1. Three pair cubical dice are thrown simultaneously. What is the probability that allthree dice have same number is .......

[EC : GATE-2017_Paper-1]

Ans. ( 136 )

2. The one of the eigen value is real, rest are imaginary the real value is

A

1 2 3 4 55 1 2 3 44 5 1 2 33 4 5 1 22 3 4 5 1

(a) –2.5 (b) 0(c) 15 (d) 25

[EC : GATE-2017_Paper-1]Ans. (b)3. If x(t) is input of LTI system is given by x(t) = 4 cos 200t + 8 cos 400t.

If impulse response of system is given by

h(t) = 2sin 300 t t 0t

600 t 0

& y(t) is output of the system then what is the |y(t)|max is ......[EC : GATE-2017_Paper-1]

Ans. (8)4. If x(n) & y(n) are input & response respectively.

If y(n) = n | x(n) | 0 n | 0x(n) x(n 1) otherwise

Then system will be(a) Causal but not stable (c) Causal & stable(b) Non causal but stable (d) Non causal & Non stable

[EC : GATE-2017_Paper-1]Ans. (c)

GATE 2017 ECE Session 3 Answer Key

5. In below circuit if magnitude of phase difference between V1 & V2 is 4 at a

angular frequency 0 then what is the value of 0 .........

100 cos t 1

1 1H

V1

V2

[EC : GATE-2017_Paper-1]Ans. (1)6. What is the rank of matrix M

M = 5 10 101 0 23 6 6

(a) 0 (b) 1

(c) 2 (d) 3[EC : GATE-2017_Paper-1]

Ans. (c)7. A good transconductance ampere have the following property

(a) High input & low output resistance (b) Low input & high output resistance

(c) Low input & output resistance (d) High input & output resistance[EC : GATE-2017_Paper-1]

Ans. (a)8. Pole zero pattern of phase lag controller (Lag compensator)

(a) (b)

(c) (d)

[EC : GATE-2017_Paper-1]Ans. (b)

9. If x(t) is periodic is represented by 0 n 0 n 0n 1x(t) a a cos n b sin n

have

0x(t) x( t) x t

then x(t) is

(a) having all an zero & odd terms of bn

(b) having all an zero & even term of bn

(c) having all an & bn zero(d) having odd term of an & bn zero

[EC : GATE-2017_Paper-1]Ans. (a)

10. A system haveP P 1

1q q 1

1

S b SG(S)S a S

into bode plot of this if –60 dB slope at

the probability value of P & q(a) P = 0 q = 3 (b) P = 1 q = 7(c) P = 2 q = 3 (d) P = 3 q = 5

[EC : GATE-2017_Paper-1]Ans. (a)11. In 8085 microprocessor, if clock frequency is 5MHz & time required for each

instruction is 1.4 sec. The number of possible T-states(a) 7 (b) 4(c) 3 (d) 2

[EC : GATE-2017_Paper-1]Ans. (a)

12. If a n+n diode having ND1 = 1018/cm3 & ND2 = 1015/cm3 & kT 25mVq & intrinsic

concentration = 1 × 1010/cm3 Then built in voltage is given by?(a) 0.748 Volt (b) 0.460 Volt(c) 0.288 Volt (d) 0.173 Volt

[EC : GATE-2017_Paper-1]Ans. (d)13. If SOP form of expression if A is MSB & C is LSB is f0 = M0 + M2 + M3 + M5

then expression of f0.(a) AB ABC ABC (b) AC AB ABC

(c) AC AB ABC (d) ABC AC ABC [EC : GATE-2017_Paper-1]

Ans. (b)

14. If f(x) = 2x xe Taylor series approximation of f(x) around x = 0 including all powerof x less than or equal 3.

(a) 1 + x + x2 + x3 (b) 2 331 x x x2

(c) 2 33 71 x x x2 6 (d) 1 + x + 3x2 + 7x3

[EC : GATE-2017_Paper-1]Ans. (c)

15.

1014 1014

NA1 ND

1016 1016

NA2 ND

P N P N

If two diode having doping conc NA1 & NA2 = 1014/cm3 & 1016/cm3. Respectively.

If Reverse bias voltage >> V0, then the ratio of capacitance 2

1

CC . If Reverse bias

has been same value across both diode?[EC : GATE-2017_Paper-1]

Ans. (10)

16.

CLKA B C D

XOR

In given right side SIPO shift register initial value of ABCD is 1101, A is MSB,and D is LSB. Find number of clock after which content is 1111 .....

[EC : GATE-2017_Paper-1]Ans. (1111)17. FSK signal is given by

S(t) = c

c

A cos(20000 t) For ''0 '' symbolA cos(22000 t) For ''1'' symbol

Find time period for which both signal do not interfare .......[EC : GATE-2017_Paper-1]

Ans. (1 msec)

18. A open loop gain is given by

GH = 2k

(S 2S 2)(S 2)

If k is 10 Nyquist plot do not enclose –1 + 0j.If k is 100 Nyquist enclose –1 + 0j.System is(a) Stable for k = 10 and unstable for k = 100(b) Stable for both k = 10, and k = 100(c) Unstable for both k = 10, and k = 100(d) Unstable for k = 10 & stable for k =100

[EC : GATE-2017_Paper-1]Ans. (a)

19. 4 1H

5

1 F36V2

v(t) = 10 cos t

= 3 rad/sec

+ –V1

Find magnitude of 2

1

VV .............

[EC : GATE-2017_Paper-1]Ans. (2.6)

20. 12V

RC = 4k

73k

4k CE

Vi

V0

47k

is very large find voltage gain

Av = 0

i

V ?v

[EC : GATE-2017_Paper-1]Ans. (–160)21. Given MOSFET is in saturation. Given that

n CoxW 1mA / V.L Find ID.

R = 2k1

R = 1k2

RD

NMOS

R = 1ks

VDD = + 12V

[EC : GATE-2017_Paper-1]Ans. (2 mA)

22. Let x(t) be a signal with Nyquist rate 0. Determine the Nyquist rate of dx(t)dt

(a) 0 (b) 20

(c) 20 (d) 02

[EC : GATE-2017_Paper-1]Ans. (a)

23.N-Type

x

Carrier are injected such that carrier profile

217 3

Lo Lo PP

x cmG(x) G 1 , G 10 / cm , D 100L V sec

P hole carrier life time 10–4 sec, q = 1.6 × 10–19C. Find hole diffusion currentdensity.[EC : GATE-2017_Paper-1]

Ans. (16 A/cm2 )24. E - Field component is given by

E = (x y 2jz) exp[j( t kx ky)]

EM wave is

(a) Not polarized (b) Linearly polarized(c) Circular polarized (d) Elliptical polarized

[EC : GATE-2017_Paper-1]Ans. (d)25. Schmitt trigger is given by

–

+V0

2k

1k

+– 3V

Vi

Find threshold voltages when power supply is ± 15V(a) –7V, 3V (b) –3V, +7V

(c) 2V, 6V (d) None of these[EC : GATE-2017_Paper-1]

Ans. (b)

26. A discrete sequence is given by

Output

x[n] {1,2,1}, h(0) 1,

y[n] x[n] h[n] is y[1] 3, y[2] 4

Find (10y[3] + y[4]) ...........

[EC : GATE-2017_Paper-1]Ans. (31)27. A volume R is bound as

x2 + y2 Z3, 0 Z 1 Find volume R.[EC : GATE-2017_Paper-1]

Ans. (10)28. x = 1, function f(x) = x3 + x – 1 solve this function by using Newton-Rapson

method till 2 iteration.[EC : GATE-2017_Paper-1]

Ans. (15)

29. Solve Differential equation 2dy (x y 1)dx

[EC : GATE-2017_Paper-1]Ans. (*)30. The content of accumulator of 5th instruction of the microprocessor 8085

MVI A 78 H

MVI B 33 HADD BCMA

ANI 32H(a) 10 H (b) 01 H

(c) 11 H (d) 20 H[EC : GATE-2017_Paper-1]

Ans. (a)

31.550

B

530520

500

450

A

Contour view of on city in given in which bath point A and B have level then findwhich direction to counter going from A to B

(a) down up (b) down up down

(c) up down (d) up down of

[EC : GATE-2017_Paper-1]

Ans. (a)

32. For a lag compensator the pole zero diagram

Z P

G(s) =2

2k(s s 1)(s s 1)

for unity feedback- The root locus for k

(a) k > 1.5 (b) 0 < k < 1.5

(c) k < 1.5 (d) 0 < k < 1

[EC : GATE-2017_Paper-1]

Ans. (a)

33. What happen if si replaces Ga in GaAs or As in GaAs.

[EC : GATE-2017_Paper-1]

Ans. (*)

34. A = 10v5 Vo

Vin

Find V0 = ?[EC : GATE-2017_Paper-1]

Ans. (*)35. If there are a group of 3 Indian men and 3 foreigner men group. Then how many

ways a group is selected in which at least are one Indian man is present.(a) 56 (b) 52(c) 48 (d) 50

[EC : GATE-2017_Paper-1]Ans. (a)36. S, T, U, V, W, X, Y, Z are sitting in a circular table. U is sitting second to the left

of T and second to the right of W.

VS

Y

T

Z

U

X

W

W in the neighbour of X and V.S is not the neighbour of T.Z is sitting in front of V.

[EC : GATE-2017_Paper-1]Ans. (c)37. Find the person who is third to the left of Y

(a) W (b) X(c) V (d) Z

[EC : GATE-2017_Paper-1]Ans. (b)

38.

12 kVin

5V

4.8k

0

Vin

tT

2V

Input given as shown in fig. if T is large, transistor is in saturation region & VCEsat = 0.2V. So calculate minimum value of .

VBEON = 0.7V

[EC : GATE-2017_Paper-1]

Ans. (0.90)

VCEsat = 0.2V

IC = 5 0.2 1 A4 5k

KVL at input side

Vin – IB × 12 k – 0.7 k = 0

IB = 1.3 0.108 A12k

So = C

B

I 1mA 9.25I 0.108

= 9.25 0.901 10.25

39. s4 + s2 + 1 = 0, poles are

(a) All four, complex poles in LHP

(b) Two poles on the RHP

(c) Three poles on the LHP

(d) All poles line on the imaginary axis

[EC : GATE-2017_Paper-1]

Ans. (b)

40. In a one lane road truck and car are moving with a constant speed of 36 km/hr.Length of the bus and car are Respectively 20 meter and 15 meter and there isa gap after bus and car 10 meter and 5 meter respectively. Calculate the numberof vehicle passed through the lane in one hour

(a) 1440 (b) 770(C) 500 (d) 1000

[EC : GATE-2017_Paper-1]Ans. (a)41. Some table are chair.

All chair are shelf.Atleast some shelf are bench.

(a) at least some bench are table (b) All bench are table(c) at leant some shelf are table (d) All chair are bench

[EC : GATE-2017_Paper-1]

Ans. (c)42. Consider in ASM machine of is 00, 01, 10, 11. If DA and DB are two D filp-flop

and QA QB = 00 initially then

DBDA QB

QA

Din= 1

CLK

[EC : GATE-2017_Paper-1]Ans. (11)43. Find the roots for the initial value of x = 1 using newton raphson method of the

x3 + x = 1[EC : GATE-2017_Paper-1]

Ans. ( 34 )

44. The attunation constant in dB of the given wave R = (.1 + j40), e–l+j30

for = .1Np/sec.

Ans. (0.6868 dB)

45.

12

2k7k

8k

V0

47k 2k

If kT = 25 mV & assume IC & Ie are equal than calculate midband gain o

in

VV

[EC : GATE-2017_Paper-1]

Ans. (–128)