01. The pole-zero plots of three discrete-time systems P, Q and R on the z-plane are shown below.

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2 : : EE GATE 07 SOLUTIONS 0. The pole-zero plot of three dicrete-time ytem P, Q and R on the z-plane are hown below. pole P Im(z) Q Im(z) R Im(z) 0.5 Re(z) 0.5 Re(z) Re(z) Unit Circle Unit Circle Unit Circle Which one of the following i TRUE about the frequency electivity of thee ytem? (a) All three are high-pa filter (b) All three are band-pa filter (c) All three are low-pa filter (d) P i a low-pa filter, Q i a band-pa filter and R i a high-pa filter. 0. An: (b) Sol: Conider P :- H z z z z 0 z z H j j e e j e H(e j ) H(e j ) j 0 0 It i a band pa filter. Conider Q :- z z z z z 0.5jz 0.5j z 0. 5 H H e j e j e j 0.5 H(e j ) H(e j )

3 : 3 : Forenoon Seion It i alo band pa filter. Conider R :- z z z z z jz j z H H e j e e j j H(e j ) H(e j ) It i a band pa filter. 0. The initial charge in the F capacitor preent in the circuit hown i zero. The energy in joule tranferred from the DC ource until teady tate condition i reached equal. (Give the anwer up to one decimal place.) F 0V An: 00 Sol: F 0V F 0V + 5

4 Total energy tranferred capacitor = CV = (0) = 00J : 4 : EE GATE 07 SOLUTIONS 03. The normal - circuit of a tranmiion line i hown in the figure. Z X X Impedance Z = 0080 and reactance X = The magnitude of the characteritic impedance of the tranmiion line, in, i. (Give the anwer up to one decimal place.) 03. An: Sol: In nominal circuit Z = 0080 Y j 3300 Charactertic impedance = = Where B = Z = 0080 ZY C Y 4 A. C B C B D j 3300 j j j 650 j j = j [ j0.9848] = j( ) = j C =

5 : 5 : Forenoon Seion Z C B C 00 ZC Let y y + = x and x +y = 5. The value of x + y equal. (Given the anwer up to three decimal place) 04. An: 5.73 Sol: Let y y+ = x (y ) = x y x 5 y 5 x y 4 x y 4 x 6 x 8 x x 6 x 8 x 6 8 x 0 8( x 0 x x 4 Alo we know that y 5 x 3 x y The figure how the per-phae repreentation of a phae-hifting tranformer connected between bue and where i a complex number with non-zero real and imaginary part. Ideal tranformer Bu- Z : Bu- For the given circuit, Y bu and Z bu are bu admittance matrix and bu impedance matrix, repectively, each of ize. Which one of the following tatement i true?

6 : 6 : EE GATE 07 SOLUTIONS (a) Both Y bu and Z bu are ymmetric (b) Y bu i ymmetric and Z bu i unymmetric (c) Y bu i unymmetric and Z bu i ymmetric (d) Both Y bu and Z bu are unymmetric 05. An: (d) 06. If a ynchronou motor i running at a leading power factor, it excitation induced voltage (E f ) i (a) equal to terminal voltage V t (b) higher than the terminal voltage V t (c) le than terminal voltage V t (d) dependent upon upply voltage V t 06. An: (b) Sol: For a ynchronou motor V t jx E t I a E t = V t ji a X For a leading pf condition I a V t 0 I a X E t I a, leading V t E t magnitude i higher than V t It i over excited 07. In the circuit hown, the diode are ideal, the inductance i mall, and I 0 0. Which one of the following tatement i true? D ~ D I o

7 : 7 : Forenoon Seion (a) D conduct for greater than 80 and D conduct for greater than 80 (b) D conduct for more than 80 and D conduct for 80 (c) D conduct for 80 and D conduct for 80 (d) D conduct for more than 80 and D conduct for 80 07: An: (b) Sol: DC output voltage v d t for the given circuit i hown in the figure below: V D 0 D will conduct from 0 to 80 and D will conduct from 80 to (80+μ) Hence, option B i elected 08. Conider a function f(x, y, z) given by f (x, y, z) = (x + y z )(y + z ) The partial derivative of thi function with repect to x at the point x =, y = and z = 3 i. 08. An: 40 Sol: f(x, y, z) = (x + y z ) (y + z ) f x y x z f x At (,, 3), A tationary cloed Liajou pattern on an ocillocope ha 3 horizontal tangencie and vertical tangencie for a horizontal input with frequency 3 khz. The frequency of the vertical input i (a).5 khz (b) khz (c) 3 khz (d) 4.5 khz 09. An: (d) Sol: f y Horizontal tangencie Vertical tangencie 3 3kHz = 4.5 khz f x

8 : 8 : EE GATE 07 SOLUTIONS 0. When a unit ramp input i applied to the unity feedback ytem having cloed loop tranfer function C() K b R() a b, (a > 0, b > 0, K > 0), the teady tate error will be (a) 0 0. An: (d) (b) a b k b CLTF Sol: OLTF = a b CLTF k b a b G() = k v k b a k b lt.g() 0 a k Error = k v a k b (c) a K b (d) a K b. Aume that in a traffic junction, the cycle of the traffic ignal light i minute of green (vehicle doe not top) and 3 minute of red (vehicle top). Conider that the arrival time of vehicle at the junction i uniformly ditributed over 5 minute cycle. The expected waiting time (in minute) for the vehicle at the junction i. An: 0.9 Sol: Let x be the arrival time at the light (that ha U(0,5) and y be the waiting at the junction. Then 0, x y 5 x, x x E(y) = y f (y)dy y dy = 5 x = 5 x dx 5x = 0.9 minute 5. Conider a olid phere, of radiu 5 cm made of a perfect electric conductor. If one million electron are added to thi phere, thee electron will be ditributed (a) uniformly over the entire volume of the phere (b) uniformly over the outer urface of the phere (c) concentrated around the centre of the phere (d) along a traight line paing through the centre of the phere.

9 : 9 : Forenoon Seion. An: (b) Sol: Even if we give any number of charge, the charge will reide on it urface only. 5cm Sphere 3. The mean quare value of the given periodic waveform f(t) i 4 f(t) t 3: An: 6 Sol: One cycle time = + + = 4 unit Mean quare value = A phae-controlled, ingle-phae, full-bridge converter i fed from a 30 V, 50 Hz AC ource. The fundamental frequency in Hz of the voltage ripple on the DC ide i (a) 5 (b) 50 (c) 00 (d) An: (c) Sol: Output ripple frequency of pule converter, f f Hz o i 5. Let x and y be integer atifying the following equation x + y = 34 x + y = The value of (x + y) i. 5. An: 7 Sol: x + y = 34 () x + y = () olving () and (), we have x = 3, y = 4 x + y = 7

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11 : : Forenoon Seion 6. The tranfer function C() of a compenator i given below: C() = () 0 The frequency range in which the phae (lead) introduce by the compenator reache the maximum i (a) 0. < < (b) < < 0 (c) 0 < < 00 (d) > An: (a) Sol: Pole zero plot i given below 0. Lead G() = G() = tan 0. tan Phae lead occur from = 0. to = Range 0. < < For the given -port network, the value of tranfer impedance z in ohm i 4 7. An: 3 Sol: V = Z I +Z I V = Z I +Z I Z V I I 0 By applying KVL V +I +I = 0 V = 3I I 4 I + V I + V Z = 3

12 : : EE GATE 07 SOLUTIONS 8. An urn contain 5 red ball and 5 black ball. In the firt draw, one ball i picked at random and dicarded without noticing it colour. The probability to get a red ball in the econd draw i (a) (b) 4 9 (c) 5 9 (d) An: (a) Sol: Given Urn contain 5 red & 5 black ball here we come acro two cae 0. firt drawn ball can be red or black 0. econd drawn ball i red. Probability of firt drawn ball i red and econd drawn ball i red = Probability of firt drawn ball i black and econd drawn ball i red = P A 3-phae, 4-pole, 400 V, 50 Hz quirrel-cage induction motor i operating at a lip of 0.0. The peed of the rotor flux in mechanical rad/ec. ened by a tationary oberver, i cloet to (a) 500 (b) 470 (c) 57 (d) An: (c) Sol: Given A 3-, 4 pole, 50Hz quirrel cage induction motor operating at a lip of 0.0 0F Synchronou peed = rpm P rpm 4 rotor peed = ( )N = ( 0.0)(500) = 470 rpm 0 F The peed of rotor field with repect to rotor i 30rpm P The peed of rotor field with repect to tator i = =500 rpm 500) = rad /ec 60 = rad/ec

13 : 3 : Forenoon Seion 0. In a load flow problem olved by Newton-Raphon method with polar coordinate, the ize of the Jacobian i If there are 0 PV bue in addition to PQ bue and a lack bu, the total number of bue in the ytem i. 0. An: 6 Sol: Size of jacobian matrix i 0000 PV Bue equation PQ Bue equation Slack Bu 0 PV Bue 0 equation Total number of equation 00 Load Bu equation 00 0 = 80 Number of load Bue 40 Total number of bue are 0+40+= 6. The figure how diagramatic repreentation of vector field X, Y,and Z, repectively. Which one of the following choice i true? X Y Z (a). X = 0, Y 0, Z = 0 (b). X 0, Y = 0, Z 0 (c). X 0, Y 0, Z 0 (d). X = 0, Y = 0, Z = 0. An: (c) Sol: X Y Z. X 0 X 0. Y 0 Y 0. Z 0 Z 0

14 : 4 : EE GATE 07 SOLUTIONS. A three-phae voltage ource inverter with ideal device operating in 80 conduction mode i feeding a balanced tar-connected reitive load. The DC voltage input i V dc. The peak of the fundamental component of the phae voltage i (a) Vdc. An: (b) (b) Vdc Sol: Peak value of fundamental component of phae voltage i (c) 3Vdc V 6 3 dc V dc (d) 4Vdc

15 : 5 : Forenoon Seion 3. Two reitor with nominal reitance value R and R have additive uncertaintie R and R, repectively. When thee reitance are connected in parallel, the tandard deviation of the error in the equivalent reitance R i (a) R R R R R R (b) R R R R R R (c) 3. An: (a) R R R R R R (d) R R R R R R 4. The figure below how the circuit diagram of a controlled rectifier upplied from a 30 V, 50 Hz, -phae voltage ource and a 0: ideal tranformer. Aume that all device are ideal. The firing angle of the thyritor T and T are 90 o and 70 o, repectively. 0 : T T 30V 50Hz ~ D 3 R D D i D3 The RMS value of the current through diode D 3 in ampere i 4. An: 0 Sol: D 3 i freewheeling diode and there i no freewheeling action when load i reitive in nature. Hence, RMS value of current through the diode D 3 = 0 A 5. For a 3-input logic circuit hown below, the output Z can be expreed a P Q Z R (a) Q + R (b) PQ+R (c) Q + R (d) P + Q + R 5. An: (c) Sol: Z P.Q.Q.Q. R P.Q = Q Q. R Q R Q Q.R

16 : 6 : EE GATE 07 SOLUTIONS x, x 6. Let g(x) = and x x x, x 0 f(x) =., x x 0 Conider the compoition of f and g, i.e., ( f g) x f gx. The number of dicontinuitie in ( f g) (x) preent in the interval (, 0) i (a) 0 (b) (c) (d) 4 6. An: (a) Sol: Given (f g) (x) = f [g(x)] In (, 0), g(x) = x f[g(x)] = f( x) = ( x) f[g(x)] = + x f[g(x)] ha no dicontinuou point in (, 0)

17 : 7 : Forenoon Seion 7. In the circuit hown all element are ideal and the witch S i operated at 0 khz and 60% duty ratio. The capacitor i large enough o that the ripple acro it i negligible and at teady tate acquire a voltage a hown. The peak current in ampere drawn from the 50 V DC ource i. (Give the anwer up to one decimal place.) S 50V + 0.6mH - 75V An: 40 Sol: Given circuit i buck boot converter. Source current i ame witch current. Peak value of witch current mean, i w, peak V 50 dc I L DT L Io 5 I L 37.5 A D I L, max A 3 I 5 A L,max I L I L 8. For the circuit hown below, aume that the OPAMP i ideal. R R R R R + 0 R Which one of the following i TRUE? (a) 0 = (b) 0 =.5 (c) 0 =.5 (d) 0 = 5 8. An: (c) Sol: Given Circuit can be redrawn a R c R V S R R I I a b R + I 3 R I 4 V 0

18 : 8 : EE GATE 07 SOLUTIONS Since V d 0 V a = V b V b = V R V 4R Apply KCL at a I = I Va R Va Vc R V V c a V Apply KCL at c I = I 3 + I 4 V R Vc Vc V R R Va c 0 V 0 = 3V c V a V = 3V V 0 =.5 V 9. In the circuit hown below, the value of capacitor C required for maximum power to be tranferred to the load i R S =0.5 5mH (t) = 0in(00t) C (a) nf (b) F (c) mf (d) 0 mf 9. An: (d) j Sol: Z [ jx C ] j j jxc jx jxc jx X c c c Load (t) = 0in(00t) R S =0.5 5mH C j X j X c c Xc X c z Load

19 : 9 : Forenoon Seion X = 0 X X X c c X c c X c c 0 X c 4 4() X c C c 00 = 0.0F = 0 mf 30. The output y(t) of the following ytem i to be ampled, o a to recontruct it from it ample uniquely. The required minimum ampling rate i X() 000 X(t) X() 000 in(500t) h(t) t y(t) co(000t) (a) 000 ample/ (b) 500 ample/ (c) 000 ample/ (d) 3000 ample/ 30. An: (b) Sol: X() Output of multiplier i = x(t). co(000t) = Output of multiplier

20 : 0 : EE GATE 07 SOLUTIONS in 500t h(t) t H() Y() = X().H() The maximum frequency in y(t) = 500 m = 500 f n = 750 (f ) min = f n = 500 Hz = 500 ample/ec

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22 : : EE GATE 07 SOLUTIONS 3. A thin oap bubble of radiu R = cm, and thickne a = 3.3 m (a << R), i at a potential of V with repective to a reference point at infinity. The bubble burt and become a ingle pherical drop of oap (auming all the oap i contained in the drop) of radiu r. The volume of the oap in the thin bubble i 4R 4 a and that of the drop i r 3. The potential in volt, of the reulting ingle 3 pherical drop with repect to the ame reference point at infinity i. (Give the anwer up to two decimal place.) a R Soap Bubble Burt Soap drop Of radiu r 3. An: 0.03 Sol: a R Soap bubble Soap droplet (r) 4 3 ( 4R a) r 3 charge denity (c/m 3 ) Y = (3R a) /3 The potential of the bubble. Q V. 4 R Q 4 RV Q = Potential of the oap drop Q V. 4 r 40 0 V 40 0 V = / 3

23 : 3 : Forenoon Seion 3. A cacade ytem having the impule repone h (n) = {, -} and h (n) = {, } i hown in the figure below, where ymbol denote the time origin. x(n) h (n) h (n) y(n) The input equence x(n) for which the cacade ytem produce an output equence y(n) = {,,,,, } i (a) x(n) = {,,, } (b) x(n) = {,,, } (c) x(n) = {,, } (d) x(n) = {,,, } 3. An: (d) Sol: h(n) = h (n) * h (n) h(n) = [, 0, ] Given y(n) = [,,,,, ] y(n) = x(n) * h(n) y(z) = x(z) H(z) y(z) x(z) H z y(z) = + z + z z 3 z 4 z 5 H(z) = z z ) z z z z z z z z z 3 z x(z) = + z +z - +z 3 x(n) = [,,, ] z 3 4 z z z z z 0 z z 5 ( z z z 3

24 : 4 : EE GATE 07 SOLUTIONS 33. Which of the following ytem ha maximum peak overhoot due to a unit tep input? (a) (b) (c) (d) An: (c) 00 Sol: (a) n = 0, = (b) n = 0, = (c) n = 0, = 0. 5 n Thi ha maximum peak over hoot. (d) n = 0, = n n n A 3-phae, -pole, 50 Hz, ynchronou generator ha a rating of 50 MVA, 0.8 pf lagging. The kinetic energy of the machine at ynchronou peed i 00 MJ. The machine i running teadily at ynchronou peed and delivering 60 MW power at a power angle of 0 electrical degree. If the load i uddenly removed, auming the acceleration i contant for 0 cycle, the value of the power angle after 5 cycle i electrical degree. 34. An:.7 Sol: H = 0 4MJ P = P e = 60MW = + t P P t M e 5H 80f

25 : 5 : Forenoon Seion = 0+.7= For the network given in figure below, the Thevenin voltage V ab i 0 0 6A a b 6V (a).5 V (b) 0.5 V (c) 0.5 V (d).5 V 35. An: (a) Sol: a 6A 5 V TH 0 + b 6V V 6 V 30 VTH TH TH VTH 3VTH 48 VTH V TH = 3 V TH.5V 36. A 0½ digit timer counter poee a bae clock of frequency 00 MHz. When meauring a particular input, the reading obtained i the ame in: (i) Frequency mode of operation with a gating time of one econd and (ii) Period mode of operation (in the 0 n cale). The frequency of the unknown input (reading obtained) in Hz i. 36. An: Sol: Frequency counter mode of operation : GATE Counted pule T G = GATE Unknown frequency f x =? n Counter 0 ½ digit Diplay

26 : 6 : EE GATE 07 SOLUTIONS n number of pule are counted within a gating time of one econd. i.e., n = f x.() Period mode of operation: Unknown Time period T x =? GATE 00 Mhz 0n 00MHz n Counter 0 ½ digit Diplay n number of pule are counted within an unknown period of T x. i.e, n = T x 00 MHz () Now, equating the expreion() and ().ince it i given that ame reading i obtained in both mode of operation. f x = T x 00 MHz T x = and f x = 00 MHz n = 00 MHz = = 0 8 pule So, the reading i If the primary line voltage rating i 3.3 kv (Y ide) of a 5 kva, Y- tranformer (the per phae turn ratio i 5 : ), then the line current rating of the econdary ide (in Ampere) i. 37. An: Sol: Given tranformer i Y/ Primary (Y) Secondary () V line = 3.3 kv I line =? VA rated = 5kVA

27 : 7 : Forenoon Seion 5: 3.3kV V V V phae voltage primary V (phae voltage econdary) V 5 V Volt VA 3V I (Delta ide) L L I L I L = 37.88A 38. The figure below how a half-bridge voltage ource inverter upplying a RL-load with R = and L = H. The deired fundamental frequency of the load voltage i 50 Hz. The witch control ignal of the converter are generated uing inuoidal pule width modulation with modulation index, M = 0.6. At 50 Hz, the RL-load draw an active power of.44 kw. The value of DC ource voltage V DC in volt i V DC + R L S V DC + S (a) 300 (b) 500 (c) 500 (d) An: (c) 0.3 Sol: R 40 Ω and X L Ω Load impedance, Z R X Ω Po 440 I o I o L 6 A

28 : 8 : EE GATE 07 SOLUTIONS MVDC 0.6VDC RMS value of fundamental output voltage, Vo V 0.6 V 506 I 6 VDC 500 V Z 0.6 o DC But, o A tar-connected,.5 kw, 08 V (line), 3-phae, 60 Hz quirrel cage induction motor ha following equivalent circuit parameter per phae referred to the tator. R = 0.3, R = 0.3, X = 0.4, X = 0.4. Neglect hunt branch in the equivalent circuit. The tarting current (in Ampere) for thi motor when connected to an 80 V (line), 0 Hz, 3-phae, AC ource i 39. An: 70.9 A Sol: Given parameter of tar-connected SCIM at 60Hz are r = 0.3, r = 0.3 X = 0.4, X = 0.4 Now, if frequency changed to 0 Hz, leakage reactance magnitude will change. 0 X 36 (new) X 36 (new) j j0.36 r jx r jx 80 V 3 I at I t 80/ = 70.9 A 40. Conider the ytem decribed by the following tate pace repreentation x (t) 0 x (t) 0 x(t) 0 u(t) x (t) x(t) y(t) = 0 x(t) If u(t) i a unit tep input and three decimal place) i x(0), the value of output y(t) at t = ec (rounded off to x 0 0

29 : 9 : Forenoon Seion 40. An:.84 Sol: 0 X(0) 0,,C 0,B 0 0 A Input = (unit tep) Y(t) = c X(t) X(t) = L [X()] X() = (SI A) X(0) + (SI A) BU() [SI A] = 0 [SI A] = 0 X() = = X(t) = L [X()] = t t 0.5e e t Y(t) = [ 0] X(t) = [+0.5t e -t ] Y() = = A 0 V, 0 kw, 900 rpm eparately excited DC motor ha an armature reitance R a = 0.0. When the motor operate at rated peed and with rated terminal voltage, the electromagnetic torque developed by the motor i 70 Nm. Neglecting the rotational loe of the machine, the current drawn by the motor from the 0 V upply i (a) 34. A (b) 30 A (c) A (d) 4.84 A 4. An: (b) Sol: V t = 0V; N = 900 rpm T e = 70 N-m T e = K a I a =70 N-m

30 : 30 : EE GATE 07 SOLUTIONS Developed power = T e = E b I a E b Ia (V t I a r a ) I a = [ 0 I a (0.0)] I a = I a Ia 0Ia Solving above equation I a 30.06A I a = For the ynchronou equential circuit hown below, the output Z i zero for the initial condition Q A Q B Q C = Q A Q B Q C = 00. The minimum number if clock cycle after which the output Z would again become zero i. 4. An: 6 Sol: clk Q A Q B Q C Q ' C Q A ' B Q B Q Z ' Q Q A 'B ' Q C Q ' QC Q C Thu after (6) pule, Z again become 0

31 Clk Q A Q B Q ' ' ' C Q Q Q : 3 : Forenoon Seion A B C 43. Two generating unit rated 300 MW and 400 MW have governor peed regulation of 6% and 4% repectively from no load to full load. Both the generating unit are operating in parallel to hare a load of 600 MW. Auming free governor action, the load hared by the larger unit i MW. 43. An: Sol: If both are having ame full load frequencie. P 4 x 400 P 4 x= 00 (4 x) P 6 x 300 P 6 x= 50 (6 x) P = 00 (4 x) + 50 (6 x) x x = 600 x = P = 00 (4 x) = 00 ( ) = MW P = 50 (6 x) = 50 ( ) = 66.7 MW 43. An: 400 Sol: If both are having ame no load frequencie. From the ymmetrical triangle P x P 00x () P x P 50x () P + P = 00x + 50x = 600 x = 4 The load hared by larger unit i,e.,400 MW unit i P = 00x = 00 4 = 400 MW 6% 300MW 4% P 6 x 400MW 4 x x 4% X% P P P 4% 400MW 6% 300 MW 44. A 5 kva, 400 V, -connected, 3-phae, cylindrical rotor ynchronou generator require a field current of 5 A to maintain the rated armature current under hort-circuit condition. For the ame field current, the open-circuit voltage i 360 V. Neglecting the armature reitance and magnetic aturation, it voltage regulation (in % with repect to terminal voltage), when the generator deliver the rated load at 0.8 pf leading at rated terminal voltage i.

32 : 3 : EE GATE 07 SOLUTIONS 44. An: 4.56 Sol: 5 kva, 400V, -connected I L I ph A A 3 I c = 0.83A when I f = 5A V oc(line) = 360V when I f = 5A X V I oc c If given 360(phae voltage) (phae current) For a given leading pf load [co = 0.8 lead] E Vco I r Vin I 0 a a ax = 34. Volt/ph E V voltage regulation 00 V = 4.56% 45. The value of the contour integral in the complex-plane taken counter-clockwie i 3 z z3 dz along the contour z = 3, z (a) 8 i (b) 0 (c) 4 i (d) 48 i 45. An: (c) Sol: C: Z =3 Z = lie inide Z = 3 C Z 3 Z dz Z 3 dz Z Z C

33 : 33 : Forenoon Seion = i() [ where (Z) = Z 3 Z+3] = i[8-4+3] = 4i 46. In the circuit hown in the figure, the diode ued i ideal. The input power factor i (Give the anwer up to two decimal place). 00in(00t) V ~ An: Sol: Input power factor V or P R o Vor V V I or V V R Vm lag Vm 47. A peron decide to to a fair coin repeatedly until he get a head. He will make at mot 3 toe. Let the random variable Y denote the number of head. The value of var{y}, where var{.} denote the variance, equal (a) An: (c) Sol: Let y = number of head Y 0 P(Y) (b) (c) 7 64 (d) E(Y) 8 7 E Y 8 V(Y) = E(Y ) (E(Y)

34 : 34 : EE GATE 07 SOLUTIONS = = The root locu of the feedback control ytem having the characteritic equation + 6K = 0 where K > 0, enter into the real axi at (a) = - (b) = 5 (c) = 5 (d) = An: (b) Sol: CF = + 6k = 0 6k 0 5 I +G() H() = 0 6k G()H() 0 Break point 5 ` I d d 6 0 ( ++) (6) 6 (+) = = = i a breakpoint 49. The range of K for which all the root of the equation K = 0 are in the left half of the complex -plane i (a) 0 < K < 6 (b) 0 < K < 6 (c) 6 < K < 36 (d) 6 < K < An: (a) Sol: k 6 k k 3 k > 0 and k < 6 0 < k < 6

35 : 35 : Forenoon Seion 50. A 3-phae, 50 Hz generator upplie power of 3 MW at 7.3 kv to a balanced 3-phae inductive load through an overhead line. The per phae line reitance and reactance are 0.5 and 3.95 repectively. If the voltage at the generator terminal i 7.87 kv, the power factor of the load i. 50. An: Sol: V =7.87kV V r =7.3kV R = 0.5 X L = 3.95 Z P r co co Co (-) = (-) = Q r V Vr Z in X V Z r in =.8483VAR pf co tan Qr Pr.8483 = co tan 3 = lag

36 : 36 : EE GATE 07 SOLUTIONS 5. For the balanced Y-Y connected 3-phae circuit hown in the figure below, the line-line voltage i 08 V rm and the total power aborbed by the load i 43 W at a power factor of 0.6 leading. a an n Z A N cn bn Z Z c b i b C B The approximate value of the impedance Z i (a) o (b) (c) (d) An: (c) Sol: P I L Z 3V I L L co phae Vphae Iphae 3 VCC 5. For the circuit hown in the figure below, it i given that V CE = V BE = 0.7 V when the B-E junction i forward biaed. V CC = 0V. The tranitor ha = 9 and R B 4R B R C =9 E R B For thi circuit, the value of R i (a) 43 (b) 9 (c) (d) 9 5. An: (d) Sol: Given that, V CC = 0 V V CE = V CC 5V, = 9

37 : 37 : Forenoon Seion V BE = 0.7 V 0V I B 4R (I C + I B ) R B I C + VCC VCE R (I C + I B ) 5 V Apply KCL through C-E 0 (I C + I B ) 4R 5 (I C + I B ) R = 0 5R (I C + I B ) = 5 R(+) I B = Apply KVL through B-E 0 4R(I C + I B ) I B R B 0.7 R(I C + I B ) = R (I C + I B ) = I B R B = I B R B = 4.3 Then R B R IBR R B 4.3 I B 4.3 = = The eigen value of the matrix given below are (a) (0,, 3) (b) (0,, 3) (c) (0,, 3) (d) (0,, 3) 53. An: (a) Sol: Tr (A) = ( 4) = 4 A = 0 Tr (A) = um of eigen value A = Product of eigen value By verification from option, The eigen value are (0,, 3)

38 : 38 : EE GATE 07 SOLUTIONS 54. Conider an overhead tranmiion line with 3-phae, 50 Hz balanced ytem with conductor located at the vertice of an equilateral triangle of length D ab = D bc = D ca = m a hown in figure below. The reitance of the conductor are neglected. The geometric mean radiu (GMR) of each conductor i 0.0 m. Neglect the effect of ground, the magnitude of poitive equence reactance in /km (rounded off to three decimal place) i c D ca D bc a D ab b 54. An: 0.89 Sol: L phae GMD n H / km GMR = H/km X = fl= = 0.89 ohm 4 n 0 n(00) A 0 V DC hunt motor take A at no load. It take 7 A on full load while running at 00 rpm. The armature reitance i 0.8 and the hunt field reitance i 40. The no load peed, in rpm, i 55. An: 4.8 Sol: V t = 0V, DC hunt motor At No-load: IL A I f Vt 0 = 0.5A r 40 I f a.5a ; Eb Vt Ia r a N = 0 (.5)(0.8) no load? At Full load: IL 7A = 8.8V

39 : 39 : Forenoon Seion I f Vt 0 = 0.5A r 40 f Ia 6.5A Ea Vt I a r = 0 (6.5) (0.8) = 4.8V N full-load = 00 rpm a E b = K a ; = cont[ I f = cont] E E b b N N N N E E b b = 4.8rpm

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41 : 4 : Forenoon Seion General Aptitude 0. Chooe the option with word that are not ynonym. (A) averion, dilike (B) luminou, radiant (C) plunder, loot (D) yielding, reitant 0. An: (D) Sol: Yielding mean tending to do where a reitant mean oppoed to omething, o both are not ynonym. 0. There are five building called V, W, X, Y and Z in a row (not necearily in that order). V i to the Wet of W, Z i to the Eat of X and the Wet of V, W i the Wet of Y. Which i the building in the middle? (A) V (B) W (C) X (D) Y 0. An: (A) Sol: From the given data, the following Row i formed X Z V W Y N W E Wet The building V i in the middle Eat S 03. There are 3 red ock, 4 greed ock and 3 blue ock. You chooe ock. The probability that they are of the ame colour i (A) /5 (B) 7/30 (C) ¼ (D) 4/5 03. An: (D) Sol: Red ock = 3 Green ock = 3 Blue ock = 3 The probability that they are of the ame colour of pair = 3 0 C C 4 0 C C 3 0 C C = = =

42 : 4 : EE GATE 07 SOLUTIONS 04. A tet ha twenty quetion worth 00 mark in total. There are two type of quetion. Multiple choice quetion are worth 3 mark each and eay quetion are worth mark each. How many multiple choice quetion doe the exam have? (A) (B) 5 (C) 8 (D) An: (B) Sol: Total mark in the tet = 00 For multiple choice quetion = 3 mark For eay quetion = mark Option (A) Mark for multiple choice quetion = 3 = 36 Mark for eay type quetion = = i not diviible by Option (A) i not correct. Option (B) Mark for multiple choice quetion = 5 3 = Mark for eay type quetion = = = 5 Eay type quetion are 5 No Option (B) i correct Option(C) Mark for multiple choice quetion = 8 3 = 54 Mark for eay type quetion = = i not diviible by Option (C) i not correct. Option (D) Mark for multiple choice quetion = 9 3 = 57 Mark for eay type quetion = = i not diviible by Option (D) i not correct.

43 : 43 : Forenoon Seion 05. Saturn i to be een on a clear night with the naked eye. (A) enough bright (B) bright enough (C) a enough bright (D) bright a enough 05. An: (B) Sol: The word enough a an adverb falt after the adjective o bright enough i the right anwer 06. The number of root or e x + 0.5x = 0 in the range [ 5, 5] i (A) 0 (B) (C) (D) An: (C) Sol: e x x = 0 in the range [ 5, 5] f(x) = e x x f( 5) = 0.50 f( 4) = 6.0 f( ) = 0.35 () f( ) =.3 f(0) = () f() =. f() = 7.38 A there are ign change from +ve to ve & ve to +ve. Two root will be there in the range[ 5, 5] 07. There are three boxe. One contain apple, another contain orange and the lat one contain both apple and orange. All three are known to be incorrectly labelled. If you are permitted to open jut one box and then pull out and inpect only one fruit, which box would you open to determine the content of all three boxe? (A) The box labelled Apple (B) The box labelled Apple and Orange (C) The box labelled Orange (D) Cannot be determined 07. An: (B) Sol: The peron who i opening the boxe, he knew that all 3 are marked wrong. Suppoe if three boxe are labelled a below. () Apple () Orange (3) Apple & Orange

44 : 44 : EE GATE 07 SOLUTIONS If he inpected from Box (), picked one fruit, found orange, then he don t know whether Box contain orange (or) both apple & orange. Similarly if he picked one fruit from box(), found apple then he don t know whether box contain apple (or) both apple & orange. But if he picked one fruit from box(3), i.e., labelled a apple & orange, if he found apple then he can decide compulorily that box (3) contain apple and a he knew all boxe are labeled a incorrect, he can tell box() contain both apple & orange, box() contain remaining orange. So, he hould open box labelled apple & orange to determine content of all the three boxe. 08. We lived in a culture that denied any merit to literary work, conidering them important only when they were handmaiden to omething eemingly more urgent-namely ideology. Thi wa a country where all geture, even the mot private, were interpreted in political term. The author belief that ideology i not a important a literature i revealed by the word: (A) culture (B) eemingly (C) urgent (D) political 08. An: (B) Sol: It appear to be B, o the right option i B. 09. X i a 30 digit number tarting with the digit 4 followed by the digit 7. Then the number X 3 will have (A) 90 digit (B) 9 digit (C) 9 digit (D) 93 digit 09. An: (A) Sol: X = (47.) 30 digit Suppoe (47) 3 = + + digit in (47) 3 Similarly (47.) 3 30 digit = contain digit = 90 digit 0. An air preure contour line join location in a region having the ame atmopheric preure. The following i an air preure contour plot of a geographical region. Contour line are hown at 0.05 bar interval in thi plot

45 : 45 : Forenoon Seion R S 0.95 P Q km If the poibility of a thundertorm i given by how fat air preure rie or drop over a region. Which of the following region i mot likely to have a thundertorm? (A) P (B) Q (C) R (D) S 0. An: (C) Sol: Region Air preure difference P = 0.05 Q = 0.05 R = 0.0 S = 0.05 In general thundertorm are occurred in a region where uddenly air preure change (i.e.,) udden rie (or) udden fall of air preure. From the given contour map in R Region only more change in air preure o, the poibility of a thundertorm in thi region. option(c) i correct.

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