Electrical Engineering

Transcription

1 EE GATE-7-PAPER-I Electrical Engineering Q. N. 5 Carry One Mark Each. Cnsider gt Here, t t, t, where t t t, therwise t represents the largest integer less than r equal t t and t dentes the smallest integer greater than r equal t t. The cefficient f the secnd harmnic cmpnent f the Furier series representing g(t) is. Key: t t t Given gt t t therwise If we plt the abve signal, we get gt Since this wave frm cntain hidden half wave symmetry, even harmnics des nt exist. Thus cefficient f secnd harmnic cmpnent f Furier series will be zer.. A surce is supplying a lad thrugh a -phase, -wire transmissin system as shwn in figure belw. The instantaneus vltage and current in phase-a are V an =sin t V and ia sin t A, respectively. Similarly fr phase-b the instantaneus vltage and current V cs t V and i cs t A, respectively. are bn b a ia a' Surce b V an i b b' Lad n V bn n' Key: (A) The ttal instantaneus pwer flwing frm the surce t the lad is (A) W (B) sin t W (C) 44 W (D) sint cs tw ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

2 Pinstaneus Van ia Vbn ib EE GATE-7-PAPER-I cs tcs t sin t sin t t sin t cs t W. A three-phase, 5Hz, star-cnnected cylindrical-rtr synchrnus machine is running as a mtr. The machine is perated frm a 6.6 kv grid and draws current at unity pwer factr (UPF). The synchrnus reactance f the mtr is per phase. The lad angle is. The pwer delivered t the mtr in kw is. Key: 85 t 84 E Vt 6.6kV b ~ cs I a I a V IX a s E b Eb cs E csv E E b b b V 66 cs cs 44 vlts E.V X b P. sin. sin P 88. kw s z 4. Fr a cmplex number z, lim is zi z z i z (A) -i (B) -i (C) i (D) i Key: (D) z z i i zi zi z lim lim i z z i z 5. Cnsider an electrn, a neutrn and a prtn initially at rest and placed alng a straight line such that the neutrn is exactly at the center f the line jining the electrn and prtn. At t=, the particles are released but are cnstrained t mve alng the same straight line. Which f these will cllide first? (A) The particles will never cllide (B) All will cllide tgether (C) Prtn and Neutrn (D) Electrn and Neutrn Key: (D) e n p q me mn m p e q q e ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

3 EE GATE-7-PAPER-I The Gravitatinal frce f alteratin between any tw particles shwn abve is made much negligible when cmpared t clumbic frce f alteratin between electrn and prtn. Frce f alteratin e F F, accelleratin q ;q q 4 r M e p Due t this frce, the electrn as well as the prtn will mve twards each ther, since m m, the speed and acceleratin f the electrn will be much greater than that f prtn. e p This causes electrn t cllide with the neutrn faster when cmpared t prtn. 6. Let zt xt yt, where dentes cnvlutin. Let C be a psitive real-valued Key: (A) cnstant. Chse the crrect expressin fr z (ct). (A) c.x ct yct (B) x ct yct (C) c.x t yct (D) c.x ct yt zt x t * yt z s x s.ys Cnverting int Laplace transfrm and applying time sealing prperty. zct zs / c c s / c ys / c c c s / c y s / c c c z ct c.x ct * yct 7. A -bus pwer system is shwn in the figure belw, where the diagnal elements f Y-bus matrix are Y jpu, Y j5pu and Y j7pu Bus jq Bus jr jp Key: (B) The per unit values f the line reactances p, q and r shwn in the figure are (A) p., q., r.5 (B) p., q., r.5 (C) p 5, q, r (D) p 5, q, r Y y y y j jq jr Bus ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

4 q r EE GATE-7-PAPER-I Y j5 y y y jq jp p q 5 p r 7 Y j7 y y y jp jr slving P 5,q,r admit tan ces P.,q.,r.5 reac tan ces 8. The equivalent resistance between the terminals A and B is. A 6 6 Key:.9 t. The Ckt will becme B.8 A B.8 RAB The Blean expressin AB AC BC simplifies t (A) BC AC (B) AB AC B (C) AB AC (D) AB BC Key: (A) AB AC BC BC A BC AC BC AC. The fllwing measurements are btained n a single phase lad: V V %, I 5.A % and W 555W %. If the pwer factr is calculated using these measurements, the wrst case errr in the calculated pwer factr in percent is. ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 4

5 Key: 4 t 4 P VIcs EE GATE-7-PAPER-I P 555 % 555 % cs.54 4% V.I % 5 % % V s s. The transfer functin f a system is given by, Let the utput f the system be V s s i fr the input v t V sin t m values f (in radians) are respectively (A) Key: (D) i and V s s Hs V s s (B) and H Tan, If, V t V sin t Tan m If, v t V sin t. Then the minimum and maximum i m (C) and (D) and. The matrix A has three distinct eigenvalues and ne f its eigenvectrs is Which ne f the fllwing can be anther eigenvectr f A? (A) Key: (C) (B) (C) (D) By the prperties f Eigen values and Eigen vectrs, anther eigen vectr f A is The eigen vectrs crrespnding t distinct eigen values f a real symmetric matrix are rthgnal i.e., pair wise dt prduct is zer.. Fr the pwer semicnductr devices IGBT, MOSFET, Dide and Thyristr, which ne f the fllwing statements is TRUE? (A) All f the fur are majrity carrier devices. (B) All the fur are minrity carrier devices (C) IGBT and MOSFET are majrity carrier devices, whereas Dide and Thyristr are minrity carrier devices. (D) MOSFET is majrity carrier device, whereas IGBT, Dide, Thyristr are minrity carrier devices. ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 5

6 EE GATE-7-PAPER-I Key: (D) MOSFET Majrity carrier device (NMOS, PMOS) Dide bth majrity & minrity carrier device Transister Npn, pnp IGBT input is MOSFET, Output is BJT 4. Cnsider the unity feedback cntrl system shwn. The value f K that results in a phase margin f the system t be is. Key:. t.6 PM 8 G gc Us Ke s s Ys s Ke Gs s K Fr gc Gs 8 gc K G s K 9 8 K 6 K A slid irn cylinder is placed in a regin cntaining a unifrm magnetic field such that the cylinder axis is parallel t the magnetic field directin. The magnetic field lines inside the cylinder will (A) bend clser t the cylinder axis (B) bend farther away frm the axis (C) remain unifrm as befre (D) cease t exist inside the cylinder Key: (A) Flux always chses less reluctance path. S flux tried t flw inside the cnductr and clser t the axis f the cylinder. 6. Let I c R xy dxdy, where R is the regin shwn in the figure and equals. y 4 c 6. The value f I R 5 x ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 6

7 Key:.99 t. EE GATE-7-PAPER-I xy dxdy xy dxdy xy dxdy R R R OR R x y 5 5 x 5 5 x x y y xy dxdy xy dx x dx x y x y x x x 8x 8dx C xy dxdy x xy dxdy xy dy dx R 5 x 5 y 8 x dx x x dx 5 8 x C xy dxdy R n 7. Cnsider the system with fllwing input-utput relatin yn xn where, x[n] is the input and y[n] is the utput. The system is (A) invertible and time invariant (B) invertible and time varying (C) nn-invertible and time invariant (D) nn-invertible and time varying Key: (D) n Given yn xn Fr time invariance n n n y' n x n n () y n n x n n () Since () is nt equal t () System is time variant Fr inverse system xn, there shuld be unique yn Fr each unique If x n n n y n n ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 7

8 y if x n n EE GATE-7-PAPER-I n y n n y()= Fr tw different inputs we have same utput. Thus ne t ne mapping is nt pssible. Hence the systems is nn invertible 8. The slpe and level detectr circuit in a CRO has a delay f ns. The start-stp sweep generatr has a respnse time f 5 ns. In rder t display crrectly, a delay line f (A) 5 ns has t be inserted int the y-channel (B) 5 ns has t be inserted int the x-channel (C) 5 ns has t be inserted int bth x and y channels (D) ns has t be inserted int bth x and y channels Key: (A) The delay line shuld be inverted in VDP (Y-channel) nly. 9. A -phase vltage surce inverter is supplied frm a 6V DC surce as shwn in the figure belw. Fr a star cnnected resistive lad f per phase, the lad pwer fr device cnductin, in kw is. 6V Key: 8.5 t 9.5 V 6V dc R L / Ph md e RMS value f phase vltage V.48V 44.9V Vph 44.9 Lad pwer 8.99kW 9kW R P dc s Ks K s. Fr. A clsed lp system has the characteristic equatin given by this system t be stable, which ne f the fllwing cnditins shuld be satisfied? (A) < K <.5 (B).5 < K < (C) < K < (D) K > Key: (D) CE s ks k s Given ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 8

9 Fr stable k k k k k k k k k (OR) By R-H criteria EE GATE-7-PAPER-I s k s k k k s k s k k k K k k k. A 4 ple inductin machine is wrking as an inductin generatr. The generatr supply frequency is 6 Hz. The rtr current frequency is 5 Hz. The mechanical speed f the rtr in RPM is (A) 5 (B) 65 (C) 95 (D) 5 Key: (C) N s 6 8 rpm 4 Rtr speed shuld be greater than syn.speeed, t ge inductance generatr mde. Nr NS S N S f 5 f 6 r Nr NS S fr sf s Nr 8 95 rpm. Fr the circuit shwn in the figure belw, assume that dides D, D and D are ideal. R D v t sin t V v D D R v The DC cmpnents f vltages v and v, respectively are (A) V and V (B) -.5 V and.5 V (C) V and.5 V (D) V and V ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 9

10 Key: (B) Fr half wave Rectifier EE GATE-7-PAPER-I Vm Vdc V Vdc fr ve pulse Vdc fr ve pulse.5v V.5V. A -bus pwer system cnsists f fur generatr buses indexed as G, G, G, G4 and six lad buses indexed as L, L, L, L4, L5, L6. The generatr bus G is cnsidered as slack bus, and the lad buses L and L4 are vltage cntrlled buses. The generatr at bus G cannt supply the required reactive pwer demand, and hence it is perating at its maximum reactive pwer limit. The number f nn-linear equatins required fr slving the lad flw prblem using Newtn-Raphsn methd in plar frm is. Key: 4 t 4 Ttal n f buses= Given G =slack bus, G =generatr/pq bus G,G are PV buses 4 PQ buses L,L,L,L (4) 5 6 Vltagecntrlled PV buses L, L () 4 Minimum n f nnlinear equatins t be slved The pwer supplied by the 5 V surce in the figure shwn belw is W. Key: 48 t 5 KCL I.4I 4.4I 4 I A The pwer supplied by 5 V = 5 5W 5V I R 7V 4A R.4I 5. In the cnverter circuit shwn belw, the switches are cntrlled such that the lad vltage v (t) is a 4 Hz square wave. S S V LOAD v t S4 S The RMS value f the fundamental cmpnent f v (t) in vlts is. Key : 96 t ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

11 EE GATE-7-PAPER-I 4V 4V 5 n,,5 n 4 VS Vn Vt n Vs V 4 VS Vl.9VS V V V s S V t sin t sin t sin 5t sin nt s t Q. N Carry Tw Marks Each 6. The utput expressin fr the Karnaugh map shwn belw is AB CD (A) BD BCD (B) BD AB (C) BD ABC (D) BD ABC Key: (D) CD AB BD ABC 7. A V DC series mtr runs drawing a current f A frm the supply. Armature and field circuit resistances are.4 and. respectively. The lad trque varies as the square f the speed. The flux in the mtr may be taken as being prprtinal t the armature current. T reduce the speed f the mtr by 5% the resistance in hms that shuld be added in series with the armature is. Key: 9.5 t E.5 5 vlts b E I.5 R b a X Given T N and I R We knw that, in series mtr T I a ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

12 EE GATE-7-PAPER-I T I N N N a Ia Ia.5. I a 5 Amp I a. A. I a Eb N N N E E b b.5n 5.5 R x N 5 5 R.75 x.4 E b V R x.4 E b V 8. The transfer functin f the system Y(s)/U(s) whse state-space equatins are given belw is: t x t x t u t x t x t x y t x t (A) Key: (D) Given s s s (B) s s s 4 x t x t u(t) x t x t x t Ax Bu Transfer functin = Here D = C A B C SI A B D s s 4 s s 4 T / F s s 4 s T / F s s s s 4 s s 4 (C) s 4 s s 4 (D) s 4 s s 4 ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

13 EE GATE-7-PAPER-I 9. The lad shwn in the figure is supplied by a 4 V (line t line) -phase surce (RYB sequence). The lad is balanced and inductive, drawing 464 VA. When the switch S is in psitin N, the three watt-meters W, W and W read W each. If the switch is mved t psitin Y, the readings f the watt-meters in watts will be: (A) W 7and W W (B) W, W 7and W (C) W 866, W, W 866 (D) W W and W 7 Key: (D) R W Supply Y W lad B W Y S N N If the switch is cnnected t Neutral, then each wattmeter will read pwer. W W W.V.I cs 7.5 ph ph cs.5agg. 6 V 4 Given that, lad drawing Apparent pwer f 464 VA. I V I 464 L L L 464 5A 4 If the switch cnnected t Y, then W = V B4 V B V R 6 I 4 I R V 4 ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

14 EE GATE-7-PAPER-I W V I cs V & I V I cs V & I pc cc pc cc Ry R Ry R 45cs 9 W By B By B W V I cs V & I 4 5cs 7watts. Tw passive tw-prt netwrks are cnnected in cascade as shwn in figure. A vltage surce is cnnected at prt. Given V AV BI I C V D I V A V B I I C V D I A,B,C,D,A,B,C andd are the generalized circuit cnstants. If the Thevenin equivalent circuit at prt cnsists f a vltage surce V T and impedance Z T cnnected in series, then V A B B D V,Z (A) T T AA AA BC V A B B D V,Z (C) T T A A A A Key: (D) We can write V,I in terms f V I V A B A B V I C D C D I V A A B C V A B B D I I C A D C V C B D D I T find Vth rvc I V A A B C V th Vth Vc A A T find ISC V V B C V V AB BD ISC ISC A B B D T find R th R th V A B B D I A A B C OC SC V A B B D V,Z (B) T T AA BC AA V A B B D V,Z (D) T T AA BC AA BC ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 4

15 EE GATE-7-PAPER-I The circuit shwn in the figure uses matched transistrs with a thermal vltage VT 5mV. The base currents f the transistrs are negligible. The value f the resistance R in k that is required t prvide A bias current fr the differential amplifier blck shwn is. Key: 7 t 74 V I IC IC T C R ln ; I ma;i A C C 5 R ln 7.7k 6 6. The figure belw shws an uncntrlled dide bridge rectifier supplied frm a V, 5 Hz -phase ac surce. The lad draws a cnstant current I 4A. The cnductin angle f the dide D in degrees is. Key: t Average reductin in utput vltage due t L s V 4fsLsI V Vm V cs cs fr a dide, Vm V cs 8 cs 44.7 cnductin angle f dide ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 5

16 EE GATE-7-PAPER-I dy Cnsider the differential equatin t 8 5ty sin t with y. There exists a dt unique slutin fr this differential equatin when t belngs t the interval (A) (-,) (B) (-,) (C) (-,) (D) (,) Key: (A) D.E is I.F = dy 5t sin t y dt t 8 t 8 5t 5 t 8 e e t 8 dt ln t 8 5/ is a first rder linear eq. Slutin is 5/ sin t 5/ / y t 8 t 8 t 8 sin tdt c t 8 / t 8 t 8 t 8.sin tdt C y 5/ 5/ If t 9,9 then the slutin exists. Optins (b), (c), (d) cntain either -9 r 9 r bth. S answer is ptin A 4. A separately excited DC generatr supplies 5 A t a 45 V DC grid. The generatr is running at 8 RPM. The armature resistance f the generatr is.. If the speed f the generatr is increased t RPM, the current in amperes supplied by the generatr t the DC grid is. Key: 548 t 55 5A 45V Grid 5A 45V Grid R a. R a. E g E g 8 rpm rpm E E g g 6V g N E cnstant N N E E g g Eg 6 vlts 8 E I. 45 g a I. I. I 55 amps a a a ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 6

17 EE GATE-7-PAPER-I 5. In the circuit shwn belw, the maximum pwer transferred t the resistr R is W. Key: t. T find th V th 5 6 I.A V V T find R th 5 5 R th The maximum pwer transferred t Vth 5.5 R.5W 4R 4.5 th 5V V V th I V 5 R th 6. Let a causal LTI system be characterized by the fllwing differential equatin, with initial rest cnditin d y dy 7 y t 4xt 5 dt dt dt dx t Where x(t) and y(t) are the input and utput respectively. The impulse respnse f the system is (u(t) is the unit step functin) (A) 5t (B) t 5t e ut 7e ut t e u(t) 7e u t (C) t 5t 7e ut e u t (D) t 5t 7e ut e ut Key: (B) Given causal LTI system d y t 7dy t 5dx(t) y t ux t dt dt dt s y s 7sy s y s u x s 5sx(s) Hs ht (impulse respnse). Ys 4 5s 5s 4 X s s 7s s s 5 Inverse Laplace transfrm will give 7 Hs s s 5 h t e u t 7e u t t 5t ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 7

18 EE GATE-7-PAPER-I 7. The apprximate transfer characteristic fr the circuit shwn belw with an ideal peratinal amplifier and dide will be Key: (A) 8. The switch in the figure belw was clsed fr a lng time. It is pened at t =. The current in the inductr f H fr t, is (A) Key: (A) at t 4t.5e (B) I 6 4t 5e 8 (C).5t.5e (D) 5e.5t 5V 8 IL O 5 I 5A IL.5A ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 8

19 EE GATE-7-PAPER-I Fr t 8 8 H.5A L T Req 8 4 I bc itisasurcefreeckt L t/t 4t il t IL IL IL e.5e 9. The bus admittance matrix fr a pwer system netwrk is j9.9 j j j j9.9 j pu j j j9.9 There is a transmissin line, cnnected between buses and, which is represented by the circuit shwn in figure. If this transmissin line is remved frm service, What is the mdified bus admittance matrix? (A) (C) j9.9 j j j9.9 j pu j j9.9 j9.95 j j j9.9 j pu j j9.95 Key: (C) When the line - is remved z.5 z y j, y y.5 y ' Half line shunt susceptance = j.5 ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India (B) (D) y' y new = y ld y j9.9 j j.5 j9.95 y' y new = y ld y j9.9 j j.5 j9.95 j9.95 j j j9.9 j pu j j9.95 j9.95 j j j j9.9 j pu j j j9.95 j9.95 j Mdified Bus admittance matrix: ybusnew j j9.9 j j j9.95 pu 9

20 EE GATE-7-PAPER-I 4. In the system whse signal flw graph is shwn in the figure, U (s) and U (s) are inputs. The transfer functin Y(s) is U (s) (C) Key: (A) k (A) JLs JRs k k k U R sl JLs JR UL s kk UR s Ys U U s By Masns gain frmula P Ys U s L L k Here P. k LJ R L Ls L. k k LJ s k Ys. s LJ U s R.. k k L s LJ s k T / F s LJ srj k k k (B) JLs JRs k k (D) k U sl R JLs JR UL s kk UR s 4. Fr a system having transfer functin G s, a unit step input is applied at time t=. s The value f the respnse f the system at t=.5 sec is. Key:.55 t.556 Y s s R s s ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

21 s Ys. s s Ys s s Apply Inverse L.T EE GATE-7-PAPER-I t.5 y t u t e u t y.5 e.4466 y The magnitude f magnetic flux density (B) in micr Teslas T at the center f a lp f wire wund as a regular hexagn f side length m carrying a current (I=A), and placed in vacuum as shwn in the figure is. Key:.65 t.75 Fr a finite length cnductr B at a pint P I 4r B cs cs P Fr a given hexagn 4 fr a side r 6 I 4r Ttal flux density B 6 cs cs cs 6 cs 6 4 / Tesla 6 6 I 6 ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

22 EE GATE-7-PAPER-I 4. The figure shws the single line diagram f a pwer system with a duble circuit transmissin line. The expressin fr electrical pwer is.5 sin, where is the rtr angle. The system is perating at the stable equilibrium pint with mechanical pwer equal t pu. If ne f the transmissin line circuits is remved, the maximum value f as the rtr swings, is. radian. If the expressin fr electrical pwer with ne transmissin line circuit remved is P max sin, the valuef P in pu is. max, Key:. t. Given m.rad Pm sin.5.5 sin rad Using equal area criterin A =A m m m max m P P sin d P sin P d By slving abve integratin P max Pm m..797.pu cs cs cs4.8 cs69.95 m P C.5.5sin P m = P m = m Pm sin 44. A 75W, V, 5 Hz capacitr start single-phase inductin mtr has the fllwing cnstants fr the main and auxiliary windings (at starting): Z.5 j5.75 a m (main winding), Z 4.5 j.75 (auxiliary winding). Neglecting the magnetizing branch the value f the capacitance (in F ) t be added in series with the auxiliary winding t btain maximum trque at starting is. Key: 95 t X x x m a e tan tan 9 Rm Ra Xc tan tan Xc.75 Xc 5.56 tan 9 tan Xc.79 Xc Xc 98.87F 5.94 ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

23 45. A functin f(x) is defined as EE GATE-7-PAPER-I f (x) x e, x nx ax bx, x fllwing statements is TRUE? (A) f(x) is NOT differentiable at x= fr any values f a and b. (B) f(x) is differentiable at x = fr the unique values f a and b (C) f(x) is differentiable at x = fr all values f a and b such that a + b = e (D) f(x) is differentiable at x = fr all values f a and b. Key: (A) Nt matching with IIT key x f x f e a b Lf Lt Lt x x x x x where x. Which ne f the des nt exists, fr any values f a and b fx is nt differentiable at x, fr any values f a and b. 46. Cnsider a causal and stable LTI system with ratinal transfer functin H(z). Whse crrespnding impulse respnse begins at n =. Furthermre, 5 H. The ples f H(z) are 4 k Pk expj fr k =,,,4. The zers f H(z) are all at z =. Let g[n] = j n h[n]. 4 The value f g[8] equals. Key:.6 t Only ne f the real rts f f x x x lies in the interval x and bisectin methd is used t find its value. Fr achieving an accuracy f., the required minimum number f iteratins is. Key: t b a a, b and. using bisectin methd n n n is the minimum number f iteratins 48. Tw parallel cnnected, three-phase, 5Hz, kv, star-cnnected synchrnus machines A and B, are perating as synchrnus cndensers. They tgether supply 5 MVAR t a kv grid. Current supplied by bth the machines are equal. Synchrnus reactances f machine A and machine B are and respectively. Assuming the magnetic circuit t be linear, the rati f excitatin current f machine A t that f machine B is. kv Key:.5 t. syn. Cndencrs current s supplied bth the machines are same 64. I I.59 Amps As the tw mtrs, supplying reactive pwer nly, the phasr diagaram will be I I ~ ~ ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India A B 5 MVAR 6 5 IL 64.

24 EE GATE-7-PAPER-I E ji X V a s t E V ji X a s Cnsider magnitudes E V I X A a S E V I X E vlts a s I a V t 9 IX a s E B fb E Vlts IfA E 58.7 I E 44.4 A B The psitive, negative and zer sequence reactances f a wye-cnnected synchrnus generatr are. pu,. pu, and. pu, respectively. The generatr is n pen circuit with a terminal vltage f pu. The minimum value f the inductive reactance, in pu, required t be cnnected between neutral and grund s that the fault current des nt exceed.75 pu if a single line t grund fault ccurs at the terminals is (assume fault impedance t be zer). Key:. t. Ef If Z Z Z Z n Zn Zn.P.U k x t t k be passed thrugh an LTI system with frequency respnse H, as given in the figure belw 5. Let the signal k Key: (C) The Furier series representatin f the utput is given as (A) 4+4cs t 4cs 4 t (B) cs t cs 4 t (C) 4cs t (D) cs t Given xt is a peridic signal fr which Furier transfrm x is t be calculated ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 4

25 EE GATE-7-PAPER-I x D n n n D n is expnential Furier series cefficient fr x(t) x t Define xt ver ne perid xt t t Where as T sec; rad/sec jn t Dn e ; t T n D n e j n D n At i.e., n,,4,...d n = D n fr even valuesf n fr dd values f n x D D D D 4 D 4...] x D D D D t Given x is x t 5 5 Thus the filtered utput is y D D D D y 4 yt 4cs t ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 5

26 EE GATE-7-PAPER-I 5. The lgical gate implemented using the circuit shwn belw where. V and V are inputs (with V as digital and 5 V as digital ) and V OUT is the utput is (A) NOT (B) NOR (C) NAND (D) XOR Key: (B) V V Q Q V ut Lgic Level OFF OFF 5V OFF ON V ON OFF V ON ON V S, this lgic level /p is shwing the functinality f NOR-gate. 5. A lad is supplied by a V, 5 Hz surce. The active pwer P and the reactive pwer Q cnsumed by the lad are such that kw P kw and kvar Q kvar. A capacitr cnnected acrss the lad fr pwer factr crrectin generates kvar reactive pwer. The wrst case pwer factr after pwer factr crrectin is (A).447 lag (B).77 lag (C).894 lag (D) Key: (B) Under wrst case, P P Q max max kw kvar Q tan 45 P cs 45.77lag 5. The input vltage V DC f the buck-bst cnverter shwn belw varies frm V t 7 V. Assume that all cmpnents are ideal, inductr current is cntinuus, and utput vltage is ripple free. The range f duty rati D f the cnverter fr which the magnitude f the steady state utput vltage remains cnstant at 48 V is (A) D 5 5 (B) D (C) D (D) D 4 Key: (A) ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 6

27 EE GATE-7-PAPER-I V V V 7V dc V 48V V 48V V D V D V D V D dc 48 D D D D D D D D D D 5D 5D D D 5 5 D 5 5 dc dc 54. A three-phase, three winding / / Y (.kv/6.6kv/4 V) transfrmer is energized frm AC mains at the. kv side. It supplies 9 kva lad at.8 pwer factr lag frm the 6.6 kv winding and kva lad at.6 pwer factr lag frm the 4 V winding. The RMS line current in ampere drawn by the. kv winding frm the mains is. Key: 6 t 67, winding T F / / Y per phase representatin.kv ~ I 6.6 kv I 9 kva.8 I 9 Iph I 78.7 Amps 6.6 I KI I I 4. Amp 4 I I I ph L 4 I 4. I I I I I I I I 4 kva.6 ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 7

28 EE GATE-7-PAPER-I Cnsider the line integral C belw. I x iy dz where z = x + iy. The line C is shwn in the figure The value f I is (A) i (B) i Key: (B) curve C is y x dy dx (C) i 4 x I x i x dx idx i x dx i i (D) 4 i 5 General Aptitude Q. N. 5 Carry One Mark Each. Research in the wrkplace reveals that peple wrk fr many reasns. (A) mney beside (B) beside mney (C) mney besides (D) besides mney Key: (D). The prbability that a k-digit number des NOT cntain the digits.5, r 9 is (A). k (B).6 k (C).7 k (D).9 k Key: (C) k digits Each digit can be filled in 7 ways as, 5 and 9 is nt allwed, s each f these places can be filled by,,, 4, 6, 7, 8. 7 S required prbability is k k r.7.. Find the smallest number y such that y 6 is a perfect cube. (A) 4 (B) 7 (C) (D) 6 Key: (D) Factrizatin f 6 is y6 is a perfect cube y Perfect cube Fr perfect cube 's & 's are tw mre required each. ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 8

29 EE GATE-7-PAPER-I 4. After Rajendra Chla returned frm his vyage t Indneisa, he t visit the temple in Thanjavur. (A) was wishing (B) is wishing (C) wished (D) had wished Key: (C) 5. Rahul, Murali, Srinivas and Arul are seated arund a square table. Rahul is sitting t the left f Murali. Srinivas is sitting t the right f Arul. Which f the fllwing pairs are seated ppsite each ther? (A) Rahul and Murali (B) Srinivas and Anil (C) Srinivas and Murali (D) Srinivas and Rahul Key: (C) Srinivas Rahul Arul Murali Q. N. 6 Carry Tw Marks Each 6. Six peple are seated arund a circular table. There are at least tw men and tw wmen. There are at least three right-handed persns. Every wman has a left-handed persn t her immediate right. Nne f the wmen are right-handed. The number f wmen at the table is (A) (B) (C) 4 (D) Cannt be determined Key: (A) Out f six peple, place definitely ccupied by right handed peple as atleast wmen are there s these tw will sit adjacently. Nw as nly ne seat is left it will be ccupied by a left handed man because n right side f this seat is sitting an right handed man. R m R m R m Therefre, answer shuld be wmen. L w L w? 7. The expressin x y x y (A) the maximum f x and y (C) Key: (B) is equal t (B) the minimum f x and y (D) nne f the abve ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 9

30 EE GATE-7-PAPER-I If x y x y x y Exp If x y y min x y y x Exp xmin x y x y The expressin is equal tminimumf x & y 8. A cntur line jins lcatins having the same height abve the mean sea level. The fllwing is a cntur plt f a gegraphical regin. Cntur lines are shwn at 5m intervals in this plt. If in a fld, the water level rises t 55m. Which f the villages P,Q,R,S,T get submerged? (A) P, Q (C) R,S,T Key: (C) (B) P,Q,T (D) Q,R,S The given cntur is a hill statin, the peak pint f this hill statin is P, it is under a cntur f 55. At flds, the water level is 55m. S the village f R, S and T are under a cntur f 5. Therefre these villages are submerged. 9. Arun, Gulab, Neel and Shweta must chse ne shirt each frm a pile f fur shirts clured red, pink, blue and white respectively. Arun dislikes the clur red and Shweta dislikes the clur white, Gulab and Neel like all the clurs. In hw many different ways can they chse the shirts s that n ne has a shirt with a clur he r she dislikes? (A) (B) 8 (C) 6 (D) 4 Key: (D) As there are 4 peple A,G,N,S and 4 clurs s withut any restrictin ttal ways have t be 44 6 Nw, Arun dislikes Red and Shweta dislikes white S 6-=4 ways. The hld f the natinalist imaginatin n ur clnial past is such that anything inadequately r imprperly natinalist is just nt histry. Which f the fllwing statements best reflects the authr s pinin? (A) Natinalists are highly imaginative. (B) Histry is viewed thrugh the filter f natinalism. (C) Our clnial past never happened (D) Natinalism has t be bth adequately and prperly imagined. Key: (B) ICP Intensive Classrm Prgram egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India