GATE. Topicwise Solved Paper. Year By RK Kanodia & Ashish Murolia. For more GATE Resources, Mock Test and Study material

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1 GATE ELECTRONICS & COMMUNICATION Toicwie Solved Paer Year 996 By RK Kanodia & Ahih Murolia F me GATE Reource, Mock Te and Sudy maerial Join he Communiy h://

2 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page UNIT ENGINEERING MATHEMATICS ONE MARK. The maximum value of q unil which he aroximaion in q. q hold o wihin % err i (A) c (B) 8c (C) 5c (D) 9c. The minimum eigen value of he following marix i R 5 V S W S5 7W S 7 5W T X (A) (B) (C) (D). A olynomial fx () ax + ax + ax + ax a wih all coefficien oiive ha (A) no real roo (B) no negaive real roo (C) odd number of real roo (D) a lea one oiive and one negaive real roo TWO MARKS. Le A be an m# n marix and B an n# m marix. I i given ha deerminan ^Im + ABh deerminan ^In + BAh, where I k i he k# k ideniy marix. Uing he above roery, he deerminan of he marix given below i R V S W S W S W S W S W T X (A) (B) 5 (C) 8 (D) 6 (C) x (D) TWO MARKS d y() dy().8 Conider he differenial equaion + + y () d() d d dy wih y () and d dy The numerical value of i d (A) + (B) (C) (D).9 The direcion of vec A i radially ouward from he igin, wih n A kr. where r x + y + z and k i a conan. The value of n f which d : A i (A) (B) (C) (D). A fair coin i oed ill a head aear f he fir ime. The SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy robabiliy ha he number of required oe i odd, i (A) / (B) / (C) / (D) /. The maximum value of fx () x 9x+ x+ 5 in he inerval [ 6, ] i (A) (B) 5 (C) (D) 6. Given ha 5 A > and I H > H, he value of A i (A) 5A+ I (B) 9A+ I (C) 7A+ 5I (D) 7A+ I ONE MARK.5 Wih iniial condiion x(). 5, he oluion of he differenial equaion dx + x, i d (A) x (B) x (C) x (D) x.6 Given fz (). z + z + If C i a couner clockwie ah in he z lane uch ha z +, he value of fzdz () # i j C (A) (B) (C) (D).7 If x, hen he value of x x i (A) e / (B) e / ONE MARK. Conider a cloed urface S urrounding volume V. If rv i he oiion vec of a oin inide S, wih n he uni nmal on S, he value of he inegral ## 5rv $ nds i (A) V (B) 5V (C) V (D) 5V S. dy The oluion of he differenial equaion ky, y() c i dx (A) x ce ky (B) x ke cy (C) y ce kx (D) y ce.5 The value of he inegral # z + dz where c i he circle ( z + z + 5 c ) z i given by (A) (B) / (C) /5 (D)

3 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page TWO MARKS.6 A numerical oluion of he equaion fx () + x can be obained uing Newon Rahon mehod. If he aring value i x f he ieraion, he value of x ha i o be ued in he nex e i (A).6 (B).79 (C).69 (D).6.7 The yem of equaion x+ y+ z 6 x+ y+ 6y x+ y+ lz m ha NO oluion f value of l and μ given by (A) l 6, m (B) l 6, m Y (C) l Y 6, m (D) l Y 6, m TWO MARKS. If e x, hen y ha a (A) maximum a x e (B) minimum a x e (C) maximum a x e (D) minimum a x e. A fair coin i oed indeendenly four ime. The robabiliy of he even he number of ime head hown u i me han he number of ime ail hown u (A) /6 (B) / (C) / (D) 5/6. If Av xyax+ x a y, hen # Av $ dlv over he ah hown in he figure i C.8 A fair dice i oed wo ime. The robabiliy ha he econd o reul in a value ha i higher han he fir o i (A) /6 (B) /6 GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii (C) 5/ (D) / ONE MARKS.9 The eigen value of a kewymmeric marix are (A) alway zero (B) alway ure imaginary (C) eiher zero ure imaginary (D) alway real. The rigonomeric Fourier erie f he wavefm f () hown below conain (A) only coine erm and zero value f he dc comonen (B) only coine erm and a oiive value f he dc comonen (C) only coine erm and a negaive value f he dc comonen (D) only ine erm and a negaive value f he dc comonen. A funcion nx () aified he differenial equaion d n() x nx () dx L where L i a conan. The boundary condiion are : n() K and n( ). The oluion o hi equaion i (A) nx () Kex(/ xl) (B) nx () Kex( x/ L) (C) nx () Kex( xl / ) (D) nx () Kex( xl / ) (A) (B) (C) (D).5 The reidue of a comlex funcion xz () z zz ( )( z) a i ole are (A), and (B), and (C), and (D), and dy() x.6 Conider differenial equaion yx () x, wih he iniial dx condiion y(). Uing Euler fir der mehod wih a e ize of., he value of y(.) i (A). (B). (C).6 (D)..7 Given () + ; + + ( ) E. If lim f (), hen he value " of k i (A) (B) (C) (D) F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// 9 ONE MARK.8 The der of he differenial equaion dy dy y e d d + c m + i (A) (B) (C) (D).9 A fair coin i oed ime. Wha i he robabiliy ha only he fir wo oe will yield head? (A) c m (B) C b l (C) c m (D) C b l

4 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page. If fz () c+ cz + fz (), hen # dz i given by z uni circle (A) c (B) ( + c) (C) jc (D) ( + c) 9 TWO MARKS. The Tayl erie exanion of in x x a x i given by ( x ) (A) + ( x ) +... (B) +...!! ( x ) (C) ( x ) +... (D) !!. Mach each differenial equaion in Grou I o i family of oluion curve from Grou II Grou I Grou II dy y A.. Circle dx x dy y B.. Sraigh line dx x dy C. x. Hyerbola dx y dy D. x dx y (A) A,B,C,D (B) A,B,C,D (C) A,B,C,D (D) A,B,C,D. The Eigen value of following marix are R V S 5W S 6W S W T X (A), + 5 j, 6 j (B) 6+ 5, j + j,j (C) + j, j, 5+ j (D), + j, j 8 ONE MARKS. All he four enrie of he # marix P G are nonzero, and one of i eigenvalue i zero. Which of he following aemen i rue? (A) (B) (C) (D) +.5 The yem of linear equaion x+ y 7 x+ y 6 ha (A) a unique oluion (B) no oluion (C) an infinie number of oluion (D) exacly wo diinc oluion.6 The equaion in() z ha (A) no real comlex oluion (B) exacly wo diinc comlex oluion (C) a unique oluion (D) an infinie number of comlex oluion.7 F real value of x, he minimum value of he funcion fx () ex() x+ ex( x) i (A) (B) (C).5 (D).8 Which of he following funcion would have only odd ower of x in i Tayl erie exanion abou he oin x? (A) in( x ) (B) in( x ) (C) co( x ) (D) co( x ).9 Which of he following i a oluion o he differenial equaion dx() + x ()? d (A) x () e (B) x () e (C) x () (D) x () 8 TWO MARKS. The recurion relaion o olve x e uing Newon Rahon mehod i SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy (A) x n+ e x xn (C) x ( + x ) e + e n n+ n x n. The reidue of he funcion fz () (B) x x e (D) x n+ (A) (B) 6 (C) (D) 6 n x n xn xn e ( xn) xn x e n+ n a z i ( z + ) ( z ). Conider he marix P G. The value of e i e e e e e + e e e (A) > H (B) > H e e 5e e e e e + e 5e e e e e e e e (C) > H (D) > H e 6e e + 6 e + e e + e. In he Tayl erie exanion of ex() x + in() x abou he oin x, he coefficien of ( x ) i (A) ex( ) (B) 5. ex( ) (C) ex( ) + (D) ex( ). The value of he inegral of he funcion gxy (,) x+ y along he raigh line egmen from he oin (,) o he oin (,) in he x y lane i (A) (B) 5 (C) (D) 56.5 Conider oin P and Q in he x y lane, wih P (,) and Q Q (,). The line inegral # ( xdx + ydy) along he emicircle P wih he line egmen PQ a i diameer (A) i (B) i

5 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page (C) i (D) deend on he direcion (clockwie aniclockwie) of he emicircle.5 Three funcion f(), f () and f () which are zero ouide he inerval [, T] are hown in he figure. Which of he following aemen i crec? 7 ONE MARK.6 The following lo how a funcion which varie linearly wih x. The value of he inegral I # ydx i (A). (B).5 (C). (D) 5..7 F x <<, coh ( x ) can be aroximaed a (A) x (B) x GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii (C) x (D) x (A) f () and f () are hogonal (B) f () and f () are hogonal (C) f () and f () are hogonal D) f () and f () are honmal.5 If he emicircular conrol D of radiu i a hown in he figure, hen he value of he inegral # d i ( ) D.8 lim q " q in q b l i (A).5 (B) (C) (D) no defined.9 Which one of following funcion i ricly bounded? (A) /x (B) e x (C) x (D) e x.5 F he funcion e x, he linear aroximaion around x i (A) ( xe ) (B) x (C) 6+ ( (D) e 7 TWO MARKS dy.5 The oluion of he differenial equaion k y y dx under he boundary condiion (i) y y a x and (ii) y y a x, where ky, and y are conan, i (A) y ( y y )ex x a + y k k (B) y ( y y )ex x a + y k k (C) y y y inh x ^ h a + y k k (D) y y y ex x ^ h a + y k k.5 The equaion x x + x i o be olved uing he Newon Rahon mehod. If x i aken a he iniial aroximaion of he oluion, hen nex aroximaion uing hi mehod will be (A) / (B) / (C) (D) / (A) j (B) j (C) (D).55 I i given ha X, X... X M a M nonzero, hogonal vec. The dimenion of he vec ace anned by he M vec X, X,... XM, X, X,... XM i (A) M (B) M + (C) M (D) deenden on he choice of X, X,... F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// Conider he funcion fx () xx. The maximum value of fx () in he cloed inerval [, ] i (A) 8 (B) (C) 5 (D) indeerminae.57 An examinaion coni of wo aer, Paer and Paer. The robabiliy of failing in Paer i. and ha in Paer i.. Given ha a uden ha failed in Paer, he robabiliy of failing in Paer i.6. The robabiliy of a uden failing in boh he aer i (A).5 (B).8 (C). (D).6 X M

6 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 5 6 ONE MARK R V S W.58 The rank of he marix S W i S W (A) T X (B) (C) (D) ##, where P i a vec, i equal o (A) P## P P.59 P (B) P+ ( # P) (C) P+ # P (D) $ ( P) P.6 ## ( # P) $ d, where P i a vec, i equal o (A) P$ dl (B) (C) (D) # # # ### $ # # P$ dl # P$ dl Pdv.6 A robabiliy deniy funcion i of he fm a x x () Ke, x! (, ) The value of K i (A).5 (B) (C) 5a. (D) a.6 A oluion f he differenial equaion x o () + x () d() wih iniial condiion x ( ) i (A) e u() (B) e u() (C) e u() (D) eu() 6 TWO MARKS.6 The eigenvalue and he creonding eigenvec of # marix are given by Eigenvalue Eigenvec l 8 v G l v G The marix i (A) 6 6 G (B) 6 6 G (C) G (D) 8 8 G.6 F he funcion of a comlex variable W ln Z (where, W u+ jv and Z x+ jy, he u conan line ge maed in Z lane a (A) e of radial raigh line (B) e of concenric circle (C) e of confocal hyerbola (D) e of confocal ellie.65 The value of he conan inegral # z + dz i oiive ene i z j (A) j (B) j (C) (D).66 The inegral # in qdq i given by (A) (B) (C) (D) 8.67 Three comanie XY, and Z uly comuer o a univeriy. The ercenage of comuer ulied by hem and he robabiliy of hoe being defecive are abulaed below Comany % of Comuer Sulied Probabiliy of being ulied defecive X 6 %. Y %. Z %. Given ha a comuer i defecive, he robabiliy ha wa ulied by Y i (A). (B). (C). (D)..68 F he marix G he eigenvalue creonding o he eigenvec G i SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy (A) (B) (C) 6 (D) 8 dy.69 F he differenial equaion dx are + ky he boundary condiion (i) y f x and (ii) y f x a The fm of nonzero oluion of y (where m varie over all ineger) are (A) y A in mx / m (B) y A co mx / m a a m m m mx (C) y / Am x a (D) y / Am e a m.7 A x increaed from o, he funcion fx () e x + e (A) monoonically increae (B) monoonically decreae (C) increae o a maximum value and hen decreae (D) decreae o a minimum value and hen increae 5 ONE MARK.7 The following differenial equaion ha dy dy c y m+ c + + d d m x (A) degree, der (B) degree, der (C) degree, der (D) degree, der.7 A fair dice i rolled wice. The robabiliy ha an odd number will follow an even number i (A) / (B) /6 (C) / (D) / m x

7 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 6.7 A oluion of he following differenial equaion i given by dy dy 5 + 6y dx dx x x (A) y e + e x x (B) y e + e (C) y e x + x x (D) y e + e x 5 TWO MARKS.7 In wha range hould Re() remain o ha he Lalace ranfm of he funcion e ( a+ ) + 5 exi. (A) Re() > a+ (B) Re() > a+ 7 (C) Re() < (D) Re() > a The derivaive of he ymmeric funcion drawn in given figure will look like GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii Le,. A a G and A G. Then ( a+ b) b (A) 7/ (B) / (C) 9/6 (D) /.79 The value of he inegral I ex x # c dx 8 m i (A) (B) (C).8 Given an hogonal marix R V S W S W A S W S W T X 6 AA i R V S W S (A) W S W S W S W T X R V S W S W (C) S W S W T X (D) R S S (B) S S S T R S S (D) S S S T V W W W W W X V W W W W W X.76 Mach he following and chooe he crec combinaion: Grou I Grou E. NewonRahon mehod. Solving nonlinear equaion F. Rungekua mehod. Solving linear imulaneou equaion G. Simon Rule. Solving dinary differenial equaion H. Gau eliminaion. Numerical inegraion 5. Inerolaion 6. Calculaion of Eigenvalue (A) E6,F,G5,H (B) E,F6,G,H (C) E,F,G,H (D) E5,F,G,H F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// Given he marix G, he eigenvec i (A) G (B) G (C) G (D) G

8 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 7 SOLUTIONS. Oion (B) i crec. Here, a we know Lim in q. q " bu f % err, we can check oion (B) fir, q 8 c 8 c#. 8c in q in 8c. 9 % err.. 9 %. %. 9 # 9 Now, we check i f q 5c q 5c 5 c#. 87 8c in q in 5c. 77 % err %. 87 o, he err i me han %. Hence, f err le han %, q 8c can have he aroximaion in q. q. Oion (A) i crec. F, a given marix 6 A@ he eigen value i calculaed a A li where l give he eigen value of marix. Here, he minimum eigen value among he given oion i l We check he characeriic equaion of marix f hi eigen value A li A (f l ) ^6 9h5^5 h+ ^5 h 55 + Hence, i aified he characeriic equaion and o, he minimum eigen value i l. Oion (D) i crec. Given, he olynomial fx ^ h ax + ax + ax + ax a Since, all he coefficien are oiive o, he roo of equaion i given by fx ^ h I will have a lea one ole in righ hand lane a here will be lea one ign change from ^a h o ^a h in he Rouh marix column. Alo, here will be a creonding ole in lef hand lane i.e.; a lea one oiive roo (in R.H.P) and a lea one negaive roo (in L.H.P) Re of he roo will be eiher on imaginary axi in L.H.P. Oion (B) i crec Conider he given marix be R V S W S W Im + AB S W S W S W T X where m o, we obain R V R S W S S W S AB S W S S W S S W S T X T R V R V S W SW S W SW S S W S W W S W S W SW Hence, we ge T X T X SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy R V SW SW A S S W, B 8B W SW T X R V Therefe, BA 8B SW SW S S W W SW From he given roery T X De ^Im + ABh De^Im + BAh R V ZR V _ S W ] S W b S W ] S W b & DeS S W De[ S + W W ` S W S W ] S W b T X \ T X a + 5 Noe : Deerminan of ideniy marix i alway..5 Oion (D) i crec. dx d dx d dx d + x + x V W W W W W X 6@ + Px Q (General fm) # # Inegraing fac, IF e Pd ln e e Soluion ha he fm, # # x# IF ^Q# IFhd+ C x# ()() d+ C

9 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 8 Taking he iniial condiion, So,.6 Oion (C) i crec. fz () z + z + GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii x + C x() C & C x & x fzdz () # um of he reidue of he ole which lie j C inide he given cloed region. C & z + Only ole z inide he circle, o reidue a z i. fz () z + ( z + )( z + ) ( z+ )( z+ ) lim z " ( z + )( z + ) So fzdz () # j C.7 Oion (A) i crec. x i co + i in So, x e i x x e i x ^ h & e i i ^ h e.8 Oion (D) i crec. d y() dy() + + y () d() d d By aking Lalace ranfm wih iniial condiion dy ; Y ()y() [ y() y()] Y() d E + + & 6Y () + 6Y () + Y () Y ()[ + + ] Y () + + L We know ha, If, y () Y () hen, dy() d So, Y() y() L Y() y() () + ( + + ) ( + + ) Y() y() ( + ) ( + ) ( + ) + + ( + ) Taking invere Lalace ranfm A +, dy d dy() d e u() + e u() e Oion (A) i crec. Divergence of A in herical codinae i given a d :A ( ) r r r A r ( ) r r kr n+ k ( n ) r n+ + r n kn ( + ) r (given) n + & n. Oion (C) i crec. Probabiliy of aearing a head i. / If he number of required oe i odd, we have following equence of even. H, TTH, TTTTH,... 5 Probabiliy P +... b + + l b l P. Oion (B) i crec. fx () x 9x + x+ 5 df() x x 8x+ dx & df() x x 6x+ 8 dx x, x d f() x 6x 8 dx d f() x F x, 8 6 < dx So a x, fx () will be maximum fx () max () 9() + () Oion (B) i crec. Characeriic equaion. A li 5 l l 5l+ l + 6 F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// l + 5l+ 6 Since characeriic equaion aifie i own marix, o A + 5A+ 6 & A 5A6I Mulilying wih A A + 5A + 6A A + 5( 5A 6 I) + 6A A 9A+ I. Oion (D) i crec. From Divergence heem, we have ### $ v Adv v A v $ nd #

10 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 9 The oiion vec rv ^ux x + uy y + uz z h Here, Av 5rv, hu $ A u u u c x + y + z : ux x + uy y + uz z x y z m ^ h dx dy dz c dx dy dz m # 5 5 So, ## 5rv $ nd ### 5dv 5V. Oion (C) i crec. We have dy dx ky Inegraing dy # kdx+ A y # ln y kx + A Since y() c hu ln c A So, we ge, ln y kx + ln c kx ln y ln e + ln c y ce kx.5 Oion (A) i crec. C R Inegral i # z + dz where C i circle z z + z+ 5 C # fzdz () if ole are ouide C. C Now z + z+ 5 ( z + ) + Thu z,! j & z, > So ole are ouide he uni circle..6 Oion (C) i crec. We have fx () x+ x fl () x + x Subiuing x we ge fl ( x ). 555 and fx ( ) +. Newon Rahon Mehod fx ( ) x x f l ( x) Subiuing all value we have x Oion (B) i crec. Wriing AB : we have R V S : 6 W S 6 : W S l : mw T X Aly R" R R R V S : 6 W S 6 : W S l6 : mw T X F equaion o have oluion, rank of A and AB : mu be ame. Thu f no oluion; l 6, m!.8 Oion (C) i crec. Toal oucome are 6 ou of which favable oucome are : (, ), (, ), (, ), (, 5), (, 6), (, ), (, ), (, 5), (, 6); (, ), (, 5), (, 6), (, 5), (, 6), (5, 6) which are 5. Thu PE ( ) No. of favourable oucome 5 No. of oal oucome Oion (C) i crec. Eigen value of a Skewymmeric marix are eiher zero ure imaginary in conjugae air.. Oion (C) i crec. F a funcion x () rigonomeric fourier erie i o / n n n x () A + [ A co nw+ B in nw] Where, A o () T # xd T " fundamenal eriod A n SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy T x ()conwd T # T B n x ()inn d T # w T F an even funcion x (), Bn Since given funcion i even funcion o coefficien B, only coine and conan erm are reen in i fourier erie rereenaion. Conan erm : A T/ xd () T # T/ T/ Ad Ad T/ T :# + # D T/ T/ T TA A T A : D Conan erm i negaive.. Oion (D) i crec. Given differenial equaion d n() x nx () dx L Le nx () Ae lx l lx So, Al e Ae L l L x & l! Boundary condiion, n( ) o ake nx () Ae x L L l L n() Ae K & A K So, nx () Ke (/ xl). Oion (A) i crec. Given ha e y x x ln e y ln x x y ln x x dy Now + ln x^x x dx xx h ln x x F maxima and minima : dy ( ln x) dx x ln x " x e n

11 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page d y Now ln x dx x x x x b l b l ln x + x x x d x + < dy e e e a x e So, y ha a maximum a x e. Oion (D) i crec. Accding o given condiion head hould come ime ime P( Head come ime ime) C C b l + b l b l : 6 + : : Oion (C) i crec. A v xyax+ x ay dl v dxax+ dyay # Av : dl v ( xyax+ x ay) : ( dxax+ dyay) C C # GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii # ( xydx + x dy) C / / xdx xdx # + # + # dy + dy / / # [ ] [ ] : D + : D Oion (C) i crec. Given funcion Xz () z zz ( )( z) Pole are locaed a z, z, and z A Z reidue i R z: X() z Z # ( )( ) a z, R ( Z) : X( Z) Z # ( ) A z, R ( z) : X( z) z # ( ).6 Oion (B) i crec. Taking e ize h., y() x y dy dy x+ y yi+ yi+ h dx dx y +. ( ).. y +. (. ).... y # From able, a x., y( x. )..7 Oion (D) i crec. Given ha f () L + ; + + ( K) E lim f () " By final value heem lim f () lim F() " " : ( + ) lim " + + ( K ) ( + ) lim " [ + + ( K )] K K.8 Oion (B) i crec. The highe derivaive erm reen in DE i of nd der..9 Oion (C) i crec. Number of elemen in amle ace i. Only one elemen " HHTTTTTTTT,,,,,,,,,, i even. Thu robabiliy i. Oion (C) i crec. We have fz () c+ cz () f () z fz c c z z z z( + c) + c z Since f () z ha double ole a z, he reidue a z i z( + c) + c Re f () z z lim z. f ( z) lim z. z " z " c m c z Hence [ + fz ( )] # f () z dz # dz j [Reidue a z ] z uni circle uni circle jc. Oion (D) i crec. We have fx () in x x Subiuing x y,we ge in( y + ) in y fy ( + ) ( in y ) y y y... y y 5 y y c + m! 5! F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// y y fy ( + ) ! 5! Subiuing x y we ge ( x ) ( x ) fx () ! 5!. Oion (A) i crec. (A) dy y dx x dy # dx # y x log y log x+ log c

12 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page y cx Sraigh Line Thu oion (A) and (C) may be crec. (B) dy y dx x dy # dx # y x log y log x+ log c log y log + log c x y c x Hyerbola. Oion (D) i crec. Sum of he rincial diagonal elemen of marix i equal o he um of Eigen value. Sum of he diagonal elemen i +.In only oion (D), he um of Eigen value i.. Oion (C) i crec. The roduc of Eigen value i equal o he deerminan of he marix. Since one of he Eigen value i zero, he roduc of Eigen value i zero, hu deerminan of he marix i zero. Thu.5 Oion (B) i crec. The given yem i x 7 G y G 6 G We have A and A Rank of marix r( A) < Now C 7 6 r ( C ) Since r( A)! r ( C) here i no oluion..6 Oion (A) i crec. in z can have value beween o +. Thu no oluion..7 Oion (A) i crec. x x We have fx () e + e x F x >, e > and < e < F x <, < e < and e > Thu fx () have minimum value a x and ha i e + e..8 Oion (A) i crec. 5 in x x + x + x +...! 5! co x + x + x +...!! Thu only in( x ) will have odd ower of x..9 Oion (B) i crec. dx() We have + x() d ( D+ ) x( ) Since m, x () Ce Thu only (B) may be oluion.. Oion (C) i crec. We have x e fx () xe f'( x ) + e The NewonRahon ieraive fmula i fx ( n) x n + xn f'( xn) Now fx ( n ) xn e x n f'( x n ) + e x n x x n n Thu x n + x xn e n ( + xn) e xn + xn e + e. Oion (A) i crec. n Re fz () d n z a ( z a) f( z) ( n )! n z dz Here we have n and a Thu Re fz () z SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy a d ( z ) ( )! dz ; ( z ) ( z ) + E z d dz ; ( z ) E ; ( z + ) E 6. Oion (D) i crec. e P L 6 ( L e G Go L e o + G + ( )( ) L f + + ( + )( + ) e e + z a ( + )( + ) ( + )( + ) e e > H G e + e e + e a z a. Oion (B) i crec. Tayl erie i given a ( ) fx () fa ( ) x a x a + f '( a ) + f "( a ) +...!! F x we have ( ) Thu fx () f( ) x x + f'( ) + f"( x)...!! x Now fx () e + in x x f'( x ) e + co x x f"( x ) e in x f"( ) e in e f"( ) Thu he coefficien of ( x ) i!. Oion (A) i crec. The equaion of raigh line from (,) o (,) i y x. Now gxy (,) x + y, gx (, x) x + 6x Now # gx (, x) # ( x + 6x ) dx

13 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 5 [ x + x ].5 Oion (B) i crec. Q Q Q I # ( xdx + ydy) # xdx + # ydy P # xdx + ydy.6 Oion (B) i crec. The given lo i raigh line whoe equaion i x y + y x + Now I # ydx ( x+ ) dx ( x + ) ; E Oion (C) i crec. coh x coh x inh x a x <<, coh x. and inh x. x GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii Thu coh x..8 Oion (A) i crec. lim in q ^ h lim in q ^ h q " q q " q ^ h.9 Oion (D) i crec. We have, lim x " x lim x x x " x lim e x " x lim e x " x lim e x " # # P lim in q ^ h q q ^ h " P 5. Thu e x i ricly bounded..5 Oion (A) i crec. We have fx () e x e ( x ) ( x ) e e ( x ) ( x )... + ; Ee! 6( e Neglecing higher ower ( xe ).5 Oion (D) i crec. dy We have k yy dx dy y y dx k k A.E. D k D! k x k C.F. Ce + Ce x k P.I. y y D c m k Thu oluion i k x x k k y Ce + Ce + y From y() y we ge C+ C yy From y( ) y we ge ha C mu be zero. Thu C yy x k y ( y y) e + y.5 Oion (B) i crec. We have fx () x x + x f'( x ) x x+ Taking x in NewonRahon mehod fx ( ) + () x x f'( x) () () +.5 Oion (C) i crec. F wo hogonal ignal fx () and gx () + # fxgxdx () () i.e. common area beween fx () and gx () i zero..5 Oion (A) i crec. We know ha # d j [um of reidue] D Singular oin are a! bu only + lie inide he given conour, Thu Reidue a + i lim( ) f( ) lim( ) " " # d j j ` j D.55 Oion (C) i crec. F wo hogonal vec, we require wo dimenion o define hem and imilarly f hree hogonal vec we require hree dimenion o define hem. M vec are baically M hogonal vec and we require M dimenion o define hem..56 Oion (A) i crec. We have fx () x x+ F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// f'( x ) x x " f"( x ) Since f"( x) >, hu x i minimum oin. The maximum value in cloed inerval will be a x x Now maximum value max[ f( ), f()] max( 8, ) 8.57 Oion (C) i crec. Probabiliy of failing in aer i PA ( ). Poibiliy of failing in Paer i PB ( ).

14 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page Probabiliy of failing in aer, when uden ha failed in aer i P^ BA h.6 We know ha P A ( P+ B) bb l PB ( ) PA ( + B) PBP ( ) A b B l 6. #...58 Oion (C) i crec. We have R V R V S W S W A S W+ S W S W S W T X T X Since one full row i zero, r( A) < Now!, hu r ( A).59 Oion (D) i crec. The vec Trile Produc i A# ( B# C) BAC ( $ )CAB ( $ ) Thu ## P ( $ P) P( $) ( $ P) P.6 Oion (A) i crec. The Soke heem i ## ( # F) $ d # A$ dl.6 Oion (C) i crec. # a x # ax # + # ax We know xdx () Thu Ke dx Ke dx Ke dx R R K e ax k x e a a ( a) K + K a a K a.6 Oion (A) i crec. We have x o () + x () () Taking Lalace ranfm boh ide X() x() + X() X() + X() Since x( ) X () + Now aking invere Lalace ranfm we have x () e u().6 Oion (A) i crec. Sum of he Eigen value mu be equal o he um of elemen of rincial diagonal of marix. Only marix 6 6 G aify hi condiion..6 Oion (B) i crec. We have W lnz u+ jv ln( x+ jy) e u+ jv x+ jy u jv ee x+ jy u e ( co v+ jin v) x+ jy u u Now x e co v and y e in v Thu x + y e u Equaion of circle.65 Oion (D) i crec. We have # dz # z + ( z+ i)( zi) dz z j z j P(,) lie inide he circle z j and P(, ) doe no lie. Thu By cauchy inegral fmula I ilim( zi) i z" i ( z+ i )( zi ) # i+ i C.66 Oion (C) i crec. # I in qdq in q in q # ` dq j in q in qin q co q w q : D : D 8 + B 8 + B SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy Oion (D) i crec. Le d " defecive and y " uly by Y y Py ( + d) ad k Pd ( ) Py ( + d). #. 6. Pd ( ) 6. #. +. #. +. #. 5. y P ad k Oion (C) i crec. We have A G Now 6 A li@ [ X] l l G G G ( )( l) + ( ) l 6.69 Oion (A) i crec. dy We have + ky dx Dy+ ky The AE i m + k The oluion of AE i m! ik Thu y A in kx + B co kx From x, y we ge B and x a, y we ge Ain ka in ka k mx a Thu y A in mx / m ` a j m

15 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page.7 Oion (A) i crec. x We have fx () e x + e F x ", he value of fx () monoonically increae..7 Oion (B) i crec. Order i he highe derivaive erm reen in he equaion and degree i he ower of highe derivaive erm. Order, degree.7 Oion (D) i crec. Probabiliy of coming odd number i and he robabiliy of coming even number i. Boh he even are indeenden o each oher, hu robabiliy of coming odd number afer an even number i #..7 Oion (B) i crec. We have dy dy 5 + 6y dx dx The AE.. i m 5m+ 6 m, GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii x x The CF i y c Ce + Ce x x Since Q, hu y Ce + Ce Thu only (B) may be crec..7 Oion (A) i crec. We have f () e ( a+ ) + 5 e 5. e ( a + ) Taking Lalace ranfm we ge 5 F () e ; ( a + ) E Thu Re () > ( a+ ).75 Oion (C) i crec. F x > he loe of given curve i negaive. Only (C) aify hi condiion..76 Oion (C) i crec. Newon Rahon Runge kua Mehod Simon Rule Gau eliminaion.77 Oion (C) i crec. We have Characeriic equaion i " MehodSolving nonlinear eq. " Solving dinary differenial eq. " Numerical Inegraion " Solving linear imulaneou eq. A G A li Le x & x, Thu.78 Oion (A) i crec. We have ( A li) X i ( 5) x 8 G x G G F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// x G x G G R R x + x Now AA I X. a G G b G a. b b G G G Eigen vec. A G and A a. and b Thu olving above we have b and a Therefe a+ b a G b.79 Oion (A) i crec. Gauian PDF i ( x ) fx () m e # dx f # x # # and fxdx () Subiuing m and in above we ge x 8 e dx # x # e dx 8 x # e dx 8.8 Oion (C) i crec. From hogonal marix [ AA T ] I Since he invere of I i I, hu [ AA T ] I I l l ( l)( l) 8 + l+ l 8 l + l l 5, Eigen value Eigen vec f l 5

16 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 5 UNIT NETWORKS (A) 5/ and 8/ (B) / and 8/ (C) / and / (D) 8/ and 8/ ONE MARK. Conider a dela connecion of rei and i equivalen ar connecion a hown below. If all elemen of he dela connecion are caled by a fac k, k >, he elemen of he creonding ar equivalen will be caled by a fac of.6 Three caaci C, C and C whoe value are m F, 5m F, and m F reecively, have breakdown volage of V, 5V and V reecively. F he inerconnecion hown below, he maximum afe volage in Vol ha can be alied acro he combinaion, and he creonding oal charge in m C ed in he effecive caaciance acro he erminal are reecively, (A) k (B) k (C) /k (D) k V ^h. The ranfer funcion of he circui hown below i V ^ h SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy (A) 5 ṡ + + (B) (C) + + (D) + +. A ource v ^h Vco ha an inernal imedance of ^+ jhw. If a urely reiive load conneced o hi ource ha o exrac he maximum ower ou of he ource, i value in W hould be (A) (B) (C) 5 (D) 7 TWO MARKS. In he circui hown below, if he ource volage V S + 5.cV hen he Thevenin equivalen volage in Vol a een by he load reiance R L i (A).8 and 6 (B) 7 and 9 (C).8 and (D) 7 and 8 Common Daa F Q. 8 and 9: Conider he following figure (A) + 9c (B) 8+ c (C) 8+ 9c (D) + 6c.5 The following arrangemen coni of an ideal ranfmer and an aenua which aenuae by a fac of.8. An ac volage V WX V i alied acro WX o ge an oen circui volage V YZ acro YZ. Nex, an ac volage V YZ V i alied acro YZ o ge an oen circui volage V WX acro WX. Then, VYZ/ VWX, VWX/ VYZ are reecively,.7 The curren I S in Am in he volage ource, and volage V S in Vol acro he curren ource reecively, are (A), (B) 8, (C) 8, (D),.8 The curren in he W rei in Am i (A) (B). (C) (D).9 Two magneically uncouled inducive coil have Q fac q and q

17 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 6 a he choen oeraing frequency. Their reecive reiance are R and R. When conneced in erie, heir effecive Q fac a he ame oeraing frequency i (A) q+ q (B) ^/ qh+ ^/ qh (C) ^qr + qr h/ ^R+ Rh (D) ^qr + qr h/ ^R+ Rh ONE MARK. In he following figure, C and C are ideal caaci. C ha been charged o V befe he ideal wich S i cloed a. The curren i () f all i (A).8 W (C) W. If V V 6V hen V V i A B C D (B). W (D).8 W (A) zero (B) a e funcion GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii (A) 5V (B) V (C) V (D) 6 V Common Daa F Q. 8 and 9 : Wih V dc conneced a A in he linear nonrecirocal wo newk hown below, he following were oberved : (i) W conneced a B draw a curren of A (ii).5 W conneced a B draw a curren of A (C) an exonenially decaying funcion (D) an imule funcion. The average ower delivered o an imedance ( j) W by a curren 5 co( + ) A i (A). W (B) 5 W (C) 6.5 W (D) 5 W. In he circui hown below, he curren hrough he induc i.5 Wih V dc conneced a A, he curren drawn by 7 W conneced a B i (A) /7 A (B) 5/7 A (C) A (D) 9/7 A.6 F he ame newk, wih 6V dc conneced a A, W conneced a B draw 7/ A. If 8V dc i conneced o A, he oen circui volage a B i (A) 6V (B) 7V (C) 8V (D) 9V (A) (C) A (B) A + j + j A (D) A + j ONE MARK F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// In he circui hown below, he Non equivalen curren in amere wih reec o he erminal P and Q i TWO MARKS. Auming boh he volage ource are in hae, he value of R f which maximum ower i ranferred from circui A o circui B i (A) 6. j 8. (B) 6.56 j 787. (C) + j (D) 6 + j.8 In he circui hown below, he value of R L uch ha he ower

18 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 7 ranferred o R L i maximum i (A) i ( ) 5 ex( # ) A (B) i () 5 ex( # ) A (C) i ( ) ex( # ) A (D) i () 5 ex( # ) A (A) 5 W (C) 5 W (B) W (D) W ONE MARK. F he wo newk hown below, he hcircui admiance arameer marix i.9 The circui hown below i driven by a inuoidal inu v V co( / RC). The eady ae ouu v o i i (A) > S H (B) 5. > S 5. H (A) ( V /) co( / RC) (B) ( V /) in( / RC) (C) ( V /) co( / RC) (D) ( V /) in( / RC) TWO MARKS. In he circui hown below, he curren I i equal o (A).+ c A (B).+c A (C).8+ c A (D).+ c A. In he circui hown below, he newk N i decribed by he following Y marix:. S. S Y >. S. S H. he volage gain V i V SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy 5. (C) > S 5. H (D) > S H. F arallel RLC circui, which one of he following aemen i NOT crec? (A) The bandwidh of he circui decreae if R i increaed (B) The bandwidh of he circui remain ame if L i increaed (C) A reonance, inu imedance i a real quaniy (D) A reonance, he magniude of inu imedance aain i minimum value. TWO MARKS.5 In he circui hown, he wich S i oen f a long ime and i cloed a. The curren i () f $ + i (A) /9 (B) /9 (C) /99 (D) /. In he circui hown below, he iniial charge on he caaci i.5 mc, wih he volage olariy a indicaed. The wich i cloed a ime. The curren i () a a ime afer he wich i cloed i (A) i ( ).5.5e A (B) i ( ).5.5e A (C) i ( ).5.5e A (D) i ( ).75e A.6 The curren I in he circui hown i (A) ja (B) ja

19 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 8 (C) A (D) A baery deliver during hi alkime?.7 In he circui hown, he ower ulied by he volage ource i (A) J (C). kj (B) kj (D). J (A) W (C) W (B) 5 W (D) W GATE 9 TWO MARK. An AC ource of RMS volage V wih inernal imedance Z ( + j) W feed a load of imedance ZL ( 7+ j) W in he figure below. The reacive ower conumed by he load i GATE 9 ONE MARK.8 In he inerconnecion of ideal ource hown in he figure, i i known ha he 6 V ource i abbing ower. GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii (A) 8 VAR (B) 6 VAR (C) 8 VAR (D) VAR. The wich in he circui hown wa on oiion a f a long ime, and i move o oiion b a ime. The curren i () f > i given by 5 (A). e u( ) ma 5 (B) e u( ) ma 5 (C). e u( ) ma (D) e u( ) ma Which of he following can be he value of he curren ource I? (A) A (B) A (C) 5 A (D) 8 A.9 If he ranfer funcion of he following newk i Vo () V() + CR i. In he circui hown, wha value of R L maximize he ower delivered o R L? F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// The value of he load reiance R L i (A) R (C) R (B) R (D) R. A fully charged mobile hone wih a V baery i good f a minue alkime. Aume ha, during he alkime he baery deliver a conan curren of A and i volage dro linearly from V o V a hown in he figure. How much energy doe he

20 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 9 (A) W. (C) W (B) 8 W (D) 6 W. The ime domain behavi of an RL circui i rereened by L di / + Ri V ( Be R L in ) u( ) d +. F an iniial curren of i() V, he eady ae value of he R curren i given by (A) i () " V (B) i ()" V R R (C) i () V " ( + B) (D) i () V " ( + B) R R The comonen value are (A) L 5 H, R.5 W, C. F (B) L. H, R.5 W, C 5F (C) L 5 H, R W, C.F (D) L. H, R W, C 5F.9 The circui hown in he figure i ued o charge he caaci C alernaely from wo curren ource a indicaed. The wiche S and S are mechanically couled and conneced a follow: F nt # # ( n + ) T, ( n,,,..) S o P and S o P F ( n+ ) T # # ( n+ ) T, ( n,,,...) S o Q and S o Q GATE 8 ONE MARK.5 In he following grah, he number of ree ( P ) and he number of cue ( Q ) are (A) P, Q (B) P, Q 6 (C) P, Q 6 (D) P, Q.6 In he following circui, he wich S i cloed a. The rae of change of curren di ( + ) i given by d SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy (A) (C) ( R+ R ) I L (B) RI L (D) GATE 8 TWO MARKS.7 The Thevenin equivalen imedance Z h beween he node P and Q in he following circui i (A) (B) + + (C) + + (D) The driving oin imedance of he following newk i given by Z () Aume ha he caaci ha zero iniial charge. Given ha u () i a uni e funcion, he volage vc () acro he caaci i given by / (A) () n u( nt) n / (B) u () + () n u ( nt) n / (C) u( ) + () n u( nt)( nt) n ( nt) ( nt) (D) / 65. e + 5. e T@ n Common Daa F Q.. &. : The following erie RLC circui wih zero condiion i excied by a uni imule funcion d ().

21 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page. F >, he ouu volage vc ^h i (A) ^e e h (B) e (C) e co c m (D) e in c. F >, he volage acro he rei i (A) _ e e i (B) e co in c m c mg (C) (D) e e inc coc m m m (A) a lowa filer (B) a higha filer (C) a banda filer (D) a bandrejec filer GATE 7 TWO MARKS.6 Two erie reonan filer are a hown in he figure. Le he db bandwidh of Filer be B and ha of Filer be B. he value B i B Saemen f linked Anwer Queion.5 &.6: A wo newk hown below i excied by exernal DC ource. The volage and he curren are meaured wih volmeer V, V GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii (A) (B) (C) / (D) /.7 F he circui hown in he figure, he Thevenin volage and reiance looking ino X Y are and ammeer. A, A (all aumed o be ideal), a indicaed (A) V, W (B) V, W (C) V, W (D) V,W Under following condiion, he reading obained are: () S oen, S cloed A, V.5 V, V.5V, A A () S oen, S cloed A A, V 6 V, V 6V, A.8 In he circui hown, v C i vol a ec. F >, he caaci curren i (), where i in econd i given by C. The z arameer marix f hi newk i (A) G (B) G (C) G (D) G. The harameer marix f hi newk i (A) 67. G (B) 67. G (C) 67. G (D) 67. G GATE 7 ONE MARK. An indeenden volage ource in erie wih an imedance Z R+ jx deliver a maximum average ower o a load imedance Z L when (A) ZL R+ jx (B) ZL R (C) Z jx (D) Z R jx L.5 The RC circui hown in he figure i L (A) 5. ex( 5) ma (B) 5. ex( 5) ma F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// (C).5 ex(.5 ) ma (D) 5. ex( 65. ) ma.9 In he ac newk hown in he figure, he ha volage V AB (in Vol) i (A) (B) 5+ c (C). 5+ c (D) 7+ c

22 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page GATE 6 TWO MARKS.5 A wo newk i rereened by ABCD arameer given by V A B V I G C D G I G If i erminaed by R L, he inu imedance een a i given by (A) A+ BRL (B) ARL + C C + DR L BR L + D (C) DRL + A (D) B+ ARL BR + C D + CR L.5 In he wo newk hown in he figure below, Z and Z and reecively L (A) R # Re Z ( jw), w (B) R # Z ( jw), w neg 6 neg 6 (C) R # Im Z ( jw), w (D) R # + Z ( jw), w neg 6 neg 6 GATE 5 ONE MARK.56 The condiion on RL, and C uch ha he e reone y () in he figure ha no ocillaion, i (A) r e and b r (B) and br (C) and b r o (D) r e and br.5 The fir and he la criical frequencie (ingulariie) of a driving oin imedance funcion of a aive newk having wo kind of elemen, are a ole and a zero reecively. The above roery will be aified by (A) RL newk only (B) RC newk only (C) LC newk only (D) RC a well a RL newk SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy A mh induc wih ome iniial curren can be rereened a hown below, where i he Lalace Tranfm variable. The value of iniial curren i (A).5 A (B). A (C). A (D). A.5 In he figure hown below, aume ha all he caaci are iniially uncharged. If vi () u() Vol, vo () i given by (A) R $ L (B) R $ L C C (C) R $ L (D) R C LC.57 The ABCD arameer of an ideal n: ranfmer hown in he figure are n > x H (A) 8e Vol (B) 8( e ) Vol (C) 8 u () Vol (D) 8 Vol.55 A negaive reiance R neg i conneced o a aive newk N having driving oin imedance a hown below. F Z () o be oiive real, The value of x will be (A) n (B) n (C) n (D) n.58 In a erie RLC circui, R kw, L H, and C mf The reonan frequency i (A) # Hz (B) # Hz (C) Hz (D) # Hz.59 The maximum ower ha can be ranferred o he load rei R L from he volage ource in he figure i

23 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page he figure, hen he reading in he ideal volmeer conneced beween a and b i (A) W (C).5 W (B) W (D).5 W.6 The fir and he la criical frequency of an RC driving oin imedance funcion mu reecively be (A) a zero and a ole (B) a zero and a zero (C) a ole and a ole (D) a ole and a zero (A). 8 V (B).8 V (C). 8 V (D) V.65 The h arameer of he circui hown in he figure are GATE 5 TWO MARKS.6 F he circui hown in he figure, he inananeou curren i () i GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii (A)... G (B) 5. G (C) G (D) 5. G.66 A quare ule of vol amliude i alied o C R circui hown in he figure. The caaci i iniially uncharged. The ouu volage V a ime ec i (A) 9c A (B) (C) 5 6c A (D) 5 6c A.6 Imedance Z a hown in he given figure i 9c A (A) V (B) V (C) V (D) V GATE ONE MARK.67 Conider he newk grah hown in he figure. Which one of he following i NOT a ree of hi grah? (A) j9 W (C) j9 W (B) j9 W (D) j9 W F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// F he circui hown in he figure, Thevenin volage and Thevenin equivalen reiance a erminal a b i (A) 5 V and W (B) 7.5 V and 5W. (C) V and W (D) V and 5W..6 If R R R R and R. R in he bridge circui hown in

24 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page (A) a (C) c (B) b (D) d.68 The equivalen inducance meaured beween he erminal and f he circui hown in he figure i GATE TWO MARKS.7 F he laice hown in he figure, Za j W and Zb W. The z z value of he oen circui imedance arameer 6 z z G are (A) L+ L+ M (B) L+ LM (C) L + L + M (D)L + L M.69 The circui hown in he figure, wih R W, L H and C F ha inu volage v ( ) in. The reuling curren i () i SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy (A) 5 in( + 5. c) (B) 5 in( 5. c) (C) 5 in( + 5. c) (D) 5 in( 5. c).7 F he circui hown in he figure, he ime conan RC m. The inu volage i vi ( ) in. The ouu volage vo () i equal o (A) in( 5c) (B) in( + 5c) (C) in( 5c) (D) in( + 5c) j + j j + j (A) + j + j G (B) + j j G + j + j + j + j (C) j j G (D) + j + j G.7 The circui hown in he figure ha iniial curren il ( ) A hrough he induc and an iniial volage vc ( ) V acro he caaci. F inu v () u (), he Lalace ranfm of he curren i () f $ i.7 F he R L circui hown in he figure, he inu volage vi () u(). The curren i () i (A) (B) (C) (D) Vo ().7 The ranfer funcion H () of an RLC circui i given by Vi () 6 H () The Qualiy fac (Qfac) of hi circui i (A) 5 (B) 5

25 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page (C) (D) 5.75 F he circui hown in he figure, he iniial condiion are zero. I Vc () ranfer funcion H () i V() i (C) (D).8 The differenial equaion f he curren i () in he circui of he figure i (A) (C) (B) (D) (A) di + di + i ( ) in (B) di + di + i ( ) co d d d d (C) di + di + i ( ) co (D) di + di + i ( ) in d d d d.76 Conider he following aemen S and S S : A he reonan frequency he imedance of a erie RLC circui i zero. S : In a arallel GLC circui, increaing he conducance G reul in increae in i Q fac. GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii Which one of he following i crec? (A) S i FALSE and S i TRUE (B) Boh S and S are TRUE (C) S i TRUE and S i FALSE (D) Boh S and S are FALSE GATE ONE MARK.77 The minimum number of equaion required o analyze he circui hown in he figure i GATE TWO MARKS.8 Twelve W reiance are ued a edge o fm a cube. The reiance beween wo diagonally ooie cner of he cube i (A) 5 W (B) W 6 (C) 5 6 W (D) W.8 The curren flowing hrough he reiance R in he circui in he figure ha he fm Pco where P i (A) ( 8. + j7. ) (B) ( 6. + j9. ) (C) (. 8+ j9. ) (D) (. 9 + j. ) The circui f Q..66 &.67 i given below. Aume ha he wich S i in oiion f a long ime and hrown o oiion a. (A) (B) (C) 6 (D) 7.78 A ource of angular frequency rad/ec ha a ource imedance coniing of W reiance in erie wih H inducance. The load ha will obain he maximum ower ranfer i (A) W reiance (B) W reiance in arallel wih H inducance (C) W reiance in erie wih F caaci (D) W reiance in arallel wih F caaci.79 A erie RLC circui ha a reonance frequency of khz and a qualiy fac Q. If each of RL, and C i doubled from i iginal value, he new Q of he circui i (A) 5 (B) 5 F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// A +, he curren i i (A) V R (C) V R.8 I () (B) V R (D) zero and I () are he Lalace ranfm of i () and i () reecively. The equaion f he loo curren I () and I () f he circui hown in he figure, afer he wich i brough from oiion o oiion a, are R+ L+ C L I () V (A) > L R + H C I() G G R+ L+ C L I () V (B) > L R + H I () G G C

26 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 5 R+ L+ C L I () V (C) > L R+ L+ H C I() G G R+ L+ C C I () V (D) > L R+ L+ H C I() G G.85 The driving oin imedance Z () of a newk ha he olezero locaion a hown in he figure. If Z(), hen Z () i (A) 5 V (B) 5 V (C) 5 V (D) V GATE TWO MARKS.9 In he newk of he fig, he maximum ower i delivered o R L if i value i ( + ) ( + ) (A) (B) ( + ) ( ) (C) (D) An inu volage v ( ) co( + c) + 5co( + c) V i alied o a erie combinaion of reiance R W and an inducance L H. The reuling eadyae curren i () in amere i (A) co( + 55 c) + co(+ c+ an ) (B) co( + 55 c) + co(+ 55 c) (C) co( 5 c) + co(+ can ) (D) co( 5 c) + co( 5 c).87 The imedance arameer z and z of he wo newk in he figure are (A) 6 W (C) 6 W (B) W (D) W.9 If he hae balanced ource in he figure deliver 5 W a SPECIAL EDITION ( STUDY MATERIAL FORM ) A marke Book i available in volume i.e. in book binding fm. Bu a NODIA Online Se book i available in book binding fm. Each uni of Book i in earae binding. Available Only a NODIA Online Se Click o Buy a leading ower fac.8 hen he value of Z L (in ohm) i aroximaely (A) z 7. 5W and z. 5 (B) z W and z 5. W (C) z W and z. 5 W (D).5 W and.5 W z W z (A) 9+. c (B) 8+. c (C) 8+. c (D) 9+. c GATE.88 The deenden curren ource hown in he figure ONE MARK GATE.9 The Volage e in he figure i ONE MARK (A) deliver 8 W (C) deliver W (B) abb 8 W (D) abb W.89 In he figure, he wich wa cloed f a long ime befe oening a. The volage v x a + i (A) V (B) / V (C) V (D) 8 V.9 If each branch of Dela circui ha imedance Z, hen each branch of he equivalen Wye circui ha imedance (A) Z (B) Z (C) Z (D) Z.9 The admiance arameer Y in he newk in Figure i

27 GATE Elecronic and Communicaion Toicwie Solved Paer by RK Kanodia & Ahih Murolia Page 6.98 The z arameer z and z f he newk in he figure are (A). mho (B). mho (C).5 mho (D).5 mho GATE.95 The volage e in he figure i TWO MARKS (A) z ; z 6 6 W W (B) z ; z 6 W (C) z ; z 6 6 W W (D) z ; z W W W GATE ONE MARK.99 The circui of he figure rereen a (A) 8 V (C) 6 V (B) V (D) 8 V GATE Elecronic & Communicaion by RK Kanodia Now in Volume Purchae Online a maximum dicoun from online e and ge POSTAL and Online Te Serie Free vii When he angular frequency w in he figure i varied o, he locu of he curren ha I i given by (A) Low a filer (C) band a filer (B) High a filer (D) band rejec filer. In he circui of he figure, he volage v () i (A) e a (C) ae b e (B) e + e a b be (D) ae + be a a b b. In he circui of he figure, he value of he volage ource E i (A) 6 V (B) V F me GATE Reource, Mock Te and Sudy maerial join he communiy h:// (C) 6 V (D) 6 V.97 In he figure, he value of he load rei R L which maximize he ower delivered o i i GATE TWO MARKS. Ue he daa of he figure (a). The curren i in he circui of he figure (b) (A). W (B) W (C) W (D) 8. 8 W