EE-GATE-2015 PAPER-02 General Aptitude. Q. No. 1 5 Carry One Mark Each

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1 EE-GATE-5 PAPER- General Aptitude Q. No. 5 Carry One Mark Each. A generic term that includes various items of clothing such as a skirt, a pair of trousers and a shirt as fabric textile (C) fibre (D) apparel (D). Choose the statement where underlined word is used correctly. The industrialist had a personnel jet. I write my experience in my personnel diary. (C) All personnel are being given the day off. (D) Being religious is a personnel aspect. (C). Based on the given statements, select the most appropriate option to solve the given question. What will be the total weight of poles each of same weight? Statements: (I) One fourth of the weight of a pole is 5 kg (II) The total weight of these poles is 6 kg more than the total weight of two poles. Statement II alone is not sufficient Statement II alone is not sufficient (C) Either I or II alone is sufficient (D) Both statements I and II together are not sufficient. (C) 4. Consider a function f x x on x. The value of x at which the function attains a maximum, and the maximum value of function are:,, (C), (D) -, (C) f x x on x f f f f f maximum value occurs at x = and maximum value is. India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

2 EE-GATE-5 PAPER We our friend s birthday and we how to make it up to him. completely forgot --- don t just known forget completely --- don t just know (C) completely forget --- just don t know (D) forgot completely --- just don t know (C) Q. No. 6 Carry Two Marks Each 6. In a triangle PQR, PS is the angle bisector of QPR and of PS? P o QPS 6. What is the length r q Q s p R q r qr qr q r (C) q r (D) q r qr 7. Four branches of a company are located at M,N,O, and P. M is north of N at a distance of 4 km; P is south of O at a distance of km; N is southeast of O by km. What is the distance between M and P in km? (C) 8.5 (D) M N 45 N 4 E W S P 8. If p, q, r, s are distinct integers such that: f (p, q, r, s) = max (p, q, r, s) g (p, q, r, s) = min (p, q, r, s) h (p, q, r, s) = remainder of (p q)/(r s) if (p q) > (r s) or remainder of (r s)/(p q) if (r s) > (p q) Also a function fgh (p, q, r, s) = f(p, q, r, s) g(p, q, r, s) h(p, q, r, s) India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

3 EE-GATE-5 PAPER- Also the same operations are valid with two variable function of the form f(p, q). What is the value of fg (h(, 5, 7, ), 4, 6, 8)? 8 f g (h(,5,7,),4,6,8) =fg(,4,6,8) =f(,4,6,8)xg(,4,6,8)=8x=8 9. If the list of letters, P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence? I. P,R,S,T,U II. P,R,S,T, U III. P,R,S,T,U I only I and II (C) II and III (D) I and III. Out of the following four sentences, select the most suitable sentence with respect to grammer and usage: Since the report lacked needed information, it was of no use to them. The report was useless to them because there were no needed information in it. (C) Since the report did not contain the needed information, it was not real useful to them (D) Since the report lacked needed information, it would not had been useful to them. Electrical Engineering Q. No. 5 Carry One Mark Each. Find the transformer ratios a and b that the impedance (Z in ) is resistive and equal.5 when the network is excited with a sine wave voltage of angular frequency of 5 rad/s. C F L mh R.5 : b :a a =.5, b =. a =., b =.5 (C) a =., b =. (D) a = 4., b =.5 India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

4 EE-GATE-5 PAPER- X c L j X j 5 j j5.5 a : b.5 5 Zin j5 j b a b b.5.5 ab.5 a. The synchronous generator shown in the figure is supplying active power to an infinite bus via two short, lossless transmission lines, and is initially in steady state. The mechanical power input to the generator and the voltage magnitude E are constant. If one line is tripped at time t by opening the circuit breakers at the two ends (although there is no fault), then it is seen that the generator undergoes a stable transient. Which one of the following waveforms of the rotor angle shows the transient correctly? Synchronous generator Xs ~ E Line Line Infinte Bus t time t time (C) t time (D) t time For generator is +Ve. After fault increases India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 4

5 EE-GATE-5 PAPER- In the following circuit, the input voltage Vin is sin t. For RC 5, the average voltages across R (in volts) under steady-state is nearest to V in C C R.8 (C) (D) 6.6 (C) Given circuit is voltage doubler V m = Voltage across each capacitor = V Voltage across two capacitors (in steady state) = V m = V 4. A 4-pole, separately excited, wave wound DC machine with negligible armature resistance is rated for V and 5 kw at a speed of rpm. If the same armature coils are reconnected to forms a lap winding, what is the rated voltage (in volts) and power (in kw) respectively at rpm of the reconnected machine if the field circuit is left unchanged? and 5 5 and 5 (C) 5 and.5 (D) and.5 Exp In wave wound, no. of parallel paths is. In lap wound, no of parallel paths is A = p = 4. Rated voltage 5V 4 As no. of parallel paths is divided into four from two, the voltage reduces to half but power remains the same. 5. Given f z gz hz, where f, g, h are complex valued functions of a complex variable z. Which one of the following statements is TRUE? If f(z) is differential at z, then g(z) and h(z) are also differentiable at z. If g(z) and h(z) are differentiable at z, then f(z) is also differentiable at z. (C) If f(z) is continuous at z, then it is differentiable at z. (D) If f(z) is differentiable at z, then so are its real and imaginary parts. Given f z gz hz f z,gz,hzare complex variable functions (c) is not correct, since every continuous function need not be differentiable India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 5

6 EE-GATE-5 PAPER- (D) is also not correct Let g(z) = x h(z) = iy g z x i h z iy u x v u v y x x y x x x x x y y Cauchy rieman equation as of g(z), h(z) are failed. f(z) and g(z) are not differentiable But f z x iy u x v y u v x x u u u v x y y x f(z) in differentiable i.e, f(z) is differential need not imply g(z) and h(z) are differentiable Ans i.e, g(z) and h(z) are differentiable then f(z) = g(z) + h(z) is differentiable. 6. A -bus power system network consists of transmission lines. The bus admittance matrix of the uncompensated system is j6 j j4 j j7 j5 pu. j4 j j8 If the shunt capacitance of all transmission line is 5% compensated, the imaginary part of the rd row rd column element (in pu) of the bus admittance matrix after compensation is j 7. j 8.5 (C) j 7.5 (d) j 9. y y y y y y y j4 ybus y y y y y y y j5 y y y y y y y y j8 y ( j4) ( j5) j8 y j j after compensating, y India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 6

7 EE-GATE-5 PAPER- y y y (new) j.5 j4 j5 j A shunt-connected DC motor operates at its rated terminal voltage. Its no-load speed is radians/second. At its rated torque of 5 Nm, its speed is 8 radian/second. The motor is used to directly drive a load whose load torque T L depends on its rotational speed (in radians/second), such that TL.78 T. Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load is Under steady state load torque = motor torque rad/sec T T 8. A circular turn of radius m revolves at 6 rpm about its diameter aligned with the x-axis as shown in the figure. The value of is 4 7 in SI unit. If a uniform magnetic field intensity H 7 zˆ A/m is applied, then the peak value of the inducted voltage, V in volts, is. turn Z H V turn X 47.9 emf V V B.dl Vemf Vemf L ra Ha.dl L rha.dl r rh H r () 47.9 V z 7 7 India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 7

8 EE-GATE-5 PAPER The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is Vi sin t. The amplitude of the output voltage V in Volt is. o.5 Z k; Z j. 6. s 6. s V i k.f k V o rad / sec Z V j. j.5 ZV i sin( t) sin( t) Z ( j.5).65. V.5sin t 5. Amplitude of the output voltage =.5V. In the following circuit, the transistor is in active mode and VC V. To get VC V. To get VC 4V, we replace R C with R C. Then the ratio RC RC is. V R C R B V C.75 we have Vc V; I R 8 (i) c c We have V c =4V I R 8 (ii) c ' c India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 8

9 EE-GATE-5 PAPER- ' ' () IcRc 6 Rc ;.75 () I R 8 R 4 c c c. The Laplace transform of f t 5 s s Given that laplace transform of Given as gf t gt t t ft t f t Lgt L f tds t s t is f t s s ds s s s s s s. The Laplace transform of (C) t is s. s (D) s g t t is. A capacitive voltage divider is used to measure the bus voltage V bus in a high-voltage 5 Hz AC system as shown in the figure. The measurement capacitor C and C have tolerances of % on their normal capacitance values. If the bus voltage V bus is kv rms, the maximum rms output voltage V out (in kv), considering the capacitor tolerance, is. C F % v bus C 9F % v out India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 9

10 EE-GATE-5 PAPER- X c c Vout Vbus V bus X c Xc c c c Vbus c c F % c c F % 9F %. 9.9 c %. % c c % Vout. % kv % k k (or)k k k or 8k. Match the following P. Stokes s Theorem. D.ds Q Q. Gauss s Theorem. f z dx R. Divergence Theorem. S. Cauchy s Integral Theorem 4..A dv A.ds A.ds A.dl P-, Q-, R-4, S- P-4, Q-, R-, S- (C) P-4, Q-, R-, S- (D) P-, Q-4, R-, S- 4. Consider the following Sum of Products expression, F. F ABC ABC ABC ABC ABC The equivalent Product of Sums expression is F A B CA B CA B C F A B CA B CA B C (C) F A B CA B CA B C (D) F A B CA B CA B C Given minterm is F m,,,5, 7 F m,4,6 So product of sum expression is F A B CA B CA B C India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

11 EE-GATE-5 PAPER A series RL circuit is excited at t = by closing a switch as shown in the figure. di Assuming zero initial conditions, the value of at t = + is dt R V L V L V R RV (C) (D) L (D) V i i L(t) e R Rt L dil dt di dt di dt Rt V e L L R Ve L RV L t Rt L 6. We have a set of linear equations in unknowns. 'X Y' means X and Y are equivalent statements and 'X Y' means X and Y are not equivalent statements. P: There is a unique solution. Q: The equations are linearly independent. R: All eigenvalues of the coefficient matrix are nonzero. S: The determinant of the coefficient matrix is nonzero. Which one of the following is TRUE? P R Q S P R Q S (C) P Q R S (D) P Q R S 7. Match the following: Instrument Type Used for P. Permanent magnet moving coil. DC only Q. Moving iron connected through current transformer. AC only R. Rectifier.AC and DC S. Electrodynamometer India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

12 EE-GATE-5 PAPER- P Q R S (C) P Q R S (C) P Q R S P Q (D) R S 8. Two semi-infinite dielectric regions are separated by a plane boundary at y=. The dielectric constant of region (y<) and region (y>) are and 5, Region has uniform electric field E aˆ ˆ ˆ x 4a y a z, where a ˆ x,a ˆ ˆ y, and a z are unit vectors along the x, y and z axes, respectively. The electric field region is ˆ ˆ ˆ. aˆ ˆ ˆ x 4 ay a z a x.6a y a z ˆ ˆ ˆ (D) aˆ x aˆ ˆ y.8a z (C).a x 4a y.8a z () () y y> E ax 4ay E z = y= +az E a (4a ) a 5 E a.6a a x y z z x y z 9. The filters F and F having characteristics as shown in Figures (a) and (b) are connected as shown in Figure (c). V / V o i F V / V o i F V i V V i V f f f f (a) (b) R / F R V sat V i F R V sat V The cut-off frequencies of F and F are f and f respectively. If f f, the resultant circuit exhibits the characteristics of a Band-pass filter Band-stop filter (C) All pass filter (D) High-Q filter India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India (c)

13 EE-GATE-5 PAPER- The figure shows the per-phase equivalent circuit of a two-pole three-phase induction motor operating at 5 Hz. The air-gap voltage, V g across the magnetizing inductance, is V rms, and the slip, is.5. The torque (in Nm) produced by the motor is. j.7.75 j. V I g Nyquist plot of two functions G (s) and G (s) are shown in figure. Nyquist plot of the product of G (s) and G (s) is G (s) Im Im Re G (s) Im Im Re Re Re (C) Im (D) Im Re Re India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

14 EE-GATE-5 PAPER- G (s) ; G (s) 5 s GG (s) Im Re. A -phase balanced load which has a power factor of.77 is connected to balanced supply. The power consumed by the load is 5kW. The power is measured by the twowattmeter method. The readings of the two wattmeters are.94 kw and.6 kw (C) 5. kw and. kw P VL IL cos( ) P VL IL cos( ) cos costan p p p p.94.6 cos tan 45 5 satisfiying only for o.5 kw and.5 kw (D).96 kw and.4 kw t. An open loop control system results in a response of e sin 5t cos5t impulse input. The DC gain of the control system is..4 g(t) e sin 5t cos5t 5 s G(s) (s ) 5 s 5 DC gain means G(s) 5 7 G() s for a unit 4. When a bipolar junction transistor is operating in the saturation mode, which one of the following statement is TRUE about the state of its collector-base (CB) and the baseemitter (BE) junctions? The CB junction is forward biased and the BE junction is reverse biased. The CB junction is reversed and the BE junction is forward biased. (C) Both the CB and BE junctions are forward biased. (D) Both the CB and BE junctions are reverse biased. (C) India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 4

15 EE-GATE-5 PAPER The current i (in Ampere) in the resistor of the given network is. i 5V The Network is balanced Wheatstone bridge. i Amp Q. No Carry Two Marks Each 6. A V, -phase, 4-pole, 5 Hz inductor motor of wound rotor type is supplied at rated voltage and frequency. The stator resistance, magnetizing reactance, and core loss are negligible. The maximum torque produced by the rotor is 5% of full load torque and it occurs at 5% slip. The actual rotor resistance is. / phase. The value of external resistance (in Ohm) which must be inserted in a rotor phase if the maximum torque is to occur at start is..7 S mt.5 r x r. x x For T est =T emax, mt ' r x. x x. Test SmT T em SmT s r' Extra resistance...7 / p4 India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 5

16 EE-GATE-5 PAPER Two three-phase transformers are realized using single-phase transformers as shown in the figure. A A a a B B b b V C C c c A A a B B b b V C c C c The phase different (in degree) between voltage Vand V is. Upper transformer secondary is connected in Bottom transformer secondary is connected in Y Phase angle between delta voltage & star voltage is o. 8. A balanced (positive sequence) three-phase AC voltage source is connected to a balanced, start connected through a star-delta transformer as shown in the figure. The line-to-line voltage rating is V on the star side, and 5 V on the delta side. If the magnetizing o current is neglected and I A, then what is the value of I p in Ampere? s I p I s a A R B R R b C C India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 6

17 EE-GATE-5 PAPER- o 5 It s a Ydll connection. o 5 (C) o Ip 5 I 5 p o o 5 (D) 9. Two semi-infinite conducting sheets are placed at right angles to each other as shown in the figure. A point charge of +Q is placed at a distance of d from both sheets. The net force on Q K the charge is, where K is given by 4 d y d Q d (C) ˆ i ˆj 8 8 (D) ˆ i ˆj 8 8 ˆi ˆj 4 4 x (D) F F F F y Q x y x y F da da da da 4 (d) Q F a x a y 4 d 8 8 X Q Q Q(d,d,) Q X So, Ans :(D) y. The volume enclosed by the surface f (x,y) x e over the triangle bounded by the line x=y; x=; y= in the xy plane is..7 Triangle is banded by x = y, x =, y = is xy plane. y x, B A, y x,, India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 7

18 EE-GATE-5 PAPER- Required volume AB x yx x x f x, y dxdy x e dxdy e. y x dx x x x e x dx e xe dx x x x x e e x e e.7. For the system governed by the set of equations: dx / dt x x u dx / dt x u y x the transfer function Y(s)/U(s) is given by (C) (s ) / (s s ) (s ) / (s s ) (D) dx x x 4 dt dx dt y x x 4 Considering the standard equation x Ax BU i y Cx DU x x [4] x x x y [ ] x Transform function C SI A B (s )(s s ) (s )(s s ) India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 8

19 EE-GATE-5 PAPER- s G(s) s s [ ] s s s s s s s s s s s s s 4 (s ) s s. For linear time invariant systems, that are Bounded Input Bounded stable, which one of the following statement is TRUE? The impulse response will be integral, but may not be absolutely integrable. The unit impulse response will have finite support. (C) The unit step response will be absolutely integrable. (D) The unit step response will be bounded.. In the following sequential circuit, the initial state (before the first clock pulse ) of the circuit is QQ. The state (QQ ), immediately after the rd clock pulse is Q Q J Q J Q K Q K Q CLK (C) (D) India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 9

20 EE-GATE-5 PAPER- J Q K Q J Q K Q Q Q If is a Johnson (MOD-4) counter. Divide by 4, so it will complete 8 cycle and remainder clock is, at the completion of cycles output s in at QQ so, next at rd clock pulse output is at QQ. 4. A three-phase, kv, 5 Hz, pole, star connected, cylindrical rotor synchronous motor is connected to an kv, 5 Hz source, Its synchronous reactance is 5 per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is A at unity power factor. If the load torque is increased so that the stator current is A, then the load angle (in degrees) at this node is E f = V t - I a S kv j 5 65 j5 E 88. f a f t f t I S E V E V cos cos Two coins R and S are tossed. The 4 joint events HRH S,TR T S,HRT S,TR H S have probabilities.8,.8,.,.4, respectively, where H represents head and T represents tail. Which one of the following is TRUE? The coin tosses are independent (C) S is fair, R is not (D) Given events H R H S, T R T S, H R T S, T R H S If coins are independent Corresponding probabilities will be.,.,.,.,,, respectively R is fair, R it not. (D) The coin tosses are dependent But given probabilities are.8,.8,.,.4 respectively we can decide whether R is fair or S is fair The coin tosses are dependent. India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

21 EE-GATE-5 PAPER A composite conductor consists of three conductors of radius R each. The conductors are arranged as shown below. The geometric mean radius (GMR) (in cm) of the composite conductor is kr. The value of k is. R R GMR.7788R R R.97R kr k.9 7. The z-transform of a sequence x[n] is given as X(z) = z+4-4/z+/z. If y[n] is the first difference of x[n], then Y(z) is given by z+-8/z+7/z -/z -z+-6/z+/z -/z (C) -z-+8/z-7/z +/z (D) 4z--8/z-/z +/z y(n) is first difference of x(n) So g(n) x(n) x(n ) Y(z) x(z)( z ) X(z) z X(z) Y(z) z 4 4z z 4z 4z z 4 4z z 4z 4z z z 8z 7z z 8. An open loop transfer function G(s) of a system is Gs K s s s For a unity feedback system, the breakaway point of the root loci on the real axis occurs at, (C) -.4 and -.58 G(s) (D) None of the above India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

22 EE-GATE-5 PAPER- s s s k s s s dk ds s 6s s S=-.4 is the solution makes k> 9. In the given rectifier, the delay angle of the thyristor T measured from the positive going zero crossing of V s is. If the input voltage V s is sin(πt)v, the average voltage across R (in Volt) under steady-state is. T V s D D4 D R V 6.5 V in m V cos sin t V cos 6.5V 4. Two identical coils each having inductance L are placed together on the same core. If an overall inductance of αl is obtained by interconnecting these two coils, the minimum value of α is. 4. In the given network V = V, V = - V, V = + V. The phasor current i (in Ampere) is V j V j V i (C). -6 (D). - India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

23 EE-GATE-5 PAPER- i V V V V j o o o o o o 9 9 o j i i A differential equation di.i is applicable over -< t <. If i(4) =, then i(-5) dt is..65 di.i dt D. i(t) D..t i(t) k.e, t t u; K.e K= i( 5) 4.49 e i( 5) A -phase transformer rated for kv/ kv is connected in delta/star as shown in figure. The current transformers (CTs) on low and high voltage sides have a ratio of 5/5. Find the currents i and i, if the fault current is A as shown in figure. a b c A i i i A,i A i A,i A (C) i A,i A (D) i A,i A i = since entire current flows through fault Primary kva = Secondary kva India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India

24 EE-GATE-5 PAPER- I I IL 5 L L A I Ph Iph i A A Boolean function f(a,b,c,d) = (,5,,5) is to be implemented using an 8 multiplexer (A is MSB). The inputs ABC are connected to the select inputs S S S of the multiplexer respectively S S S f A,B,C,D A B C Which one of the following options gives the correct inputs to pins,,,,4,5,6,7 in order? D,,D,,,,D,D (C) D,,D,,,,D,D D,,D,,,,D,D (D) D,,D,,,,D,D Given maxterm f A,B,C,D,5,,5 so minterm f A,B,C,D m,,,4,6,7,8,9,,,,4 I I I I I4 I5 I6 I7 D D D D D D 45. The incremental costs (in Rupees/MWh) of operating two generating units are functions of their respective powers P and P in MW, and are given by dc dp dc dp Where. P 5.4 P 4 MW P 5 MW MW P 5MW For a certain load demand, P and P have been chosen such that dc /dp = 76 Rs/MWh India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 4

25 EE-GATE-5 PAPER- and dc /dp = 68.8 Rs/MWh. If the generations are rescheduled to minimize the total cost, then P is. 6.6 dc 76.P 5 P P P 5 dp dc P 4 P dp dc dc For total cost minimization, dp dp.p 5.4p 4. 5 P 5.4P 4 P The unit step response of a system with the transfer function Gs which one of the following waveforms? y y s is given by s 5 t 5 t (C) y (D) y 5 t 5 t.75 G(s) y(t)? 5 t India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 5

26 EE-GATE-5 PAPER- Y(s) G(s) U(s) ( s) Y(s). ( s) s A B Y(s) (s) (s ) A, B t y(t) u(t) e u(t) t y(t) e u(t) 47. A symmetrical square wave of 5% duty cycle has amplitude of ±5V and time period of.4π ms. This square wave is applied across a series RLC circuit with R = 5, L = mh, and C = 4μF. The amplitude of the 5 rad/s component of the capacitor voltage (in Volt) is. L C R 9.98 at 5rad / sec T 45 V(t) sin t at circuit is under resonance c V QV 9 L 5m R 5 45 Vc 9 6 Vc 9.98 Q 48. For the switching converter shown in the following figure, assume steady-state operation. Also assume that the components are ideal, the inductor current is always positive and continuous and switching period is T 5. If the voltage V L is as shown, the duty cycle of the switch S is. V L V 5V Vin S C R V L TS 45V t.75 India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 6

27 EE-GATE-5 PAPER- V S 5V V V 45 V V 45 6V S S V S V D 5 6 D 4.75 D 49. With an armature voltage of V and rated field winding voltage, the speed of a separately excited DC motor driving a fan is rpm, and its armature current is A. The armature resistance is. The load torque of the fan load is proportional to the square of the rotor speed. Neglecting rotational losses, the value of the armature voltage (in Volt) which will reduce the rotor speed to 5 rpm is For separately excided DC motor, Torque = ki a & E=kω m. E For rpm, E 9V; for 5 rpm, E 45V I a N 5 a a Ia N V 45 I R, T N Ia.5 A V 45.5A The saturation voltage of the ideal op-amp shown below is ±V. The output voltage of the following circuit in the steady-state is k.5f V V k k Square wave of period.55 ms (C) Square wave of period.5 ms Triangular wave of period.55 ms (D) Triangular wave of period.5 ms Astable multivibrator produces square wave. R R R 4.5 India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 7

28 EE-GATE-5 PAPER- ( ).5 ( ).5 6 T Rc log.5 log T=.55 ms Square wave of period.55 ms. 5. A three-winding transformer is connected to an AC voltage source as shown in the figure. The number of turns are as follows: N =, N = 5. If the magnetizing current is neglected, and the currents in two windings are I AandI 5 A, then what is the value of the current I in Ampere? I N I I N 9 7 (C) 49 (D) 47 N I N = I N + I N I I The coils of a wattmeter have resistances. and ; their inductances may be neglected. The wattmeter is connected as shown in the figure, to measure the power consumed by a load, which draws 5A at power factor.8. The voltage across the load terminals is V. The percentage error on the wattmeter reading is. Load.5 P load = 5 8 = 6W Wattmeter measures loss in pressure coil circuit India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 8

29 EE-GATE-5 PAPER- V loss in Pc.9W R.9 error.5% 6 P 5. Consider a signal defined by x t for t jt e for t Its Fourier Transform is sin (C) sin (D) j e sin e j sin jt jt j( )t X( ) e.e dt e dt j( )t e sin( ) j( ) ( ) 54. A buck converter feeding a variable resistive load is shown in the figure. The switching frequency of the switch S is khz and the duty ratio is.6. The output voltage V is 6V. Assume that all the components are ideal, and that the output voltage is ripple-free. The value of R (in Ohm) that will make the inductor current (i L ) just continuous is. S i L 5mH 6V 6V V R 5 For Buck converter, for inductor current to be continuous, fl 5 R 5 D.6 India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India 9

30 EE-GATE-5 PAPER The following discrete-time equations result from the numerical integration of the differential equations of an un-damped simple harmonic oscillator with state variables x and y. The integration time step is h. x y k k x h y h k k y k x k For this discrete-time system, which one of the following statements is TRUE? The system is not stable for h> The system is stable for h (C) The system is stable for h (D) The system is stable for h India s No. institute for GATE Training Lakh+ Students trained till date 65+ Centers across India