EC GATE 2010 ww.gateforum.com

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1 E GATE 00 ww.gateforum.com E GATE 00 Answer Keys 3 D 4 A 5 D 6 B 7 A 8 B 9 A 0 A D D 3 B 4 A 5 6 D 7 B 8 B 9 A 0 B 3 D A 7 D B 3 D 3 A 33 A 34 A 35 B D 38 B 39 D 40 4 B D 45 D 46 A 47 B 48 B 49 A 50 D A 54 B 55 D 56 B 57 A 58 D D D 64 B 65 B Eplanations:-. For a real skew symmetric matri the non-zero eigen values are all pure imaginary and thus occurs in comple conjugate pair.. Since given waveform is even, thus it will have only cosine terms. Function f(t) has more negative value then positive, so it will have negative D omponent. 3. d d n() 0 L S n() 0, n() Ae Be L n( ) 0 B 0, n(0) k B k Bandwidth, Thus it is maimum at resonance. R Z R X X i L 9. Given circuit after removing E will behave as current-series feedback. Overall voltage gain will decrease as feedback signal comes into picture and since it is current-series feedback, input impedance increases. written permission. Discuss GATE 00 question paper at

2 E GATE 00 ww.gateforum.com 0. By rearranging R V0 R V R i v R R 3 V 0. A B A.B A B A B A B AB AB A B AB AB A B AB AB A B A B AB. B A F A B A A so, F when AAAA AAAA A7A 6A 5A 4A3A A A 0 D o o o o o o o o o o F F 5, 0,3, 4 4. X( z) 5z 4z 3 5. h ( n) delay by, h n delay by, h n *h n delay by 3 7. onstruct a signal flow graph s R( s ) Y( s) s written permission. Discuss GATE 00 question paper at

3 E GATE 00 ww.gateforum.com y s [ 0 ] s R( s) s s s 8. y( t) M( ω ) ( t) wp ω p ω p ω p, 4 p 4p 3p 4, p R 0 j R s LRs 0j 0. A DSB V V m D SSB V c 0 m m B m iswithoutovermodulation. Ac 6 36 Power 8 [ S] [ ]. S S 0 lossy S Reciprocal 3. R G Distribution less L 0. RG and Z0 RG G 500 α α 0.00NP / m h( t) s( T t) 5. P AV E η u 0 r π 0π 0π ε 4 r dy ln d 6. y ln, 0, e( ma) 7. 4 heads & 0 tail or 3 head & tail P 6 written permission. Discuss GATE 00 question paper at 3

4 8. A.d ( ya ˆ ˆ ay) ( ˆad ˆ aydy) E GATE 00 ww.gateforum.com (y d dy) d 3 d dy dy z 0 z z 9. z ( z ), ( z ) ( z), ( z ) ( z) 3. s3s ( ) ( ) s 4s ( k 3) 3 s 4s k 3 s s 0 3s k 4 k 3 3. i( f) 0.5, i( i) 0.75 π f ( i j) i t V i i e e 000t V Ls s Ls R 0R 0 j R s LRs 0j 00 ω 0 3 ~ Ls R v s 34. i 3 i 3 0v KVL 0 i 3 i 0 0 4i i 0 Power 0 i QA QB Q written permission. Discuss GATE 00 question paper at 4

5 E GATE 00 ww.gateforum.com 38. When Vi 0 V0 5 Only B option matches 39. D AB F Σm, 3,5, 7, 8, 9, 40. A B arry flag 0 RAR will A XRA B ( s ) ( s )( s 3) s ( s )( s 3) t 3t y s, y t e e u t 4. S true, S False ( meter stable nor causal ) S3 True 43. fs fm Mz 44. E( s) sr ( s) G s Gc s H s G( s) G ( s) s 0 so, G s should be maimum for low error G s s 0 s y < 0 y > 0 η 0π η 40π [ ] [ ] 40 0 π ρ 40 0 π ρ Ve E will change direction & M will not change its direction, Direction of M for incident field is in, so direction of M in the reflected field is also is in. M E ρ 4 η 0π 0π i written permission. Discuss GATE 00 question paper at 5

6 E GATE 00 ww.gateforum.com j 60 30j ρ 60 30j j Ω ρ USWR.64 ρ 60 30j Z R ( R Br ) s s B e R s r.475 c RB Bre R RL.58kV 50. Let us take two state variable as shown and Us s 0.5 s y( s), v s 0 Us 0 y ( s) [ ] 54. S n ( f) N 0 N0 R ( τ ) δ( τ) eist in fourier transform pair N0 N0 6 4 R( 0 ), Power 0 0 Variance which is equal to power power since mean is zero α 0 d Probability of error a/ α n 7 6 α a/ α e 0.5 e 0.5 e 0.5 e 56. ircuitous means round about or not direct. Therefore the closest in meaning will be indirect 57. A worker who is inactive or not working is termed as unemployed, similarly land which is inactive or not in use is called Fallow. written permission. Discuss GATE 00 question paper at 6

7 E GATE 00 ww.gateforum.com 58. The clue in this sentence is If we manage to our natural resources and better planet. This implies that the blank should be filled by a word which means preserve or keep for long time. Therefore the word conserve is the right answer. 59. The key words in the statement are casual remarks and lack of seriousness. The blank should be filled with a word meaning showed or revealed. Hence, betrayed is the correct answer. 60. Representing the given information in the Venn diagram, we have μ 5 n(h) 5 a 0 n(f) 7 b n? Let the number of people who play only hockey a The number of people who play only football b Now, a n(h) b n(f) learly, a b 0 n 5 n n 3 The number of people who play neither Hockey nor Football is 3 6. Among the answer choices, the three options B, and D can be inferred from the passage. But the main essence of the passage is that chemical agents are being used my military establishments in warfare which is not desirable. Therefore option is the statement which best sums up the meaning of the passage. 6. Given, Adding units digits i.e , but given as 5, which is 3 8 and also is carry forwarded to the tens place. i.e., Here, 7 3 i.e., 8 3 and is carry forwarded to hundreds place Now, the sum of digits in hundred s place is 4 written permission. Discuss GATE 00 question paper at 7

8 E GATE 00 ww.gateforum.com i.e., Using the same logic, we have Sum of units digits 3, sum of tens digit i.e. 0 - and carry forward and Sum of hundreds digits i.e., and one carry forward. 63. Given, 5 skilled workers can build a wall in 0 days i.e., skilled worker can build the same wall in 00 days The capacity of each skilled worker is 00 8 semi-skilled workers can build a wall in 5 days i.e., semi-skilled worker can build the same wall in 00 days the capacity of each semi-skilled worker is 00 Similarly, the capacity of unskilled worker is 300. Now, the capacity of skilled6 semi-skilled5 unskilled workers is The required numbers of days is The given digits are,,3,3,3,4,4,4,4 we have to find the numbers that are greater than 3000 The first digit can be 3 or 4 but not. Now, let us fi the first, second and third digits as 3,, and then the fourth place can be filled in 3 ways. i.e., 3 ways 3 or 3 or 4 the number of ways is 3. Similarly, we fi first, third and fourth places as 3, and respectively, so the second place can be filled in 3 ways again i.e., 3 or 3 or 4 The number of ways is 3. Now, we fi first, second and fourth places just as previous cases and we obtain the same result. The number of ways is 3 so; the total number of ways is 9. Similarly this can do by fiing the numbers as 3 and 4 (instead of ) and thereby we obtain the 9 ways in each case. The number of numbers greater than 3000 starting with 3 is 7 Similarly by taking 4 as the first digit and applying the same process, we get 7 numbers written permission. Discuss GATE 00 question paper at 8

9 E GATE 00 ww.gateforum.com The total number of numbers that are greater than 3000 is But, 3 and 4 is not possible as there are only two s (given), 3333 is also not possible as there are only three 3 s (given) The total number of numbers that are greater than 3000 is i) H G > I S ii) G - S Meaning G & S will be net to each other in the order. So the option A is ruled out. G not oldest S not youngest iii) No twins. Going by the options, we will try to solve the equation, Taking an eample with youngest aged, we can try to solve the equation, and correct the age (started with ages 4,3,,) to suit condition (i) and (ii) which gives 5,4,3, S I 4 Generalizing, we can take their ages in terms of I's age, G I 3 In this case, H G > I S H I Since I 5 > I 4 I I I In this order, G is always less than I and H is always less than S. G S H So G<I and H<S Implies GH < I S, all values are positive Defies condition i) Hence incorrect. I H In this order H< I, G<S Hence H G < I S S Defies ondition i) G Hence incorrect. written permission. Discuss GATE 00 question paper at 9

GATE 2010 Electronics and Communication Engineering

GATE 2010 Electronics and Communication Engineering Q.1 Q.25 carry one mark each. Q1. The eigen values of a skew-symmetric matrix are (A) Always zero (B) Always pure imaginary (C) Either zero or pure imaginary