Which of the following compensators has such a magnitude plot?

  1. Lead compensator
  2. Lag compensator
  3. PID compensator
  4. Lead-lag compensator
Question 58 Multiple Choice (Single Answer)

Direction: The Nyquist plot of a stable transfer function G (s) and its closed loop system in the feedback configuration are shown below.

Which of the following statements is true?

  1. G (s) is an all-pass filter.
  2. G (s) has a zero in the right half plane.
  3. G (s) is the impedance of a passive network.
  4. G (s) is marginally stable.
Question 59 Multiple Choice (Single Answer)

Directions : The Nyquist plot of a stable transfer function G (s) and its closed loop system in the feedback configuration are shown below.

The gain and phase margins of G (s) for closed loop stability are

  1. 6 dB and 1800 respectively
  2. 3 dB and 1800 respectively
  3. 6 dB and 900 respectively
  4. 3 dB and 900 respectively
Question 60 Multiple Choice (Single Answer)

If f (z) = c0 + c1z -1, then $\oint \frac{1 + f(z)}{z}$dz is given by

  1. 2$\pi$c1
  2. 2$\pi$ (1 + c0)
  3. 2$\pi$jc1
  4. 2$\pi$ (1 - c0)

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