gate 2017 ece session 5 answer key. consider the circuit shown in the figure. assume base-to-emitter...

1. Consider the circuit shown in the figure. Assume base-to-emitter voltage Vm =0.8V and common base current gain () of the transistor is unity

+18V

4k44k

16 k2 k

The value of the collector-to-emitter voltage VCE (in volts) is

Ans. (6 V)

[EC : GATE-2017_Paper-2]

2. Consider a binary memoryless channel characterized by the transition probabilitysoon in the figure

0 0

1 1

0.25

0.75

0.75

0.25

The channel is

(a) Lossless (b) Noiseless

(c) Useless (d) Determinstic

Ans. (d)


GATE 2017 ECE Session 5 Answer Key

3. An electron (qt) is moving in free space with velocity 105 m/s towards a stationaryelectron (q2) far away. The closest distance that this moving electron gets to thestationary electron before the repulsive force diverts its path is ............... 10–8m.

given mass of electron m = 9.11 × 10–31 kg.

Charge of electrons e = –1.6 × 10–19 C and permittivity 0 = 91 10 F/m36

Ans. (10.127)


4. Two n-channel MOSFETs, T1 and T2 are identical in all respects except that thewidth of T2 is double that of T1. Both the transistors are biased in the saturationregion of operation but the gate over drive voltage (VGS – VTH) of T2 is doublethat of T1, where VGS and VTH are the gate-to-source voltage and thresholdvoltage of the transistors, respectively. If the drain current and transconductanceof T1 are ID1 and gm1 respectively. The corresponding values of these two parameterfor T2 are

(a) 8ID1 and 2gm1 (b) 8ID1 and 4gm1

(c) 4ID1 and 4gm1 (d) 4ID1 and 2gm1

Ans. (d)

[EC : GATE-2017_Paper-2]5. A modulating signal given by x(t) = 5 sin(4103t – 10 cos 2 103t) V is modulator

with phase deviation constant kp = 5 rad/V. If the carrier frequency instantaneousfrequency (in kHz) at t = 0.5 ms is

(a) 4 × 103 rad/sec (b) 5 × 103 rad/sec

(c) 6 × 103 rad/sec (d) 4 × 105 rad/sec

Ans. (a)


6. The minimum value of the function 21f (x) x(x 3)3

in the interval –100 x 100

Ans. (–100 )


7. The smaller angle (m degrees) between the planes x + y + z = 1 and

2x – y + 2z = 0 is

Ans. (1cos3

)


8. In a DRAM(a) periodic refreshing is not required(b) information is stored in a capacitor(C) information is stored in a latch(d) both read and write operations can be performed simultaneously

Ans. (b)[EC : GATE-2017_Paper-2]

9. The number of 3-digit number such that the digit 1 is never to the immediate rightof 2(a) 781 (b) 791(c) 881 (d) 891

Ans. (c)[EC : GATE-2017_Paper-2]

10. Spheres S1 and S2 of raddi a and b (b > a) respectively are placed far apart andlong, thin conducting wire as shown in the figure

S2

Radius a

WireS1

Radius b

Ans. (10)[EC : GATE-2017_Paper-2]

11. With unit sample response h[n] = 5[n] – 7[n – 1] + 7 � [n – 3 ] – 5 [n – 4](a) loss pass filter (b) high pass filter(c) band reject filter (d) band stop filter


12. The figure shown V is sinusoidal voltage source. The current I is in phase with

voltage V find Voltage across the capacitor

Voltage across the resistor is

I5 5H

R L

V5F

Ans. (0.2)


13. For the circuit shown in the figure, P & Q are the input and Y is the output

PMOS

NMOS

Y

P

Q

The logic implemented by the circuit is

(a) XNOR (b) XOR (c)NOR (d) OR

Ans. (b)


14. The residues of a function f(z) = 3

1

(z 4)(z 1) at z = 4 and z = – 1 are

(a)1

27

and

1

125

(b)

1

125 and

1

125

(c)1

27

and

1

5(d)

1

125 and

1

5

Ans. (b)


15. The rank of the matrix

1 1 0 0 0

0 0 1 1 0

0 1 1 0 0

1 0 0 0 1

0 0 0 1 1

is

Ans. (5)


16. Consider the state space realization

1 1

2 2

x (t) x (t)0 0 0u(t),

x (t) x (t)0 9 45

with the initial condition

1

2

x (0) 0

x (0) 0

u(t) denotes the unit step function. The value of 2 21 2

tlim x (t) x (t)

is .

Ans. (5)


17. Which of the following statements is incorrect?

(a) Lead compensator is used to reduce the settling time

(b) Lag compensator is used to reduce the steady state error

(c) Lead compensator may increase the order of a system

(d) Lag compensator always stabilizes an unstable system

Ans. (d)


18. Figure I show a 4-bit ripple carry adder realized using full adders and figure IIshows the circuit of Full Adder (FA). The propagation delay of the XOR, AND andOR gates in figure II are 20ns, 15 ns and 10 ns respectively. Assume all the inputsto the 4-bit adder are initially reset to 0

Y3 X3

FA

Y2 X2

FA

Y1 X1

FA

Y0 X0

FAZ4 Z3 Z2 Z1

Zn

Zn+1

Z0

Figure-I

Figure-II

Xn

Yn Sn

At t = 0, the input to the 4-bit adder are changed to X3X2X1X0 = 1100, Y3Y2Y1Y0

= 0100, Z0 = 1. The output of the ripple carry adder will be stable at (m/ns)


19. If the vector function x 1 y 2 z 3ˆ ˆ ˆF a (3y k z) a (k x 2z) a (k y 1)

is irrotational, then

the values of the constants k1, k2 and k3, respectively are(a) 0.3, –2.5, 0.5 (b) 0.0, 3.0, 2.0(c) 0.3, 0.33, 0.5 (d) 4.0, 3.0, 2.0


20. A unity feedback control system is characterized by the open-loop transfer function

3 22(s 1)

G(s)s ks 2s 1

The value of k for which the system oscillates at 2 rad/s is

Ans. (0.75)[EC : GATE-2017_Paper-2]

21. A MOS capacitor is fabricated on p-type Si (Silicon) where the metal work functionis 4.1 eV and electron affinity of Si is 4.0 eV. EC – EF = 0.9 eV. where EC andEF are the conduction band the minimum and Fermi energy levels of Si, respectively.Oxide r = 3.9, 0 = 8.85 × 10–14 F/cm. Oxide thickness tox = 0.1 m and electronicscharge q = 1.6 × 10–19 C. If the measured flat band voltage of this capacitor is 1V.Then the magneitude of the fix charge at the oxide-semiconductor interface in(nC/cm2) is

Ans. (34.51)[EC : GATE-2017_Paper-2]

22. Of the diode circuit show in the figure is connected to an averaging DC volt meter.The DC volt meter in volts. Neglating the voltage drop accross the diode is

10 sin t

f = 50Hz 1K V0

+

–


23. Passengers try repeatedly to get a seat reservation in any train running betweenthey are successful. If there is 40% chance of getting reservation in any attemptthen the average number of attempts that passengers need to make to get a

Ans. (*)[EC : GATE-2017_Paper-2]

24. An npn bipolar junction transistor (BJT) is operating in the active region. If thereverse bias across the base collector junction is increased. Then

(a) the effective base width increases and common-emitter current gan increases

(b) the effective base width increases and common-emitter current gan decreases

(c) the effective base width decreases and common-emitter current gan increases

(d) the effective base width decreases and common-emitter current gan decreases

Ans. (c)

[EC : GATE-2017_Paper-2]25. Parallel combination of two LTI systems shown in the figure

h (t)1

h (t)2

+x(t) y(t)

Impulse response of the system are

h1(t) = 2(t + 2) – 3(t + 1)

h2(t) = (t – 2)

Input x(t) is a unit step signal then the energy of y(t) is


26. The order LTI system is described by the following state equations

1 2d x (t) x (t) 0dt

2 1 2d x (t) 2x (t) 3x (t) r(t)dt

x1(t) and x2(t) are the two state variables and r(t) denotes the input. The outputsystem is

(a) umdamped (oscillatory) (b) under damped

(c) cntracally damped (d) over damped

Ans. (c)


27. For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (J1) is 2.5 mA/cm2 and the open circuit voltage (Voc) is 0.451 V.consider thermal voltage (VT) to be 25 mV. If the intensity of the incident light isincreased by 20 times. Assuming that the temperature remains unchanged Voc (involts) will be

Ans. (*)[EC : GATE-2017_Paper-2]

28. In the circuit shown in the figure transistors Q1 and Q2 are biased at a collectorcurrent of 2.6 mA. Assuming that transistor current gains are sufficiently large toasssume collector current equal to emmiter current and thermal voltage of 26 mV,

the magnitude of voltage gain 0

s

VV in the midband frequency range is (up to second

decimal place)

5V

1k

Q1

V0

Q2

RB2

vS

–5V

Ans. (–100)[EC : GATE-2017_Paper-2]

29. The signal x(t) = sin (14000 t), where t is in seconds, is sampled at a rate of 9000samples per second. The sample signal is the input to an ideal lowpass filter withfrequency response H(f) as follows

1, | f | 12kHzH(f )

0, | f | 12kHz

What is the number of sinusoids in the output and their frequency in kHz?(a) Number = 1, frequency = 7 (b) Number = 3, frequency = 2, 7, 11(c) Number = 2, frequency = 2, 7 (d) Number = 2, frequency = 7, 11


30. The permititivity of water at optical frequencies is 1.75 0. It is formd that anisotrophic a distance d under water forms an illuminated circular area of radius 5mas shown in figure. The critical angle is (c)0.

dC

Light source

Water

5mAir


31. The switch in the circuit shown in the figure, was open for a long time and is closedfor a short time the current i(t) (in ampere) at t = 0.5 sec

510A2.5H

5i(t)t = 0


32. The state diagram of a Finite State Machine (FSM) designed to detect an overlapingsequence of three bits is shown in the figure. The FSM has an input ‘in’ and anoutput ‘out’. The initial state of the FSM is S0.

11

01

10

00 In = 0Out = 0

In = 1Out = 0

In = 1Out = 0

S1

S2

In = 0Out = 0

In = 1Out = 0

In = 1Out = 1In = 0

Out = 0

In = 0Out = 0

S0

S3

If the input sequence is 10101101001101. Starting with the left most bit then thenumber of time ‘out’ will be 1 is


33. Programmable logic array (PLA) shown in the figureP P Q Q R R

F

R

Q

P

Function l implemented is

(a) PQR PQR PQR

(b) (P Q R)(P Q R)(P Q R)

(c) PQR PQR PQR

(d) (P Q R)(P Q R)(P Q R)

Ans. (c)[EC : GATE-2017_Paper-2]

34. Find RTH

+–

– +

1

1 110V

1

P

Q

3i0

Ans. (–2.5)[EC : GATE-2017_Paper-2]

35. Consider an LTI system with magnitude response

| f |1 | f | 20| H(f) | 200 | f | 20

and phase response

arg {H(f)} = –2f

If the input to the system is

x(t) 8cos 20 t 16sin 40 t 24cos 80 t4 8 16

then the average of the power of the output signal y(t) is

Ans. (8)


36. Carrier power in an AM transmitter is 5 KW. This carrier is modulated by theirsignal. The maximum percentage of modulators is 50% then maximum modulatedcarrier power (in kw) that can be used with

Ans. (0.625)


37. M1 and M2 are identical and have a threshold voltage of 1 V. The state ofrespectively

2.5 V

2 V

M2

M1

3 V

(a) Saturation, Saturation (b) Linear, Linear

(c) Linear, Saturation (d) Saturation, Linear

Ans. (a)


38. A unity feedback control system is characterized by the open-loop transfer function

3 2

10K(s 2)G(s)

s 3s 10

The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the

j+j

0

s-plane

s = Rej

R

+j 5.43 K G(s)-plane

–K+j

–j 5.43 K

= 02K

Re

j Im G

Nyquist path for G(s) Nyquist plot of G(s)

If 0 < k < 1, then the number of pole of the close loop transfer function that lieright side of s plane is

Ans. (2)


gate 2017 ece session 5 answer key. consider the circuit shown in the figure. assume base-to-emitter...

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