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GATE (Graduate Aptitude Test in Engineering) Electronics and Communication Engineering is an online examination conducted to get admission in M-Tech (Masters in Technology), ME (Master of Engineering ) and PhD at IITs (Indian Institutes of Technology), NITs (National Institutes of Technology), IIITs (Indian Institutes of Information Technology) and other universities in India. GATE exam is jointly conducted by IIT Bombay, IIT Delhi, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT Madras, IIT Roorkee and Indian Institute for Science, Bangalore (IISC Bangalore). The exam is divided into two different parts General Aptitude (GA) and Candidate’s Selected Subject (Core Subjects). GATE Electronics and Communication Engineering online mock tests help candidates in preparing for the GATE exam. By attempting GATE online mock tests candidates get familiar with the pattern of actual question paper. BrPaper provides all GATE question papers completely free. Here you can practice free online mock tests of complete exam of GATE Electronics and Communication Engineering. We advise candidates to solve the online GATE Electronics and Communication Engineering mock tests to get good marks in the exam. Start practicing Electronics and CommunicationGATE 2018 Mock tests here online for free

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Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 1:

“By giving him the last ______ of the cake, you will ensure lasting _____ in our house today.” The words that best fill the blanks in the above sentence ar

A	peas, piece	B	piece, peace
C	peace, piece	D	peace, peas

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 2:

“Even though there is a vast scope for its ________, tourism has remained a/an _________ area.” The words that best fill the blanks in the above sentence are

A	improvement, neglected	B	rejection approved
C	fame, glum	D	interest, disinterested

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 3:

If the number 715∎423 is divisible by 3 (∎ denotes the missing digit in the thousandths place), then the smallest whole number in the place of ∎ is _________.

A	0	B	2
C	5	D	6

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 4:

What is the value of

1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{16} + \frac{1}{256} + . . . ?

A	2	B	$\frac{7}{4}$
C	$\frac{3}{2}$	D	$\frac{4}{3}$

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 5:

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height. What is the height of the lamp post in meters?

A	1.5	B	3
C	4.5	D	6

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 6:

Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, if the interest was compounded annually?

A	5,00,000	B	6,21,000
C	6,66,667	D	7,50,000

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 7:

Two alloys A and B contain gold and copper in the ratios of 2:3 and 3:7 by mass, respectively. Equal masses of alloys A and B are melted to make an alloy C. The ratio of gold to copper in alloy C is ______.

A	5:10	B	7:13
C	6:11	D	9:13

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 8:

The Cricket Board has long recognized John’s potential as a leader of the team. However, his on-field temper has always been a matter of concern for them since his junior days. While this aggression has filled stadia with die-hard fans, it has taken a toll on his own batting. Until recently, it appeared that he found it difficult to convert his aggression into big scores. Over the past three seasons though, that picture of John has been replaced by a cerebral, calculative and successful batsman-captain. After many years, it appears that theteam has finally found a complete captain. Which of the following statements can be logically inferred from the above paragraph?

A	Even as a junior cricketer, John was considered a good captain.	B	Finding a complete captain is a challenge.
C	Fans and the Cricket Board have differing views on what they want in a captain	D	Over the past three seasons, John has accumulated big scores.

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 9:

A cab was involved in a hit-and-run accident at night. You are given the following data about the cabs in the city and the accident. (i) 85% of cabs in the city are green and the remaining cabs are blue. (ii) A witness identified the cab involved in the accident as blue. (iii) It is known that a witness can correctly identify the cab colour only 80% of the time. Which of the following options is closest to the probability that the accident was caused by a blue cab?

A	12%	B	15%
C	41%	D	80%

Category: GATE Electronics and Communication Engineering 2018 General Aptitude

Question 10:

A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to tourists due to poor connectivity and lack of accommodation. A company has spotted the opportunity and is planning to develop a luxury resort with helicopter service to the nearest major city airport. Environmentalists are upset that this would lead to the region becoming Crowded and polluted like any other major beach resorts. Which one of the following statements can be logically inferred from the information given in the above paragraph?

A	The culture and tradition of the local people will be influenced by tourists.	B	The region will become crowded and polluted due to tourism.
C	The coral reefs are on the decline and could soon vanish.	D	Helicopter connectivity would lead to an increase in tourists coming to the region.

Category: GATE Electronics and Communication Engineering 2018

Question 11:

Two identical nMOS transistors

M_{1} a n d M_{2}

are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals.

V_{b i a s} a n d V_{D}

are so adjusted that both transistors are in saturation. The transconductance of this combination is defined a

g_{m} =

\frac{\partial i_{D}}{\partial v_{G S}}

while the output resistance is

r_{\circ} = \frac{\partial v_{D S}}{\partial i_{D}}, w h e r e i_{D}

𝐷 is the current flowing into the drain of

m_{2} . L e t g_{m 1}, g_{m 2} b e t h e t r a n s c o n d u c \tan c e s a n d r_{\circ 1}, r_{\circ 2} b e t h e o u t p u t r e s i s \tan c e s o f t r a n s i s t o r s M_{1} a n d M_{2}

respectively.

A	$g_{m} \approx g_{m 1} . g_{m 2} . r_{\circ 2} b a n d r_{\circ} \approx r_{\circ 1} + r_{\circ 2}$	B	$g_{m} \approx g_{m 1 .} g_{m 2} . a n d r_{\circ} \approx r_{\circ 1} + r_{\circ 2 .}$
C	$g_{m} \approx g_{m 1} a n d r_{\circ} \approx r_{\circ 1} . g_{m 2} . r_{\circ 2}$	D	$g_{m} \approx g_{m 1} a n d r_{\circ} \approx r_{\circ 2}$

Category: GATE Electronics and Communication Engineering 2018

Question 12:

In the circuit shown below, the op-amp is ideal and the Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e.

v_{I N} (t) = u (t)

volts. Also, at 𝑡 = 0, the voltage across each of the capacitors is zero.

The time 𝑡, in milliseconds, at which the output voltage

v_{O U T}

crosses −10 V is

A	2.5	B	5
C	7.5	D	10

Category: GATE Electronics and Communication Engineering 2018

Question 13:

A good trans-impedance amplifier has

A	low input impedance and high output impedance	B	high input impedance and high output impedance.
C	high input impedance and low output impedance.	D	low input impedance and low output impedance.

Category: GATE Electronics and Communication Engineering 2018

Question 14:

Let the input be u and the output is y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

A	$\frac{d^{3} y}{d t^{3}} + a_{1} \frac{d^{2} y}{d t^{2}} + a_{2} \frac{d y}{d t} + a_{3} y = b_{3} u + b_{2} \frac{d u}{d t} + b_{1} \frac{d^{2} u}{d t^{2}}$	B	$y (t) = \int_{o}^{t} e^{a (t - r)} β u (r) d r$
C	$y = a u + b, b \neq 0$	D	y=au

Category: GATE Electronics and Communication Engineering 2018

Question 15:

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

A	Both the criteria provide information relative to the stable gain range of the system	B	The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.
C	The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion	D	The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

Category: GATE Electronics and Communication Engineering 2018

Question 16:

Consider

p (s) = s^{3} + a_{z} s^{2} + a_{1} s + a_{o}

with all real coefficients. It is known that its derivative 𝑝′(𝑠) has no real roots. The number of real roots of 𝑝(𝑠) is

A	0	B	1
C	2	D	3

Category: GATE Electronics and Communication Engineering 2018

Question 17:

In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?

A	The hole and electron diffusion current components are in the same direction.	B	The hole and electron drift current components are in the same direction.
C	On an average, holes, and electrons drift in opposite directions.	D	On average, electrons drift and diffuse in the same direction.

Category: GATE Electronics and Communication Engineering 2018

Question 18:

The logic function f ( X , Y ) realized by the given circuit is

A	NOR	B	AND
C	NAND	D	XOR

Category: GATE Electronics and Communication Engineering 2018

Question 19:

A function 𝐹(𝐴, 𝐵, 𝐶) defined by three Boolean variables A, B and C when expressed as sum of products is given by

F = A . B . C + A . B . C + A . B . C

where

A, B, a n d C

ARE the complements of the respective variables. The product of sums (POS) form of the function F is

A	𝐹 = (𝐴 + 𝐵 + 𝐶) ⋅ (𝐴 + $B$ + 𝐶) ⋅ ( $A$ + 𝐵 + 𝐶)	B	$F = (A + B + C) . (A + B + C) . (A + B + C)$
C	$F = (A + B + C) . (A + B + C), (A + B + C) . (A + B + C) . (A + B + C)$	D	$F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)$

Category: GATE Electronics and Communication Engineering 2018

Question 20:

The points P, Q, and R is shown on the Smith chart (normalized impedance chart) in the following figure represent:

A	P: Open Circuit, Q: Short Circuit, R: Matched Load	B	P: Open Circuit, Q: Matched Load, R: Short Circuit
C	P: Short Circuit, Q: Matched Load, R: Open Circuit	D	P: Short Circuit, Q: Open Circuit, R: Matched Load

Category: GATE Electronics and Communication Engineering 2018

Question 21:

Let M be a real

4 \times 4

matrix. Consider the following statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular (invertible). Which one among the following is TRUE?

A	S1 implies S2	B	S1 implies S3
C	S2 implies S1	D	S3 implies S2

Category: GATE Electronics and Communication Engineering 2018

Question 22:

Let

f (x, y) = \frac{a x^{2} + b y^{2}}{x y}

where a and b are constants. If

\frac{\partial f}{\partial x} = \frac{\partial f}{\partial y}

at x=1 and y=2 then the relation between a and b is

A	$a = \frac{b}{4}$	B	$a = \frac{b}{2}$
C	a=2b	D	a=4b

Category: GATE Electronics and Communication Engineering 2018

Question 23:

A discrete-time all-pass system has two of its poles at

0.25 ∠ 0 ° a n d 2 ∠ 30 °

Which one of the following statements about the system is TRUE?

A	It has two more poles a $0.5 ∠ 30 ° a n d 4 ∠ 0 °$	B	It is stable only when the impulse response is two-sided.
C	It has a constant phase response over all frequencies.	D	It has a constant phase response over the entire z-plane.

Category: GATE Electronics and Communication Engineering 2018

Question 24:

Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by

a_{k}

, that is

x (t) = \sum_{k = - \infty}^{\infty} a_{k} e^{j k \frac{2 π}{T} t}

The same function 𝑥(𝑡) can also be considered as a periodic function with period 𝑇 ′ = 40. Let

b_{k}

be the Fourier series coefficients when the period is taken as T'.

I f \sum_{k = - \infty}^{\infty} |a_{k}| = 16, t h e n \sum_{k = - \infty}^{\infty} |b_{k}|

is equal to

A	256	B	64
C	16	D	4

Category: GATE Electronics and Communication Engineering 2018

Question 25:

Consider the following amplitude modulated signal:

s (t) = \cos (200 πt) + 4 \cos (2400 πt) + (2800 πt)

. The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is ___________________________.

0.11 to 0.12

0.12 to 0.13

0.13 to 0.14

0.14 to 0.15

Category: GATE Electronics and Communication Engineering 2018

Question 26:

Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in this code is at least 2. The maximum number of codewords such a code can contain is _________.

15 to 15

16 to 16

17 to 17

18 to 18

Category: GATE Electronics and Communication Engineering 2018

Question 27:

A binary source generates symbols 𝑋 ∈ {−1,1} which are transmitted over a noisy channel.bThe probability of transmitting 𝑋 = 1 is 0.5. Input to the threshold detector is 𝑅 = 𝑋 + 𝑁. The probability density function

f_{n} (n)

of the noise 𝑁 is shown below.

0.12 to 0.14

0.11 to 0.13

0.13 to 0.15

None of these

Category: GATE Electronics and Communication Engineering 2018

Question 28:

A p-n step junction diode with a contact potential of 0.65 V has a depletion width of 1μm at equilibrium. The forward voltage (in volts, correct to two decimal places) at which this width reduces to 0.6 μm is _______________________.

0.40 to 0.43

0.41 to 0.44

0.42 to 0.45

0.43 to 0.46

Category: GATE Electronics and Communication Engineering 2018

Question 29:

A traffic signal cycles from GREEN to YELLOW, YELLOW to RED and RED to GREEN. In each cycle, GREEN is turned on for 70 seconds, YELLOW is turned on for 5 seconds and the RED is turned on for 75 seconds. This traffic light has to be implemented using a finite state machine (FSM). The only input to this FSM is a clock of 5 second period. The minimum number of flip-flops required to implement this FSM is _______.

2 to 2

3 to 3

4 to 4

5 to 5

Category: GATE Electronics and Communication Engineering 2018

Question 30:

There are two photolithography systems: one with a light source of wavelength

λ_{1}

1 = 156 nm (System 1) and another with a light source of wavelength

λ_{2}

= 325 nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are

L_{m i n 1} a n d L_{m i n 2}

respectively, the ratio

L_{m i n 2} / L_{m i n 2}

(correct to two decimal places) is__________.

0.45 to 0.49

0.46 to 0.50

0.47 to 0.51

0.48 to 0.52

Category: GATE Electronics and Communication Engineering 2018

Question 31:

A lossy transmission line has a resistance per unit length R= 0.05Ω / m. The line is distortionless and has a characteristic impedance of 50Ω . The attenuation constant (in Np/m, correct to three decimal places) of the line is _______.

-0.001 to -0.001

-0.001 to 0.001

0.001 to 0.001

None of these

Category: GATE Electronics and Communication Engineering 2018

Question 32:

Consider matrix

A = [\begin{matrix} k \\ k^{2} - k \end{matrix} \begin{matrix} 2 k \\ k^{2} \end{matrix}] a n d v e c t o r x = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}]

The number of distinct real values of k for which the equation Ax=0 has infinitely many solutions is ______________________.

0 to 0

0 to 2

2 to 2

2 to 20

Category: GATE Electronics and Communication Engineering 2018

Question 33:

Let

X_{1}, X_{2}, X_{3} a n d X_{4}

be independent normal random variables with zero mean and unit variance. The probability that

X_{4}

is the smallest among the four is _______.

0.24 to 0.24

0.25 to 0.25

0.26 to 0.26

0.27 to 0.27

Category: GATE Electronics and Communication Engineering 2018

Question 34:

Taylor series expansion of

f (x) = \int_{0}^{x} e^{- (\frac{t^{2}}{2})} �� t a r o u n d �� = 0 h a s t h e f o r m f (x) = a_{0} + a_{1} x + a_{2} x^{2} + . . .

The coefficient

a_{2}

(correct to two decimal places) is equal to _____________________.

-0.01 to -0.01

-0.01 to 0.01

0.01 to 0.01

All of these

Category: GATE Electronics and Communication Engineering 2018

Question 35:

The ABCD matrix for a two-port network is defined by:

[\begin{matrix} V_{1} \\ I_{1} \end{matrix}] = [\begin{matrix} A & B \\ C & D \end{matrix}] [\begin{matrix} V_{2} \\ - I_{2} \end{matrix}]

The parameter B for the given two-port network (in ohms, correct to two decimal places) is ___________________.

4.3 to 5.3

5.3 to 6.3

6.3 to 7.3

7.3 to 8.3

Category: GATE Electronics and Communication Engineering 2018

Question 36:

The circuit shown in the figure is used to provide regulated voltage (5 V) across the 1kΩ resistor. Assume that the Zener diode has a constant reverse breakdown voltage for a current range, starting from a minimum required Zener current,

I_{z m i n} = 2 m A

to its maximum allowable current. The input voltage

V_{1}

may vary by 5% from its nominal value of 6 V. The resistance of the diode in the breakdown region is negligible.

The value of R and the minimum required power dissipation rating of the diode, respectively, are

A	186Ω and 10 mW	B	100 Ωand 40 mW
C	100 Ωand 10 mW	D	186 Ω and 40 mW

Category: GATE Electronics and Communication Engineering 2018

Question 37:

Let

A_{C} C o s (2 π f_{c} t) a n d m (t) = \cos (2 π f_{m} t) . I t i s g i v e n t h a t f_{c} > > 5 f_{m} . T h e s i g n a l c (t) + m (t)

is applied to the input of a non-linear device, whose output

v_{o} (t)

is related to the input

v_{i} (t) a s v_{o} (t) = a v_{i} (t) + b {v^{2}}_{i} (t)

where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency c f and bandwidth 3

f_{m}

, to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave on behalf of the carrier power, then

a / b

A	0.25	B	0.5
C	1	D	2

Category: GATE Electronics and Communication Engineering 2018

Question 38:

Consider a white Gaussian noise process 𝑁(𝑡) with two-sided power spectral density

S_{N} (f)

= 0.5 W/Hz as input to a filter with impulse response

0 . 5^{- t^{2} / 2}

(where 𝑡 is in seconds) resulting in output 𝑌(𝑡). The power in 𝑌(𝑡) in watts is

A	0.11	B	0.22
C	0.33	D	0.44

Category: GATE Electronics and Communication Engineering 2018

Question 39:

The state equation and the output equation of a control system are given below:

x = [\begin{matrix} - 4 & - 1.5 \\ 4 & 0 \end{matrix}] x + [\begin{matrix} 2 \\ 0 \end{matrix}] u, y = [1.5 0.625] x

The transfer function representation of the system is

A	$\frac{3 s + 5}{s^{2} + 4 s + 6}$	B	$\frac{3 s - 1.875}{s^{2} + 4 s + 6}$
C	$\frac{4 s + 1.5}{s^{2} + 4 s + 6}$	D	$\frac{6 s + 5}{s^{2} + 4 s + 6}$

Category: GATE Electronics and Communication Engineering 2018

Question 40:

Red (R), Green (G), and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The built-in voltages of red, green, and blue diodes are

V_{R}, V_{G}, a n d V_{B}

respectively. Assume donor and acceptor doping to be the same (

N_{A} a n d N_{D}

respectively) in the p and n sides of all the three diodes Which one of the following relationships about the built-in voltages is TRUE?

A	$V_{R} > V_{G} > V_{B}$	B	$V_{R} < V_{G} < V_{B}$
C	$V_{R} = V_{G} = V_{B}$	D	$V_{R} > V_{G} < V_{B}$

Category: GATE Electronics and Communication Engineering 2018

Question 41:

A four-variable Boolean function is realized using

4 \times 1

multiplexers as shown in the figure.

The minimized expression for ( F , U , V, W, X , ) is

A	$(U V + U V) W$	B	$(U V + U V) (W X + W X)$
C	$(U V + U V) W$	D	$(U V + U V) (W X + W X)$

Category: GATE Electronics and Communication Engineering 2018

Question 42:

2 \times 2

ROM array is built with the help of diodes as shown in the circuit below. Here W0 and W1 are signals that select the word lines and B0 and B1 are signals that are the output of the sense amps based on the stored data corresponding to the bit lines during the read operation.

During the read operation, the selected word line goes high and the other word line is in a high impedance state. As per the implementation shown in the circuit diagram above, what are the bits corresponding to Dij (where i = 0 or 1 and j = 0 or 1) stored in the ROM?

A	$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$	B	$[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$
C	$[\begin{matrix} 1 & 0 \\ 1 & 0 \end{matrix}]$	D	$[\begin{matrix} 1 & 1 \\ 0 & 0 \end{matrix}]$

Category: GATE Electronics and Communication Engineering 2018

Question 43:

The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 m so that the amplitude of the wave attenuates by 20 dB, is

A	0.12	B	0.23
C	0.46	D	2.3

Category: GATE Electronics and Communication Engineering 2018

Question 44:

A curve passes through the point(x=1 , y=0) and satisfies the differential equation

\frac{d y}{d x} = \frac{x^{2} + y^{2}}{2 y} + \frac{y}{x}

. The equation that describes the curve is

A	$I n (1 + \frac{y^{2}}{x^{2}}) = x - 1$	B	$\frac{1}{2} 1 n (1 + \frac{y^{2}}{x^{2}}) = x - 1$
C	$I n (1 + \frac{y}{x}) = x - 1$	D	$\frac{1}{2} 1 n (1 + \frac{y}{x}) = x - 1$

Category: GATE Electronics and Communication Engineering 2018

Question 45:

For the circuit given in the figure, the voltage

V_{C}

(in volts) across the capacitor is

A	$1.25 \sqrt{2 \sin} (5 t - 0.25 π)$	B	$1.25 \sqrt{2} \sin (5 t - 0.125 π)$
C	$2.5 \sqrt{2} \sin (5 t - 0.25 π)$	D	$2.5 \sqrt{2} \sin (5 t - 0.125 π)$

Category: GATE Electronics and Communication Engineering 2018

Question 46:

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 seconds after closing the switch is _______.

0.284 to 0.348

0.242 to 0.324

0.282 to 0.328

None of these

Category: GATE Electronics and Communication Engineering 2018

Question 47:

A dc current of 26 μA flows through the circuit shown. The diode in the circuit is forward biased and it has an ideality factor of one. At the quiescent point, the diode has a junction capacitance of 0.5 nF. Its neutral region resistances can be neglected. Assume that the room temperature thermal equivalent voltage is 26 mV.

For

ω = 2 \times 10^{6} r a d / s

, the amplitude of the small-signal component of diode current (in μA, correct to one decimal place) is ________________________.

6.1 to 6.5

6.2 to 6.6

6.3 to 6.7

6.4 to 6.8

Category: GATE Electronics and Communication Engineering 2018

Question 48:

An op-amp based circuit is implemented as shown below.

In the above circuit, assume the op-amp to be ideal. The voltage (in volts, correct to one decimal place) at node A, connected to the negative input of the op-amp as indicated in the figure is ______________________.

4.4 to 6.6

0.4 to 0.6

4.0 to 6.0

0.0 to 0.0

Category: GATE Electronics and Communication Engineering 2018

Question 49:

The input 4sinc(2𝑡) is fed to a Hilbert transformer to obtain 𝑦(𝑡), as shown in the figure below:

Here

\sin c (x) = \frac{\sin (πx)}{πx}

The value (accurate to two decimal places) of

\int_{- \infty}^{\infty} {|y (t)|}^{2} d t

is __________________.

-8 to -8

-8 to 8

8 to 8

All of these

Category: GATE Electronics and Communication Engineering 2018

Question 50:

A random variable 𝑋 takes values −0.5 and 0.5 with probabilities

\frac{1}{4} a n d \frac{3}{4},

respectively. The noisy observation of 𝑋 is Y = X + Z where 𝑍 has uniform probability density over the interval (−1, 1). 𝑋 and 𝑍 are independent. If the MAP rule-based detector outputs 𝑋̂ as

x = \{\begin{cases} - 0.5, Y < a \\ 0.5, Y \geq a \end{cases}

then the value of 𝛼 (accurate to two decimal places) is _______.

-0.5 to -0.5

-0.5 to 0.5

0.5 to 0.5

None of these

Category: GATE Electronics and Communication Engineering 2018

Question 51:

For a unity feedback control system with the forward path transfer function

G (s) = \frac{k}{s (s + 2)}

The peak resonant magnitude

M_{r}

of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is ______________________.

11 to 17

12 to 17

13 to 17

14 to 17

Category: GATE Electronics and Communication Engineering 2018

Question 52:

The figure below shows the Bode magnitude and phase plots of a stable transfer function

G (s) = \frac{n_{0}}{s^{3} + d_{2} s^{2} + d_{1} s + d_{0}}

Consider the negative unity feedback configuration with gain 𝑘 in the feedforward path. The closed-loop is stable for

k < k_{o}

. The maximum value of

k_{o}

is ______.

0.0 to 0.0

0.1 to 0.1

0.2 to 0.2

0.3 to 0.3

Category: GATE Electronics and Communication Engineering 2018

Question 53:

In the circuit shown below, the (𝑊/𝐿) value for

M_{2}

is twice that for

M_{1}

. The two nMOS transistors are otherwise identical. The threshold voltage 𝑉𝑇 for both transistors is 1.0V. Note that

V_{G S} f o r M_{2}

must be > 1.0 V.

Current through the nMOS transistors can be modeled as

I_{D S} = μ C_{O X} (\frac{W}{L}) ((V_{G S} - V_{T}) V_{D S} - \frac{1}{2} V^{2} D S) f o r V_{D S} \leq V_{G S} - V_{T} I_{D S} = μ C_{O X} (\frac{W}{L}) {(V_{G S} - V_{T})}^{2} / 2 f o r V_{D S} \geq V_{G S} - V_{T}

The voltage (in volts, accurate to two decimal places) at

V_{x}

is _______.

0.41 to 0.433

0.41 to 0.434

0.41 to 0.435

0.41 to 0.436

Category: GATE Electronics and Communication Engineering 2018

Question 54:

A solar cell of area 2 1.0 cm , operating at 1.0 sun intensity, has a short circuit current of 20 mA, and an open-circuit voltage of 0.65 V. Assuming room temperature operation and thermal equivalent voltage of 26 mV, the open-circuit voltage (in volts, correct to two decimal places) at 0.2 sun intensity is _______.

0.59 to 0.63

0.60 to 0.63

0.61 to 0.63

0.62 to 0.63

Category: GATE Electronics and Communication Engineering 2018

Question 55:

A junction is made between doping density

N_{A 1} = 10^{15} c m^{- 3} a n d p S i

with doping density

N_{A 2} = 10^{17} c m^{- 3}

Given: Boltzmann constant

k = 1.38 x 10^{- 23} J . K^{- 1},

, electronic charge q

= 1.6 \times 10^{- 19}

. Assume 100% acceptor ionization. At room temperature (T = 300K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be _________________. .

0.2 to 0.4

0.5 to 0.7

0.8 to 0.10

0.11 to 0.13

Category: GATE Electronics and Communication Engineering 2018

Question 56:

In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data

D_{i n}

using clock 𝐶𝐾. The XOR gate outputs 3.3 volts for logic HIGH and 0 volts for logic LOW levels. The data bit and clock periods are equal and the value of Δ𝑇/

T_{C K}

= 0.15, where the parameters Δ𝑇 and

T_{C K}

are shown in the figure. Assume that the Flip-Flop and the XOR gate are ideal.

If the probability of input data bit (

D_{i n}

) transition in each clock period is 0.3, the average value (in volts, accurate to two decimal places) of the voltage at node 𝑋, is _______

0.82 to 0.86

0.84 to 0.86

0.86 to 0.86

0.82 to 0.88

Category: GATE Electronics and Communication Engineering 2018

Question 57:

The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for LOW logic level at the outputs. When the pull-downs are off, high-value resistors set the output logic levels to HIGH (i.e. the pull-ups are weak). Note that some nodes are intentionally shorted to implement “wired logic”. Such shorted nodes will be HIGH only if the outputs of all the gates whose outputs are shorted are HIGH.

he number of distinct values of

X_{3} X_{2} X_{1} X_{0}

(out of the 16 possible values) that give 𝑌 = 1 is _______.

6 to 6

7 to 7

8 to 8

9 to 9

Category: GATE Electronics and Communication Engineering 2018

Question 58:

The cutoff frequency of

T E_{01}

mode of an air-filled rectangular waveguide having inner dimensions

a c m \times b c m (a > b)

is twice that of the dominant

T E_{10}

mode. When the waveguide is operated at a frequency that is 25% higher than the cutoff frequency of the dominant mode, the guide wavelength is found to be 4 cm. The value of b (in cm, correct to two decimal places) is _______.

7.0 to 8.0

0.8 to 0.8

0.7 to 0.7

0.7 to 0.8

Category: GATE Electronics and Communication Engineering 2018

Question 59:

A uniform plane wave traveling in free space and having the electric field

\vec{E} = (\sqrt{2} {\hat{a}}_{x} - {\hat{a}}_{z}) \cos [6 \sqrt{3} π \times 10^{8} t - 2 π (x + \sqrt{2} z)] V / m

is incident on a dielectric medium (relative permittivity > 1, relative permeability = 1) as shown in the figure and there is no reflected wave.

The relative permittivity (correct to two decimal places) of the dielectric medium is_________________________.

1.5 to 1.7

1.7 to 1.9

1.9 to 2.1

2.1 to 2.3

Category: GATE Electronics and Communication Engineering 2018

Question 60:

The position of a particle 𝑦(𝑡) is described by the differential equation:

\frac{d^{2} y}{d t^{2}} = \frac{d y}{d t} - \frac{5 y}{4} .

The initial conditions are 𝑦(0)=

1 a n d {\frac{d y}{d t}}_{t = 0} = 0

The position (accurate to two decimal places) of the particle at 𝑡 = 𝜋 is _______.

-0.23 to -0.19

0.23 to 0.19

-0.23 to 0.19

None of these

Category: GATE Electronics and Communication Engineering 2018

Question 61:

The contour C given below is on the complex plane

z = x + j y, w h e r e j = \sqrt{- 1}

The value of the integral

\frac{1}{πj} \oint_{c} \frac{d z}{z^{2} - 1} i s

___________________.

0 to 2

2 to 2

2 to 4

4 to 6

Category: GATE Electronics and Communication Engineering 2018

Question 62:

Let

r = x^{2} + y - z a n d z^{3} - x y + y z + y^{3} = 1

Assume that 𝑥 and 𝑦 are independent variables. At (𝑥, 𝑦, 𝑧) = (2, −1,1), the value (correct to two decimal places) of

\frac{\partial r}{\partial x}

is __________________.

4.1 to 4.6

4.2 to 4.6

4.3 to 4.6

4.4 to 4.6

Category: GATE Electronics and Communication Engineering 2018

Question 63:

Consider the network shown below with 𝑅1 = 1Ω, 𝑅2 = 2Ω and 𝑅3 = 3Ω. The network is connected to a constant voltage source of 11V.

The magnitude of the current (in amperes, accurate to two decimal places) through the source is _______.

7.1 to 8.1

7.5 to 8.1

7.7 to 8.1

7.9 to 8.1

Category: GATE Electronics and Communication Engineering 2018

Question 64:

A band-limited low-pass signal 𝑥(𝑡) of bandwidth 5 kHz is sampled at a sampling rate

f_{s}

. The signal 𝑥(𝑡) is reconstructed using the reconstruction filter 𝐻(𝑓) whose magnitude response is shown below:

The minimum sampling rate

f_{s}

(in kHz) for perfect reconstruction of 𝑥(𝑡) is _______.

11 to 11

12 to 12

13 to 13

14 to 14

Category: GATE Electronics and Communication Engineering 2018

Question 65:

Let

X [K] = k + 1, 0 \leq 7 b e 8 - p o i n t D f T o f a s e q u e n c e x [n], w h e r e X [K] = \sum_{n = 0}^{N - 1} x [n] e^{- j 2 πnk / N}

The value (correct to two decimal places) of

\sum_{n = 0}^{3} x [2 n]

is ________________________.

2.90 to 3.10

2.00 to 3.20

2.10 to 3.30

2.20 to 3.40

⮜ Back Next ⮞

Not Visited	0	Not Answered
Answered	0	Marked for Review
Answered & Marked for Review (will be considered for evaluation)

Question 1:

“By giving him the last ______ of the cake, you will ensure lasting _____ in our house today.” The words that best fill the blanks in the above sentence ar

A	peas, piece	B	piece, peace
C	peace, piece	D	peace, peas

Correct Answer : B

Question 2:

“Even though there is a vast scope for its ________, tourism has remained a/an _________ area.” The words that best fill the blanks in the above sentence are

A	improvement, neglected	B	rejection approved
C	fame, glum	D	interest, disinterested

Correct Answer : A

Question 3:

If the number 715∎423 is divisible by 3 (∎ denotes the missing digit in the thousandths place), then the smallest whole number in the place of ∎ is _________.

A	0	B	2
C	5	D	6

Correct Answer : B

Question 4:

What is the value of

1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{16} + \frac{1}{256} + . . . ?

A	2	B	$\frac{7}{4}$
C	$\frac{3}{2}$	D	$\frac{4}{3}$

Correct Answer : D

Question 5:

A	1.5	B	3
C	4.5	D	6

Correct Answer : B

Question 6:

A	5,00,000	B	6,21,000
C	6,66,667	D	7,50,000

Correct Answer : B

Question 7:

A	5:10	B	7:13
C	6:11	D	9:13

Correct Answer : B

Question 8:

A	Even as a junior cricketer, John was considered a good captain.	B	Finding a complete captain is a challenge.
C	Fans and the Cricket Board have differing views on what they want in a captain	D	Over the past three seasons, John has accumulated big scores.

Correct Answer : C

Question 9:

A	12%	B	15%
C	41%	D	80%

Correct Answer : C

Question 10:

A	The culture and tradition of the local people will be influenced by tourists.	B	The region will become crowded and polluted due to tourism.
C	The coral reefs are on the decline and could soon vanish.	D	Helicopter connectivity would lead to an increase in tourists coming to the region.

Correct Answer : D

Question 11:

Two identical nMOS transistors

M_{1} a n d M_{2}

are connected as shown below. The circuit is used as an amplifier with the input connected between G and S terminals and the output taken between D and S terminals.

V_{b i a s} a n d V_{D}

are so adjusted that both transistors are in saturation. The transconductance of this combination is defined a

g_{m} =

\frac{\partial i_{D}}{\partial v_{G S}}

while the output resistance is

r_{\circ} = \frac{\partial v_{D S}}{\partial i_{D}}, w h e r e i_{D}

𝐷 is the current flowing into the drain of

m_{2} . L e t g_{m 1}, g_{m 2} b e t h e t r a n s c o n d u c \tan c e s a n d r_{\circ 1}, r_{\circ 2} b e t h e o u t p u t r e s i s \tan c e s o f t r a n s i s t o r s M_{1} a n d M_{2}

respectively.

A	$g_{m} \approx g_{m 1} . g_{m 2} . r_{\circ 2} b a n d r_{\circ} \approx r_{\circ 1} + r_{\circ 2}$	B	$g_{m} \approx g_{m 1 .} g_{m 2} . a n d r_{\circ} \approx r_{\circ 1} + r_{\circ 2 .}$
C	$g_{m} \approx g_{m 1} a n d r_{\circ} \approx r_{\circ 1} . g_{m 2} . r_{\circ 2}$	D	$g_{m} \approx g_{m 1} a n d r_{\circ} \approx r_{\circ 2}$

Correct Answer : C

Question 12:

In the circuit shown below, the op-amp is ideal and the Zener voltage of the diode is 2.5 volts. At the input, unit step voltage is applied, i.e.

v_{I N} (t) = u (t)

volts. Also, at 𝑡 = 0, the voltage across each of the capacitors is zero.

The time 𝑡, in milliseconds, at which the output voltage

v_{O U T}

crosses −10 V is

A	2.5	B	5
C	7.5	D	10

Correct Answer : C

Question 13:

A good trans-impedance amplifier has

A	low input impedance and high output impedance	B	high input impedance and high output impedance.
C	high input impedance and low output impedance.	D	low input impedance and low output impedance.

Correct Answer : D

Question 14:

Let the input be u and the output is y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

A	$\frac{d^{3} y}{d t^{3}} + a_{1} \frac{d^{2} y}{d t^{2}} + a_{2} \frac{d y}{d t} + a_{3} y = b_{3} u + b_{2} \frac{d u}{d t} + b_{1} \frac{d^{2} u}{d t^{2}}$	B	$y (t) = \int_{o}^{t} e^{a (t - r)} β u (r) d r$
C	$y = a u + b, b \neq 0$	D	y=au

Correct Answer : C

Question 15:

The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE:

A	Both the criteria provide information relative to the stable gain range of the system	B	The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems.
C	The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion	D	The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.

Correct Answer : D

Question 16:

Consider

p (s) = s^{3} + a_{z} s^{2} + a_{1} s + a_{o}

with all real coefficients. It is known that its derivative 𝑝′(𝑠) has no real roots. The number of real roots of 𝑝(𝑠) is

A	0	B	1
C	2	D	3

Correct Answer : B

Question 17:

In a p-n junction diode at equilibrium, which one of the following statements is NOT TRUE?

A	The hole and electron diffusion current components are in the same direction.	B	The hole and electron drift current components are in the same direction.
C	On an average, holes, and electrons drift in opposite directions.	D	On average, electrons drift and diffuse in the same direction.

Correct Answer : D

Question 18:

The logic function f ( X , Y ) realized by the given circuit is

A	NOR	B	AND
C	NAND	D	XOR

Correct Answer : D

Question 19:

A function 𝐹(𝐴, 𝐵, 𝐶) defined by three Boolean variables A, B and C when expressed as sum of products is given by

F = A . B . C + A . B . C + A . B . C

where

A, B, a n d C

ARE the complements of the respective variables. The product of sums (POS) form of the function F is

A	𝐹 = (𝐴 + 𝐵 + 𝐶) ⋅ (𝐴 + $B$ + 𝐶) ⋅ ( $A$ + 𝐵 + 𝐶)	B	$F = (A + B + C) . (A + B + C) . (A + B + C)$
C	$F = (A + B + C) . (A + B + C), (A + B + C) . (A + B + C) . (A + B + C)$	D	$F = (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C) . (A + B + C)$

Correct Answer : C

Question 20:

The points P, Q, and R is shown on the Smith chart (normalized impedance chart) in the following figure represent:

A	P: Open Circuit, Q: Short Circuit, R: Matched Load	B	P: Open Circuit, Q: Matched Load, R: Short Circuit
C	P: Short Circuit, Q: Matched Load, R: Open Circuit	D	P: Short Circuit, Q: Open Circuit, R: Matched Load

Correct Answer : C

Question 21:

Let M be a real

4 \times 4

matrix. Consider the following statements: S1: M has 4 linearly independent eigenvectors. S2: M has 4 distinct eigenvalues. S3: M is non-singular (invertible). Which one among the following is TRUE?

A	S1 implies S2	B	S1 implies S3
C	S2 implies S1	D	S3 implies S2

Correct Answer : C

Question 22:

Let

f (x, y) = \frac{a x^{2} + b y^{2}}{x y}

where a and b are constants. If

\frac{\partial f}{\partial x} = \frac{\partial f}{\partial y}

at x=1 and y=2 then the relation between a and b is

A	$a = \frac{b}{4}$	B	$a = \frac{b}{2}$
C	a=2b	D	a=4b

Correct Answer : D

Question 23:

A discrete-time all-pass system has two of its poles at

0.25 ∠ 0 ° a n d 2 ∠ 30 °

Which one of the following statements about the system is TRUE?

A	It has two more poles a $0.5 ∠ 30 ° a n d 4 ∠ 0 °$	B	It is stable only when the impulse response is two-sided.
C	It has a constant phase response over all frequencies.	D	It has a constant phase response over the entire z-plane.

Correct Answer : B

Question 24:

Let 𝑥(𝑡) be a periodic function with period 𝑇 = 10. The Fourier series coefficients for this series are denoted by

a_{k}

, that is

x (t) = \sum_{k = - \infty}^{\infty} a_{k} e^{j k \frac{2 π}{T} t}

The same function 𝑥(𝑡) can also be considered as a periodic function with period 𝑇 ′ = 40. Let

b_{k}

be the Fourier series coefficients when the period is taken as T'.

I f \sum_{k = - \infty}^{\infty} |a_{k}| = 16, t h e n \sum_{k = - \infty}^{\infty} |b_{k}|

is equal to

A	256	B	64
C	16	D	4

Correct Answer : C

Question 25:

Consider the following amplitude modulated signal:

s (t) = \cos (200 πt) + 4 \cos (2400 πt) + (2800 πt)

. The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is ___________________________.

Correct Answer : 0.12 to 0.13

Question 26:

Correct Answer : 16 to 16

Question 27:

f_{n} (n)

of the noise 𝑁 is shown below.

Correct Answer : 0.12 to 0.14

Question 28:

Correct Answer : 0.40 to 0.43

Question 29:

Correct Answer : 5 to 5

Question 30:

There are two photolithography systems: one with a light source of wavelength

λ_{1}

1 = 156 nm (System 1) and another with a light source of wavelength

λ_{2}

= 325 nm (System 2). Both photolithography systems are otherwise identical. If the minimum feature sizes that can be realized using System1 and System2 are

L_{m i n 1} a n d L_{m i n 2}

respectively, the ratio

L_{m i n 2} / L_{m i n 2}

(correct to two decimal places) is__________.

Correct Answer : 0.47 to 0.51

Question 31:

Correct Answer : 0.001 to 0.001

Question 32:

Consider matrix

A = [\begin{matrix} k \\ k^{2} - k \end{matrix} \begin{matrix} 2 k \\ k^{2} \end{matrix}] a n d v e c t o r x = [\begin{matrix} x_{1} \\ x_{2} \end{matrix}]

The number of distinct real values of k for which the equation Ax=0 has infinitely many solutions is ______________________.

Correct Answer : 2 to 2

Question 33:

Let

X_{1}, X_{2}, X_{3} a n d X_{4}

be independent normal random variables with zero mean and unit variance. The probability that

X_{4}

is the smallest among the four is _______.

Correct Answer : 0.25 to 0.25

Question 34:

Taylor series expansion of

f (x) = \int_{0}^{x} e^{- (\frac{t^{2}}{2})} �� t a r o u n d �� = 0 h a s t h e f o r m f (x) = a_{0} + a_{1} x + a_{2} x^{2} + . . .

The coefficient

a_{2}

(correct to two decimal places) is equal to _____________________.

Correct Answer : -0.01 to 0.01

Question 35:

The ABCD matrix for a two-port network is defined by:

[\begin{matrix} V_{1} \\ I_{1} \end{matrix}] = [\begin{matrix} A & B \\ C & D \end{matrix}] [\begin{matrix} V_{2} \\ - I_{2} \end{matrix}]

The parameter B for the given two-port network (in ohms, correct to two decimal places) is ___________________.

Correct Answer : 4.3 to 5.3

Question 36:

I_{z m i n} = 2 m A

to its maximum allowable current. The input voltage

V_{1}

may vary by 5% from its nominal value of 6 V. The resistance of the diode in the breakdown region is negligible.

The value of R and the minimum required power dissipation rating of the diode, respectively, are

A	186Ω and 10 mW	B	100 Ωand 40 mW
C	100 Ωand 10 mW	D	186 Ω and 40 mW

Correct Answer : B

Question 37:

Let

A_{C} C o s (2 π f_{c} t) a n d m (t) = \cos (2 π f_{m} t) . I t i s g i v e n t h a t f_{c} > > 5 f_{m} . T h e s i g n a l c (t) + m (t)

is applied to the input of a non-linear device, whose output

v_{o} (t)

is related to the input

v_{i} (t) a s v_{o} (t) = a v_{i} (t) + b {v^{2}}_{i} (t)

where a and b are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency c f and bandwidth 3

f_{m}

, to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave on behalf of the carrier power, then

a / b

A	0.25	B	0.5
C	1	D	2

Correct Answer : D

Question 38:

Consider a white Gaussian noise process 𝑁(𝑡) with two-sided power spectral density

S_{N} (f)

= 0.5 W/Hz as input to a filter with impulse response

0 . 5^{- t^{2} / 2}

(where 𝑡 is in seconds) resulting in output 𝑌(𝑡). The power in 𝑌(𝑡) in watts is

A	0.11	B	0.22
C	0.33	D	0.44

Correct Answer : B

Question 39:

The state equation and the output equation of a control system are given below:

x = [\begin{matrix} - 4 & - 1.5 \\ 4 & 0 \end{matrix}] x + [\begin{matrix} 2 \\ 0 \end{matrix}] u, y = [1.5 0.625] x

The transfer function representation of the system is

A	$\frac{3 s + 5}{s^{2} + 4 s + 6}$	B	$\frac{3 s - 1.875}{s^{2} + 4 s + 6}$
C	$\frac{4 s + 1.5}{s^{2} + 4 s + 6}$	D	$\frac{6 s + 5}{s^{2} + 4 s + 6}$

Correct Answer : A

Question 40:

V_{R}, V_{G}, a n d V_{B}

respectively. Assume donor and acceptor doping to be the same (

N_{A} a n d N_{D}

respectively) in the p and n sides of all the three diodes Which one of the following relationships about the built-in voltages is TRUE?

A	$V_{R} > V_{G} > V_{B}$	B	$V_{R} < V_{G} < V_{B}$
C	$V_{R} = V_{G} = V_{B}$	D	$V_{R} > V_{G} < V_{B}$

Correct Answer : B

Question 41:

A four-variable Boolean function is realized using

4 \times 1

multiplexers as shown in the figure.

The minimized expression for ( F , U , V, W, X , ) is

A	$(U V + U V) W$	B	$(U V + U V) (W X + W X)$
C	$(U V + U V) W$	D	$(U V + U V) (W X + W X)$

Correct Answer : C

Question 42:

2 \times 2

A	$[\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$	B	$[\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$
C	$[\begin{matrix} 1 & 0 \\ 1 & 0 \end{matrix}]$	D	$[\begin{matrix} 1 & 1 \\ 0 & 0 \end{matrix}]$

Correct Answer : A

Question 43:

The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 m so that the amplitude of the wave attenuates by 20 dB, is

A	0.12	B	0.23
C	0.46	D	2.3

Correct Answer : B

Question 44:

A curve passes through the point(x=1 , y=0) and satisfies the differential equation

\frac{d y}{d x} = \frac{x^{2} + y^{2}}{2 y} + \frac{y}{x}

. The equation that describes the curve is

A	$I n (1 + \frac{y^{2}}{x^{2}}) = x - 1$	B	$\frac{1}{2} 1 n (1 + \frac{y^{2}}{x^{2}}) = x - 1$
C	$I n (1 + \frac{y}{x}) = x - 1$	D	$\frac{1}{2} 1 n (1 + \frac{y}{x}) = x - 1$

Correct Answer : A

Question 45:

For the circuit given in the figure, the voltage

V_{C}

(in volts) across the capacitor is

A	$1.25 \sqrt{2 \sin} (5 t - 0.25 π)$	B	$1.25 \sqrt{2} \sin (5 t - 0.125 π)$
C	$2.5 \sqrt{2} \sin (5 t - 0.25 π)$	D	$2.5 \sqrt{2} \sin (5 t - 0.125 π)$

Correct Answer : C

Question 46:

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 seconds after closing the switch is _______.

Correct Answer : 0.284 to 0.348

Question 47:

For

ω = 2 \times 10^{6} r a d / s

, the amplitude of the small-signal component of diode current (in μA, correct to one decimal place) is ________________________.

Correct Answer : 6.2 to 6.6

Question 48:

An op-amp based circuit is implemented as shown below.

Correct Answer : 0.4 to 0.6

Question 49:

The input 4sinc(2𝑡) is fed to a Hilbert transformer to obtain 𝑦(𝑡), as shown in the figure below:

Here

\sin c (x) = \frac{\sin (πx)}{πx}

The value (accurate to two decimal places) of

\int_{- \infty}^{\infty} {|y (t)|}^{2} d t

is __________________.

Correct Answer : 8 to 8

Question 50:

A random variable 𝑋 takes values −0.5 and 0.5 with probabilities

\frac{1}{4} a n d \frac{3}{4},

x = \{\begin{cases} - 0.5, Y < a \\ 0.5, Y \geq a \end{cases}

then the value of 𝛼 (accurate to two decimal places) is _______.

Correct Answer : -0.5 to -0.5

Question 51:

For a unity feedback control system with the forward path transfer function

G (s) = \frac{k}{s (s + 2)}

The peak resonant magnitude

M_{r}

of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is ______________________.

Correct Answer : 14 to 17

Question 52:

The figure below shows the Bode magnitude and phase plots of a stable transfer function

G (s) = \frac{n_{0}}{s^{3} + d_{2} s^{2} + d_{1} s + d_{0}}

Consider the negative unity feedback configuration with gain 𝑘 in the feedforward path. The closed-loop is stable for

k < k_{o}

. The maximum value of

k_{o}

is ______.

Correct Answer : 0.1 to 0.1

Question 53:

In the circuit shown below, the (𝑊/𝐿) value for

M_{2}

is twice that for

M_{1}

. The two nMOS transistors are otherwise identical. The threshold voltage 𝑉𝑇 for both transistors is 1.0V. Note that

V_{G S} f o r M_{2}

must be > 1.0 V.

Current through the nMOS transistors can be modeled as

I_{D S} = μ C_{O X} (\frac{W}{L}) ((V_{G S} - V_{T}) V_{D S} - \frac{1}{2} V^{2} D S) f o r V_{D S} \leq V_{G S} - V_{T} I_{D S} = μ C_{O X} (\frac{W}{L}) {(V_{G S} - V_{T})}^{2} / 2 f o r V_{D S} \geq V_{G S} - V_{T}

The voltage (in volts, accurate to two decimal places) at

V_{x}

is _______.

Correct Answer : 0.41 to 0.434

Question 54:

Correct Answer : 0.59 to 0.63

Question 55:

A junction is made between doping density

N_{A 1} = 10^{15} c m^{- 3} a n d p S i

with doping density

N_{A 2} = 10^{17} c m^{- 3}

Given: Boltzmann constant

k = 1.38 x 10^{- 23} J . K^{- 1},

, electronic charge q

= 1.6 \times 10^{- 19}

. Assume 100% acceptor ionization. At room temperature (T = 300K), the magnitude of the built-in potential (in volts, correct to two decimal places) across this junction will be _________________. .

Correct Answer : 0.11 to 0.13

Question 56:

In the circuit shown below, a positive edge-triggered D Flip-Flop is used for sampling input data

D_{i n}

using clock 𝐶𝐾. The XOR gate outputs 3.3 volts for logic HIGH and 0 volts for logic LOW levels. The data bit and clock periods are equal and the value of Δ𝑇/

T_{C K}

= 0.15, where the parameters Δ𝑇 and

T_{C K}

are shown in the figure. Assume that the Flip-Flop and the XOR gate are ideal.

If the probability of input data bit (

D_{i n}

) transition in each clock period is 0.3, the average value (in volts, accurate to two decimal places) of the voltage at node 𝑋, is _______

Correct Answer : 0.82 to 0.86

Question 57:

he number of distinct values of

X_{3} X_{2} X_{1} X_{0}

(out of the 16 possible values) that give 𝑌 = 1 is _______.

Correct Answer : 8 to 8

Question 58:

The cutoff frequency of

T E_{01}

mode of an air-filled rectangular waveguide having inner dimensions

a c m \times b c m (a > b)

is twice that of the dominant

T E_{10}

Correct Answer : 0.7 to 0.8

Question 59:

A uniform plane wave traveling in free space and having the electric field

\vec{E} = (\sqrt{2} {\hat{a}}_{x} - {\hat{a}}_{z}) \cos [6 \sqrt{3} π \times 10^{8} t - 2 π (x + \sqrt{2} z)] V / m

is incident on a dielectric medium (relative permittivity > 1, relative permeability = 1) as shown in the figure and there is no reflected wave.

The relative permittivity (correct to two decimal places) of the dielectric medium is_________________________.

Correct Answer : 1.9 to 2.1

Question 60:

The position of a particle 𝑦(𝑡) is described by the differential equation:

\frac{d^{2} y}{d t^{2}} = \frac{d y}{d t} - \frac{5 y}{4} .

The initial conditions are 𝑦(0)=

1 a n d {\frac{d y}{d t}}_{t = 0} = 0

The position (accurate to two decimal places) of the particle at 𝑡 = 𝜋 is _______.

Correct Answer : -0.23 to -0.19

Question 61:

The contour C given below is on the complex plane

z = x + j y, w h e r e j = \sqrt{- 1}

The value of the integral

\frac{1}{πj} \oint_{c} \frac{d z}{z^{2} - 1} i s

___________________.

Correct Answer : 2 to 4

Question 62:

Let

r = x^{2} + y - z a n d z^{3} - x y + y z + y^{3} = 1

Assume that 𝑥 and 𝑦 are independent variables. At (𝑥, 𝑦, 𝑧) = (2, −1,1), the value (correct to two decimal places) of

\frac{\partial r}{\partial x}

is __________________.

Correct Answer : 4.4 to 4.6

Question 63:

Consider the network shown below with 𝑅1 = 1Ω, 𝑅2 = 2Ω and 𝑅3 = 3Ω. The network is connected to a constant voltage source of 11V.

The magnitude of the current (in amperes, accurate to two decimal places) through the source is _______.

Correct Answer : 7.9 to 8.1

Question 64:

A band-limited low-pass signal 𝑥(𝑡) of bandwidth 5 kHz is sampled at a sampling rate

f_{s}

. The signal 𝑥(𝑡) is reconstructed using the reconstruction filter 𝐻(𝑓) whose magnitude response is shown below:

The minimum sampling rate

f_{s}

(in kHz) for perfect reconstruction of 𝑥(𝑡) is _______.

Correct Answer : 13 to 13

Question 65:

Let

X [K] = k + 1, 0 \leq 7 b e 8 - p o i n t D f T o f a s e q u e n c e x [n], w h e r e X [K] = \sum_{n = 0}^{N - 1} x [n] e^{- j 2 πnk / N}

The value (correct to two decimal places) of

\sum_{n = 0}^{3} x [2 n]

is ________________________.

Correct Answer : 2.90 to 3.10

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