Electrical Engineering Q. No Carry One Mark Each. 1. In the circuit shown, the diodes are ideal, the inductance is small, and Io

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1 EE GATE-07-PAPE-II Electrical Engineering Q. N. 5 Carry One Mark Each. In the circuit shwn, the dides are ideal, the inductance is small, and I 0. Which ne f the fllwing statements is true? Key: (A) (A) D cnducts fr greater than () D cnducts fr mre than (C) D cnducts fr (D) D cnducts fr mre than 80 and D cnducts fr greater than 80 and D cnducts fr 80 and D cnducts fr and D cnducts fr Fr a -input lgic circuit shwn belw, the utput Z can be expressed as 80 P Q Z (A) Q () PQ (C) Q (D) P Q Key: (C) PQ.Q.Q PQ Q Q Q Q Q QP Q Q A A A Q P PQ Q Z PQ.Q.Q. An urn cntains 5 red balls and 5 black balls. In the first draw, ne ball is picked at randm and discarded withut nticing its clur. The prbability t get a red ball in the secnd draw is (A) () 4 9 (C) 5 9 (D) 6 9 Key: (A) 5 5 4, 5 5, ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

2 EE GATE-07-PAPE-II Here is red ball, is black ball The prbability t get a red ball in the secnd draw is When a unit ramp input is applied t the unity feedback system having clsed lp transfer Cs Ks b functin a 0,b 0,K 0, the steady state errr will be (A) 0 Key: (D) Given s s as b Cs s Ts C t r t t () a b Apply L.T t abve equatins E s s T s (C) a K b (D) a Ks b s sa K s a K ess C lt S.E s lt.s. s 0 s 0 lt lt s 0 s 0 s s as b s s as b s as b a K ess b 5. A three-phase vltage surce inverter with ideal devices perating in feeding a balanced star-cnnected resistive lad. The DC vltage input is fundamental cmpnent f the phase vltage is K b 80 cnductin mde is dc. The peak f the (A) dc () dc (C) dc Key: () Furier series expansin f line t neutral vltage a is given by a s sin nt n6k n s fr n, a max value (D) 4 dc 6. The figures shw diagrammatic representatins f vectr fields X, Y and Z respectively. Which ne f the fllwing chices is true? (A).X 0, Y 0, Z 0 (C).X 0, Y 0, Z 0 ().X 0, Y 0, Z 0 (D).X 0, Y 0, Z 0 ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

3 EE GATE-07-PAPE-II Key: (C) fr x Divergence nt equal t zer x 0 Divergence 0 fr y t 0 Curl 0 Divergence 0 fr z z 0 Curl 0 7. Assume that in a traffic junctin, the cycle f the traffic signal lights is minutes f green (vehicle des nt stp) and minutes f red (vehicle stps). Cnsider that the arrival time f vehicles at the junctin is unifrmly distributed ver 5 minute cycle. The expected waiting time (in minutes) fr the vehicle at the junctin is. Key: 0.9 t Cnsider a slid sphere f radius 5 cm made f a perfect electric cnductr. If ne millin electrns are added t this sphere, these electrns will be distributed. (A) unifrmly ver the entire vlume f the sphere () unifrmly ver the uter surface f the sphere (C) cncentrated arund the centre f the sphere (D) alng a straight line passing thrugh the centre f the sphere Key: () Fr a perfect cnductr the charge is present nly n the surface. Pu 0 i.e, inside the cnductr E 0 9. The transfer functin Cs f a cmpensatr is given belw. Cs s s s s 0 The frequency range in which the phase (lead) intrduced by the cmpensatr reaches the maximum is (A) 0. () 0 (C) 0 00 (D) 00 Key: (A) 0. The figure shw the per-phase representatin f a phase-shifting transfrmer cnnected between buses and, where is a cmplex number with nn-zer real and imaginary parts. ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

4 EE GATE-07-PAPE-II Fr the given circuit, Y bus and Z bus are bus admittance matrix and bus impedance matrix, respectively, each f size. Which ne f the fllwing statements is true? (A) th () (C) Key: (D) Y bus and Z bus are symmetric Y bus is symmetric and Z bus is unsymmetric Y bus is unsymmetric and Z bus is symmetric (D) th Y US US yt a yt a z y Y bus and Z bus are unsymmetric bus yt a* yt. A phase-cntrlled, single-phase, full-bridge cnverter is supplying a highly inductive DC lad. The cnverter is fed frm a 0, 50 Hz, AC surce. The fundamental frequency in Hz f the vltage ripple n the DC side is (A) 5 () 50 (C) 00 (D) 00 Key: (C) m Q Fr ne input pulse, has pulses frequency f ripple = f supply 50 00Hz. Let x and y be integers satisfying the fllwing equatins x y 4 x y The value f x y is. Key: 7 t 7 Clearly x = and y = 4 satisfies the given tw equatin x y 7. Cnsider a functin f x, y,z given by f x, y,z x y z y z The partial derivative f this functin with respect t x at the pint, x =, y = and z = is Key: 40 t 40 f y z x at x, y, z x ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 4

5 EE GATE-07-PAPE-II 4. Fr the given -prt netwrk, the value f transfer impedance Z in hms is Key: t Z I I 0 I I I Z I I I I 4 I I x I 5. The initial charge in the F capacitr present in the circuit shwn is zer. The energy in jules transferred frm the DC surce until steady state cnditin is reached equals. (Give the answer up t ne decimal place.) Key: 99 t efre initial charge n the capacitr Final vltage c 0 c T find time cnstant 00 eq ; C 5 eq t t c t C C 0 C e 0 0e d dt C t5 ic t C e i i e We knw that t5 r C Instantaneus pwer p i 0 e 0e r t 5 t 5 t5 e pdt 0e dt J 5 t5 Energy transferred ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 5

6 EE GATE-07-PAPE-II 6. The figure belw shws the circuit diagram f a cntrlled rectifier supplied frm a 0, 50 Hz, -phase vltage surce and a 0: ideal transfrmer. Assume that all devices are ideal. The firing angles f the thyristrs T and T are 90 and 70, respectively. The MS value f the current thrugh dide D in amperes is Key: 0 t 0 0A since D is OFF and it will nt turn ON fr lad. 7. In a lad flw prblem slved by Newtn-aphsn methd with plar crdinates, the size f the Jacbian is If there are 0 P buses in additin t PQ buses and a slack bus, the ttal number f buses in the system is. Key: 6 t 6 Given the size f bus is 00*00. s [J]= 00 we have frmula fr [J] = [n-m-] 00= [n-0-] ttal n.f buses,n = 6 8. A -phase, 4-ple, 400, 50 Hz squirrel-cage inductin mtr is perating at a slip f 0.0. The speed f the rtr flux in mechanical rad/sec, sensed by a statinary bserver, is clsest t (A) 500 () 470 (C) 57 (D) 54 Key: (C) S.C.I.M 4 P s N r r tr flux speed is same as statr flux speed Ns N 500 Ws rad sec Tw resistrs with nminal resistance values and have additive uncertainties and, respectively. When these resistances are cnnected in parallel, the standard deviatin f the errr in the equivalent resistance is (A) () ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 6

7 EE GATE-07-PAPE-II (C) (D) Key: (A) eq O 0. The nminal- circuit f a transmissin line is shwn in the figure. Impedance Z and reactance X 00. The magnitude f the characteristic impedance f the transmissin line, in, is. (Give the answer up t ne decimal place.) Key: 404 t 408 y x y x 00 4 z 00 z y The ple-zer plts f three discrete-time systems P, Q and n the z-plane are shwn belw. Key: Which ne f the fllwing is TUE abut the frequency selectivity f these systems? (A) All three are high-pass filters. () All three are band-pass filters. (C) All three are lw-pass filters. (D) P is a lw-pass filter, Q is a band-pass filter and is a high-pass filter. () 0 rad / samples reprsent lwfrequencies ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 7

8 EE GATE-07-PAPE-II rad / samples reprsent highfrequencies Since zers are lcated at 0 rad / samples and rad / samples they cannt be high pass and lw pass filters. Thus they all replresent band pass filters.. The mean square value f the given peridic wavefrm ft is Key: 6 t 6 Area under the squarred functin Mean square value Perid f the functin Area vlt secnd Perid Mean square value 6 4 f 6 4 t A statinary clsed Lissajus pattern n an scillscpe has hrizntal tangencies and vertical tangencies fr a hrizntal input with frequency khz. The frequency f the vertical input is (A).5 khz () khz (C) khz (D) 4.5 khz Key: (D) 9 fr 4.5 khz n f f y x n n x y ny 4. Let y y x and x y 5. The value f x y equals. (Give the answer up t three decimal places) Key: 5.7 t 5.8 y y x x y x y 5 gives y 5 y x 4 x y ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 8

9 EE GATE-07-PAPE-II 5. If a synchrnus mtr is running at a leading pwer factr, its excitatin induced vltage E f is Key: (A) equal t terminal vltage (C) less than terminal vltage () Higher than the terminal vltage. t () higher than the terminal vltage t t (D) dependent upn supply vltage t ii X a s E f E i I a Q Q. N Carry Tw Marks Each 6. Which f the fllwing systems has maximum peak versht due t a unit step input? 00 (A) s 0s (C) s 5s 00 Key: (C) Peak ver sht e 00 () s 5s (D) s 0s 00 If 0,peak ver sht 00% Maximum In General If peak ver sht 0% Minimum Here which f the fllwing has ' ' value less, the system will have maximum ver sht. Optin A, n 0, n Optin n 0, n Optin C n 0, n Optin D n 0, n 0 S, ptin C is crrect (O) y Inspectin, see all ptins n cnstan t, nvaries, s, n less means, that system have maximum ver sht. 7. Cnsider an verhead transmissin line with -phase, 50 Hz balanced system with cnductrs lcated at the vertices f an equilateral triangle f length Dab Dbc Dca m as shwn in figure belw. The resistance f the cnductrs are neglected. The gemetric mean radius (GM) f each cnductr is 0.0m. Neglecting the effect f grund, the magnitude f psitive sequence reactance in / km (runded ff t three decimal places) is ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 9

10 Key: 0.7 t 0.0 EE GATE-07-PAPE-II D D D D m GMD eq ab bc ca DS GM 0.0m 7 Dm 7 7 Inductance/phase/m 0 ln 0 ln 9.0 H D 0.0 Inductance/phase/km eactance S H 4 L / km 8. Tw generating units rated 00 MW and 400 MW have gvernr speed regulatin f 6% and 4% respectively frm n lad t full lad. th the generating units are perating in parallel t share a lad f 600 MW. Assuming free gvernr actin, the lad shared by the larger unit is MW. Key: 95 t 405 Assume N lad speed regulatins are equal E % Speed eg A 6% x 4% F G C D 400MW H 00MW Pwer Frm similar triangles methd Pwer 6% F A x x A G 4% E 00 D C 400 H F A ED AD x P 00 6 G A CH AC x P P 50x P 00x Given that PP 600MW 50x 600 x 4 The lad supplied by largest machine is P =00 4=400MW ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 0

11 EE GATE-07-PAPE-II 9. Fr the netwrk given in figure belw, the Thevenin s vltage ab is Key: (A) -.5 () -0.5 (C) 0.5 (D).5 (A) The equivalent CKT is Apply ndal th 0 th th th th th 8 th th th a b The utput y(t) f the fllwing system is t be sampled, s as t recnstruct it frm its samples uniquely. The required minimum sampling rate is Key: (A) 000 samples/s () 500 sample/s (C) 000 samples/s (D) 000samples/s () xf Cnvlutin f cs000t f f Cnsider cs000t f 500 f 500 Input signal t the LTI system is F ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

12 EE GATE-07-PAPE-II x f f 500f 500 W f f 500 f 500 If the input signal is defined as w(t) then its Furier transfrm can be drawn as fllws: f f Given sin 50t h f 500 sinc500t t f H f rect 500 Yf Wf Hf has a max frequency 750 HZ Minimum sampling rate = 500 HZ Hf f. A 0, 0 kw, 900 rpm separately excited DC mtr has an armature resistance a 0.0. When the mtr perates at rated speed and with rated terminal vltage, the electrmagnetic trque develped by the mtr is 70 Nm. Neglecting the rtatinal lsses f the machine, the current drawn by the mtr frm the 0 supply is (A) 4. A () 0 A (C) A (D) 4.84 A Key: () Separately excited d.c. mtr NT P EbIa I a...() E b I E a a b E E b b 0E E y slving abve equatin We get Eb 9.9, E b 0.6 b b b a a a a b k 0.0 E 0 E I I I 0.5 Amps E b I a 0 ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

13 EE GATE-07-PAPE-II A cascade system having the impulse respnses h n, and h n, figure belw, where symbl dentes the time rigin. is shwn in the The input sequence xn fr which the cascade system prduces an utput sequence yn,,,,, is (A) xn,,, () xn,,, (C) xn,,, (D) xn,,, Key: (D) h(n) h [n]*h[n] {, 0, } Y[n]=h(n)*x(n) y[n] {,,,,, } Given y bservatin x[n] shuld be{,,,} Y Fr the circuit shwn in the figure belw, it is given that 9and E 0.7 when the -E junctin is frward biased. The transistr has CC CE. Fr this circuit, the value f is (A) 4 () 9 (C) (D) 9 Key: (D) ec 0 Given CE 5 ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

14 EE GATE-07-PAPE-II 0 I 4 I 0.7 I. 0 0I 4 I 0.7 0I 9. I I 50...() 0 4 I I CE 0 0I 5 0I. 5 I...() 50 0 Substituting equatin () in equatin () ; A -phase, -ple, 50 Hz, synchrnus generatr has a rating f 50 MA, 0.8 pf lagging. The kinetic energy f the machine at synchrnus speed is 000 MJ. The machine is running steadily at synchrnus speed and delivering 60 MW pwer at a pwer angle f 0 electrical degrees. If the lad is suddenly remved, assuming the acceleratin is cnstant fr 0 cycles, the value f the pwer angle after 5 cycles is electrical degrees. Key:.5 t.9 Pa Pm Pe mw GH 000 m 80f t 0cycles 0.5sec 50 5 t 5cycles 0.sec 50 P a t m 9 New rati, Fr the circuit shwn belw, assume that the OPAMP is ideal. ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 4

15 EE GATE-07-PAPE-II Which ne f the fllwing is TUE? (A) vo vs () vo.5vs (C) vo.5vs (D) vo 5vS Key: (C) At nde () s 4 s x At nde () x x y 0 ; s x y y s At nde () y x y y 0 s s s s 0; s s 5s ;.5s s x x y 6. The rt lcus f the feedback cntrl system having the characteristic equatin Key: () s 6Ks s 5 0 where K 0, enters int the real axis at (A) s () s 5 (C) s 5 (D) s 5 C.E s 6ks s 5 0 6ks 0 s s 5 G s s s 5 6ks s s 5 5 K s 6s 6 s dk ds s s 5 0 s 5 S= 5 it enters 5 j j j ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 5

16 EE GATE-07-PAPE-II 7. Fr the synchrnus sequential circuit shwn belw, the utput Z is zer fr the initial ' ' ' cnditins Q Q Q Q Q Q 00. A C A C The minimum number f clck cycles after which the utput Z wuld again becme zer is Key: 6 t 6 Upper part f the circuit is ring cunter and lwer part f the circuit is Jhnsn cunter as per the cnnectin established. Outputs f the ing cunter and Jhnsn cunter is given t Ex-O. Gates, whse utput is given t the three inputs O-gate. ing cunter utput ing cunter utput Jnsn cunter utput Q A Q Q C Q A Q Inital valume CP 0 0 CP Q C CP CP CP CP S, utput Z will becme again after 6 clck pulses. Z 8. In the circuit shwn belw, the value f capacitr C required fr maximum pwer t be transferred t the lad is ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 6

17 EE GATE-07-PAPE-II (A) nf () F (C) mf (D) 0 mf Key: (D) T get the maximum pwer the lad Ckt must be at resnance i.e. imaginary part f lad impedance is zer. jc jc Z jl jl jl jc C jc L j term 0 L L 50 C C 0 C C C C 4 Frm ptins C 0mF will satisfy the abut equatin 9. In the circuit shwn all elements are ideal and the switch S is perated at 0 khz and 60% duty rati. The capacitr is large enugh s that the ripple acrss it is negligible and at steady state acquires a vltage as shwn. The peak current in amperes drawn frm the 50 DC surce is. (Give the answer up t ne decimal place.) Key: 9 t 4 Given is uckbst cnverter D S 0 D Given s 50, D 0.6, 75 Is D I D 0.6 s 75 I 5A 5 D I s. I 5.5A D Since capacitr is very large, ic 0 i i i L avg s avg avg I I I A L s D I 5A S L fl 0, I 5 Peak current drawn frm surce is 40A L il peak IL A ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 7

18 EE GATE-07-PAPE-II In the circuit shwn in the figure, the dide used is ideal. The input pwer factr is. (Give the answer up t tw decimal places.) Key: 0.70 t 0.7 m r m S m r m Ir 0 m S S P Lad r Ir r S IPF InputA I S r S S 4. Cnsider the system described by the fllwing state space representatin xt 0 xt 0 u t 0 x t x t t x yt 0 x t If ut is a unit step input and x 0 0 ff t three decimal places) is Key:.80 t.87 Given 0 C 0 0 A 0 x 0, the value f utput s s 0 s 0 0 s Xs SI A x 0 u s / S s s 0 ss s s s x s ; y s s s s s s s yt at t = sec (runded ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 8

19 ys EE GATE-07-PAPE-II s s s s 4s s 4 s yl 4t t4t e 4t e y.88 t 4. A star-cnnected,.5 kw, 08 (line), -phase, 60 Hz squirrel cage inductin mtr has fllwing equivalent circuit parameters per phase referred t the statr: 0., 0.,X 0.4,X 0.4. Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) fr this mtr when cnnected t an 80 (line), 0 Hz, - phase AC surce is. Key: 69 t 7 eactance ffered by statr and tr will be changes, because f change in frequency. 0 x x ph Ist Iph Isc Z eq j Amps 80 v, 0Hz X X I st I sc 4. A 5 ka, 400, - cnnected, -phase, cylindrical rtr synchrnus generatr requires a field current f 5 A t maintain the rated armature current under shrt-circuit cnditin. Fr the same field current, the pen-circuit vltage is 60. Neglecting the armature resistance and magnetic saturatin, its vltage regulatin (in % with respect t terminal vltage), when the generatr delivers the rated lad at 0.8 pf leading, at rated terminal vltage is. Key: -5 t -4 5kA, 400, cnnectin c 60 I I,I 5A SC rated f phase 60 c Xs Zs 7.8 Isc phase 0.8 I I L ph Amps Amps a a a s E cs I sin I X Eph vlts % eg 4.6% 400 Hint: Obtained regulatin shuld be negative. ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 9

20 EE GATE-07-PAPE-II If the primary line vltage rating is. k (Y side) f a 5 ka. Y transfrmer (the per phase turns rati is 5:), then the line current rating f the secndary side (in Ampere) is. Key: 7 t 9 5KA, Y D,.k N : N 5: L 50 Ist.0 I I 4.74 Amps ph Transfrmer is a cnstant-pwer device E I E I N 5 N I N I I.I 4.74 N I I.869 Amps side ph I I Amps L 45. Fr the balanced Y-Y cnnected -Phase circuit shwn in the figure belw, the line-line vltage is 08 rms and the ttal pwer absrbed by the lad is 4 W at a pwer factr f 0.6 leading. Key: The apprximate value f the impedance Z is (A) (C) (C) 5. () (D) L 08, P 4W cs0.6 leading P I cs ph ph P..csz z 4 ph ph ph ph cs z zph 5. I 5. I ph ph ph ph ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 0

21 EE GATE-07-PAPE-II A thin sap bubble f radius = cm, and thickness a.m a, is at a ptential f with respect t a reference pint at infinity. The bubble bursts and becmes a single spherical drp f sap (assuming all the sap is cntained in the drp) f radius r. The vlume f the sap 4 r. in the thin bubble is 4 a and that f the drp is The ptential in vlts, f the resulting single spherical drp with respect t the same reference pint at infinity is. (Give the answer up t tw decimal places.) Key: 9.50 t 0.50 Charge must be same 4 a P r P r a The ptential f thin bubble is Q 4E 0 0 Q 40 0 C Ptential f Sap drp Q 4 r The value f the cntur integral in the cmplex-plane z z dz z Alng the cntur Z =, taken cunter-clckwise is (A) 8 i () 0 (C) 4 i Key: (C) z = is the singularity lies inside C : z (D) 48 i z z dz i z z 4 i z z C (Using Cauchy s Integral frmula) ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

22 g x EE GATE-07-PAPE-II x x x x 0 andf x x, x x, x Let Key: Cnsider the cmpsitin f f and g, i.e., f gx present in the interval,0 is: in f g x f g x. The number f discntinuities (A) 0 () (C) (D) 4 (A) x, x fg x is discntinuus at x,0 x, x The number f discntinuities in (fg) (x) present in the interval,0 is 0 Clearly Alternative Methd: f x x fr x 0 and gx x fr x < 0 th f(x) and g(x) are cntinuus when x < 0 x fg is als cntinuus fr x < 0 (Since the cmpsite functin f tw cntinuus functins is cntinuus) The number f discntinuities in the interval,0 i.e., x < 0 is A 0 DC shunt mtr takes A at n lad. It takes 7 A n full lad while running at 00 rpm. The armature resistance is 0.8, and the shunt field resistance is 40. The n lad speed, in rpm, is. Key: 5 t A 0.5 A A E b E b N E b N lad, N? Full lad, N 00rpm N E b N rpm N Eb A 0 ½ digit timer cunter pssesses a base clck f frequency 00 MHz. When measuring a particular input, the reading btained is the same in: (i) Frequency mde f peratin with a gating time f ne secnd and (ii) Perid mde f peratin (in the x 0 ns scale). The frequency f the unknwn input (reading btained) in Hz is. Key: 0000 t A persn decides t tss a fair cin repeatedly until he gets a head. He will make at mst tsses. Let the randm variable Y dente the number f heads. The value f var Y, where var. dentes the variance, equals ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

23 EE GATE-07-PAPE-II (A) 7 8 Key: (C) () (C) 7 64 (D) The figure belw shws a half-bridge vltage surce inverter supplying an L-lad with and L H. The desired fundamental frequency f the lad vltage is 50 Hz. The switch cntrl signals f the cnverter are generated using sinusidal pulse width mdulatin with mdulatin index. M = 0.6. At 50 Hz, the L-lad draws an active pwer f.44 kw. The value f DC surce vltage DC in vlts is (A) 00 () 500 (C) 500 (D) 000 Key: (C) 0. xl L 00 0 z jx 40 j L M 0.6 I L L Lad L 40 A A ILad 6 z 50 A 00rms A A dc P max m.v dc v 500 dc 6A 5. The range f K fr which all the rts f the equatin s s s K 0 are in the left half f the cmplex s-plane is (A) 0 < K < 6 () 0 < K < 6 (C) 6< K < 6 (D) 6< K < 6 Key: (A) C.E s s s k 0 If system t be stable K 06 K 0 K 6 ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India

24 EE GATE-07-PAPE-II The eigen values f the matrix given belw are Key: (A) (A) (0,-,-) () (0,-,-) (C) (0,,) (D) (0,,) Characteristic equatin is ,, are the eigen values 55. A -phase 50 Hz generatr supplies pwer f MW at 7. k t a balanced -phase inductive lad thrugh an verhead line. The per phase line resistance and reactance are 0.5and.95 respectively. If the vltage at the generatr terminal is 7.87 k, the pwer factr f the lad is. Key: 0.75 t 0.85 P MW Z ph E S f t 7. K Z 0.5 j.95 ph 7.87 K E P sin r f t t g a Zs Zs 7.87 t ph E ph sin I a a s f t f t I Z E E cs.4 A / ph PS MW cs cs0.77 f ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 4

25 EE GATE-07-PAPE-II General Aptitude Q. N. 5 Carry One Mark Each. There are five buildings called, W, X, Y and Z in a rw (nt necessarily in that rder). is t the West f W, Z is t the East f X and the West f, W is t the West f Y. Which is the building in the middle? (A) () W (C) X (D) Y Key: (A) Frm the given data, the fllwing is frmed X Z W Y N W E West The building is in the middle East S. Saturn is t be seen n a clear night with the naked eye. (A) enugh bright () bright enugh (C) as enugh bright (D) bright as enugh Key: (). Chse the ptin with wrds that are nt synnyms. (A) aversin, dislike () luminus, radiant (C) plunder, lt (D) yielding, resistant Key: (D) 4. There are red scks, 4 green scks and blue scks. Yu chse scks. The prbability that they are f the same clur is (A) /5 () 7/0 (C) /4 (D) 4/5 Key: (D) C C C 4 C A test has twenty questins wrth 00 marks in ttal. There are tw types f questins. Multiple chice questins are wrth marks each and essay questins are wrth marks each. Hw many multiple chice questins des the exam have? (A) () 5 (C) 8 (D) 9 Key: () x y 0 x MCQ x y 00 y essay type x 5, y 5 ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 5

26 EE GATE-07-PAPE-II Q. N. 6 0 Carry Tw Marks Each 6. An air pressure cntur line jins lcatins in a regin having the same atmspheric pressure. The fllwing is an air pressure cntur plt f a gegraphical regin. Cntur lines are shwn at 0.05 bar intervals in this plt. If the pssibility f a thunderstrm is given by hw fast air pressure rises r drps ver a regin, which f the fllwing regins is mst likely t have a thunderstrm? (A) P () Q (C) (D) S Key: (C) egin Air pressure difference P = 0.05 Q = = 0.0 S = 0.05 In general thunder strms are ccurred in a regin where suddenly air pressure changes (i.e.,) shuld rise (r) sudden fall f air pressure. Frm the given cntur map in regin nly mre changes in air pressure. S, the pssibility f a thunder strms in this regin. S ptin (C) is crrect. 7. There are three bxes. One cntains apples, anther cntains ranges and the last ne cntains bth apples and ranges. All three are knwn t be incrrectly labelled. If yu are permitted t pen just ne bx and then pull ut and inspect nly ne fruit, which bx wuld yu pen t determine the cntents f all three bxes? (A) The bx labelled Apples () The bx labelled Apples and Oranges (C) The bx labelled Oranges (D) Cannt be determined Key: () The persn wh is pening the bxes, he knew that all are marked wrng. Suppse if bxes are labelled as belw. () Apples () Oranges () Apples & Oranges ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 6

27 EE GATE-07-PAPE-II If he inspected frm x(), picked ne fruit, fund range, then he dn t knw whether bx cntains ranges (r) bth apples and ranges. Similarly, if he picked ne fruit frm bx(), fund apple then he dn t knw whether bx cntain apples (r) bth apples and ranges. ut if he picked ne fruit frm bx(), i.e., labelled is apples and ranges, if he fund apple then he can decide cmpulsrily that bx() cntains apples and as he knew all bxes are labelled as incrrect, he can tell bx() cntains bth apples and ranges, bx() cntain remaining ranges. S, he shuld pen bx labelled Apples and Oranges t determine cntents f all the three bxes. 8. We lived in a culture that denied any merit t literary wrks, cnsidering them imprtant nly when they were handmaidens t smething seemingly mre urgent namely idelgy. This was a cuntry where all gestures, even the mst private, were interpreted in plitical terms. The authr s belief that idelgy is nt as imprtant as literature is revealed by the wrd: (A) culture () seemingly (C) urgent (D) plitical Key: () 9. X is a 0 digit number starting with the digit 4 fllwed by the digit 7. Then the number will have (A) 90 digits () 9 digits (C) 9 digits (D) 9 digits Key: (A) X digits X Suppse 47 digits in (47) Similarly 47 cntains digits = 90 digits. 0. The number f rts f in the range 5,5 x e 0.5x 0 is (A) 0 () (C) (D) Key: (C) x f x e 0.5x f ; f 4 6.0, f 0.5; f.; f 0, f., f 7.8, f, f 4, f 5 als ve. As there are sign changes frm +ve t ve and ve t +ve, tw rts will be there in the range [-5, 5]. ICP Intensive Classrm Prgram egate-live Internet ased Classes DLP TarGATE-All India Test Series Leaders in GATE Preparatin 65+ Centers acrss India 7