GATE 2017 ECE Session 3 Answer Key

Transcription

1 1. Three pair cubical dice are thrown simultaneously. What is the probability that all three dice have same number is... Ans. ( 1 36 ). The one of the eigen value is real, rest are imaginary the real value is Ans. (b) A GATE 017 ECE Session 3 Answer Key (a).5 (b) 0 (c) 15 (d) 5 3. If x(t) is input of LTI system is given by x(t) = 4 cos 00t + 8 cos 400t. If impulse response of system is given by h(t) = sin 300t t 0 t 600 t 0 & y(t) is output of the system then what is the y(t) max is... Ans. (8) 4. If x(n) & y(n) are input & response respectively. If n x(n) 0 n 0 y(n) = x(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 Ans. (c)

2 5. In below circuit if magnitude of phase difference between V 1 & V is 4 at a angular frequency 0 then what is the value of V 1H 100 cost 1 V 1 Ans. (1) 6. What is the rank of matrix M M = (a) 0 (b) 1 (c) (d) 3 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 8. Pole zero pattern of phase lag controller (Lag compensator) (a) (b) (c) (d) Ans. (b)

3 9. If x(t) is periodic is represented by x(t) a0 an cos n0 bn sin n 0 have x(t) x( t) x t 0 (a) (b) (c) (d) 10. A system have having all a n zero & odd terms of b n having all a n zero & even term of b n having all a n & b n zero having odd term of a n & b n zero S G(S) S b S P P1 1 q a q 1 1S the probability value of P & q n1 then x(t) is into bode plot of this if 60 db slope at (a) P = 0 q = 3 (b) P = 1 q = 7 (c) P = q = 3 (d) P = 3 q = 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) 1. If a n + n diode having N D1 = /cm 3 & N D = /cm 3 & kt 5mV q & intrinsic concentration = /cm 3 Then built in voltage is given by? (a) Volt (b) Volt (c) 0.88 Volt (d) Volt Ans. (d) 13. If SOP form of expression if A is MSB & C is LSB is f 0 = M 0 + M + M 3 + M 5 then expression of f 0. Ans. (b) (a) AB ABC ABC (b) AC AB ABC (c) AC AB ABC (d) ABC AC ABC

4 14. If f(x) = e Taylor series approximation of f(x) around x = 0 including all power of x less than or equal 3. (c) Ans. (c) x x (a) 1 + x + x + x 3 (b) 1 x 3 x 7 x 6 1 x 3 x x 3 3 (d) 1 + x + 3x + 7x N A1 N D N A N D P N P N If two diode having doping conc N A1 & N A = /cm 3 & /cm 3. Respectively. C If Reverse bias voltage >> V 0, then the ratio of capacitance C has been same value across both diode? 1. If Reverse bias Ans. (10) 16. XOR CLK A B C D 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 Ans. (1111) 17. FSK signal is given by A S(t) = c cos(0000t) For ''0'' symbol Accos(000t) For ''1'' symbol Find time period for which both signal do not interfare... Ans. (1 msec)

5 18. A open loop gain is given by k GH = (S S )(S ) 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 = V H v(t) = 10 cos t = 3 rad/sec 1 F 36 5 V Find magnitude of Ans. (.6) 0. 47k V V... 1 R C = 4k 1V V 0 V i 73k 4k C E

6 is very large find voltage gain A v = V 0? v i Ans. ( 160) 1. Given MOSFET is in saturation. Given that n C ox W 1mA / V. L Find I D. V DD = + 1V R = k 1 R D NMOS R = 1k R s = 1k Ans. ( ma). Let x(t) be a signal with Nyquist rate 0. Determine the Nyquist rate of dx(t) dt (a) 0 (b) 0 0 (c) 0 (d)

7 3. N-Type x Carrier are injected such that carrier profile 17 3 G(x) G x cm Lo 1, GLo 10 / cm, DP 100 L P V sec P hole carrier life time 10 4 sec, q = C. Find hole diffusion current density. Ans. (16 A/cm ) 4. E - Field component is given by Ans. (d) E = (xˆ ŷ jẑ) exp[j( t kx ky)] EM wave is (a) Not polarized (b) Linearly polarized (c) Circular polarized (d) Elliptical polarized 5. Schmitt trigger is given by V i + k V 0 1k + 3V Find threshold voltages when power supply is ± 15V (a) 7V, 3V (b) 3V, +7V (c) V, 6V (d) None of these Ans. (b)

8 6. A discrete sequence is given by Output Ans. (31) x[n] {1,,1}, h(0) 1, y[n] x[n] h[n] is y[1] 3, y[] 4 Find (10y[3] + y[4]) A volume R is bound as Ans. (10) x + y Z 3, 0 Z 1 Find volume R. 8. x = 1, function f(x) = x 3 + x 1 solve this function by using Newton-Rapson method till iteration. Ans. (15) dy 9. Solve Differential equation (x y 1) dx Ans. (*) 30. The content of accumulator of 5 th instruction of the microprocessor 8085 MVI A 78 H MVI B 33 H ADD B CMA ANI 3H (a) 10 H (b) 01 H (c) 11 H (d) 0 H

9 31. A B 450 Contour view of on city in given in which bath point A and B have level then find which direction to counter going from A to B (a) down up (b) down up down (c) up down (d) up down of 3. For a lag compensator the pole zero diagram Z P k(s s 1) G(s) = for unity feedback- The root locus for k (s s 1) (a) k > 1.5 (b) 0 < k < 1.5 (c) k < 1.5 (d) 0 < k < What happen if si replaces Ga in GaAs or As in GaAs. Ans. (*)

10 V in A = 10 v V o Ans. (*) Find V 0 =? 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) 5 (c) 48 (d) 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. V S Y W T X Z U W in the neighbour of X and V. S is not the neighbour of T. Z is sitting in front of V. Ans. (c) 37. Find the person who is third to the left of Y (a) W (b) X (c) V (d) Z Ans. (b)

11 38. 5V 4.8k V in V in 1 k V 0 T t Input given as shown in fig. if T is large, transistor is in saturation region & V CE sat = 0.V. So calculate minimum value of. V BEON = 0.7V Ans. (0.90) V CEsat = 0.V I C = A 4 5k KVL at input side V in I B 1 k 0.7 k = 0 I B = A 1k So = IC 1mA 9.5 I B = s 4 + s + 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 Ans. (b)

12 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 0 meter and 15 meter and there is a gap after bus and car 10 meter and 5 meter respectively. Calculate the number of vehicle passed through the lane in one hour (a) 1440 (b) 770 (C) 500 (d) Some table are chair. Ans. (c) 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 4. Consider in ASM machine of is 00, 01, 10, 11. If D A and D B are two D filp-flop and Q A Q B = 00 initially then Q A D A D B Q B D in = 1 Ans. (11) CLK 43. Find the roots for the initial value of x = 1 using newton raphson method of the x 3 + x = 1 Ans. ( 3 4 )

13 44. The attunation constant in db of the given wave R = (.1 + j40), e l+j30 for =.1N p /sec. Ans. ( db) 1 7k k k k 8k V 0 If kt = 5 mv & assume I C & I e are equal than calculate midband gain Ans. ( 18) V V o in