EE-GATE-03 PAPER Q. No. 5 Carry One Mark Each. Given a vector field F = y xax yzay = x a z, the line integral F.dl evaluated along a segment on the x-axis from x= to x= is -.33 (B) 0.33 (D) 7 : (B) x 0. The equation = x has 0 no solution non-zero unique solution : (D) x 0 (B) only one solution = x 0 (D) multiple solutions 3. Square roots of i, where i =, are i, i (B) (D) : (B) π π 3π 3π cos isin, cos isin 3 3 cos π isin π, cos π isin π 3 3 3 3 cos π isin π, cos π isin π. Three moving iron type voltmeters are connected as shown below. Voltmeter readings are V, V and V as indicated. The correct relation among the voltmeter readings is j Ω jω V V V I V V V = (B) V = V V V = VV (D) V = V V : (B) 5. Leakage flux in an induction motor is flux that leaks through the machine (B) flux that links both stator and rotor windings flux that links none of the windings (D) flux that links the stator winding or the rotor winding but not both : (D)
EE-GATE-03 PAPER 6. The angle δ in the swing equation of a synchronous generator is the : (D) angle between stator voltage and current (B) angular displacement of the rotor with respect to the stator angular displacement of the stator mmf with respect to a synchronously rotating axis. (D) angular displacement of an axis fixed to the rotor with respect to a synchronously rotating axis. 7. Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k>0, the elements of the corresponding star equivalent will be scaled by a factor of R a R C R B R b R c R A k (B) k k (D) k (B) 8. A band-limited signal with a maximum frequency of 5 khz is to be sampled. According to the sampling theorem, the sampling frequency in khz which is not valid is 5 (B) 5 (D) 0 π 9. For a periodic signal v(t) = 30 sin 00 t 0 cos 300 t 6 sin(500 t ), the fundamental frequency in radians/s is 00 (B) 300 500 (D) 500 0. A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles an AND gate (B) an OR gate an XOR gate (D)a NAND gate
EE-GATE-03 PAPER. The Bode plot of a transfer function G(s) is shown in the figure below. Gain(dB) 0 3 0 0 8 0 00 ω(rad / s) The gain (0log G(s)) is 3 db and -8 db at radians/s and 0 radians/s respectively. The phase is negative for all ω. Then G(s) is 39.8 s 39.8 (B) s 3 s 3 (D) s (B). In the feedback network shown below, if the feedback factor k is increased, then the V in V A 0 V out V f = kv out k input impedance increases and other output impedance decreases (B) input impedance increases and output impedance also increases. input impedance decreases and output impedance also decreases. (D) input impedance decreases and output impedance increases. : 3. The input impedance of the permanent magnet moving coil (PMMC) voltmeter is infinite. Assuming that the diode shown in the figure below is ideal, the reading of the voltmeter in Volts is kω.sin(3t)v 00 kω Voltmeter :.6 (B) 3.5.3 (D) 0 3
EE-GATE-03 PAPER. The curl of the gradient of the scalar field defined by xyax 6yzay 8zxaz (B) ax 6ay 8az ( ) ( ) ( ) (D) 0 : (D) xy z a x 6yz a 3y 8zx a x y z V = x y 3y z z x is 5. A continuous random variable X has a probability density function x f(x) = e,0 < x <. Then P{X > } is 0.368 (B) 0.5 0.63 (D).0 : 6. The flux density at a point in space is given by The value of constant k must be equal to B = xax kyay 8az Wb / m. - (B) -0.5 0.5 (D) : 7. A single-phase transformer has no-load loss of 6 W, as obtained from an opencircuit test. When a short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, he measured loss is 8 W. The transformer has maximum efficiency when operated at : 50.0% of the rated current. 80.0% of the rated current. (B) 6.0% of the rated current. (D) 88.8% of the rated current. 8. A single-phase load is supplied by a single-phase voltage source. If the current flowing from the load to the source is 0 50 A and if the voltage at the load terminals is 00 60 V, then the load absorbs real power and delivers reactive power. (B) load absorbs real power and absorbs reactive power. load delivers real power and delivers reactive power. (D) load delivers real power and absorbs reactive power. : (B) 9. A source v s(t) = V cos 00π t has an internal impedance of ( j3 ) Ω. If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in Ω should be 3 (B) 5 (D) 7
EE-GATE-03 PAPER 0. Two systems with impulse responses h (t) and h (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by product of h (t) and h (t) (B) Sum of h (t) and h (t) Convolution of h (t) and h (t) (D) subtraction of h (t) and h (t). Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? All the poles of the system must lie on the left side of the jω axis (B) Zeros of the system can lie anywhere in the s-plane All the poles must lie within s = (D) All the roots of the characteristic equation must be located on the left side of the jω axis. The impulse response of a system is h(t) = tu(t). For an input u(t ), the output is t u(t) (t ) u(t ) (D) (B) t(t ) u(t ) (t ) u(t ) 3. Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is U(s) s Y(s) u(t) (B) tu(t) (B) t u(t) (D) t e u(t) V (s). The transfer function of the circuit shown below is V (s) 00 µ F V (s) 0kΩ V (s) 00 µ F 5
EE-GATE-03 PAPER 0.5s s (B) 3s 6 s s s (D) s s (D) 5. In the circuit shown below what is the output voltage (V out) in Volts if a silicon transistor Q and an ideal op-amp are used? Q 5V kω 5 V 5 V V BE V out -5 (B) -0.7 0.7 (D) 5 (B) Q. No. 6 55 Carry Two Marks Each 6. When the Newton-Raphson method is applied to solve the equation : 3 f ( x) = x x = 0, the solution at the end of the first iteration with the initial guess value as x0 =. is -0.8 (B) 0.9 0.705 (D).69 7. A function : (B) y = 5x 0x is defined over an open interval x = (,). Atleast at one point in this interval, dy/dx is exactly 0 (B) 5 30 (D) 35 8. A -pole induction motor, supplied by a slightly unbalanced three-phase 50Hz source, is rotating at 0 rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is : (B) 00 (B) 98 5 (D) 8 9. Thyristor T in the figure below is initially off and is triggered with a single pulse of 00 00 width 0 µ s. It is given that L = µ H and C = F π µ. Assuming latching π and holding currents of the thyristor are both zero and the initial charge on C is zero, T conducts for 6
EE-GATE-03 PAPER 5V T L C : 0 µ s (B) 50 µ s 00 µ s (D) 00 µ s 30. The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8. An ac voltage VWX = 00V is applied across WX to get an open circuit voltage across YZ. Next, an ac voltage V YZ =00V is applied across YZ to get an open circuit voltage V WX across WX. Then, VYZ VWX, are respectively, VWX VYZ W :.5 Y X Z 5/00 and 80/00 (B) 00/00 and 80/00 00/00 and 00/00 (D) 80/00 and 80/00 3. Two magnetically uncoupled inductive coils have Q factors q and q at the chosen operating frequency. Their respective resistances are R and R. When connected in series, their effective Q factor at the same operating frequency is q R q R (B) q /R q /R ( q R q R ) / ( R R ) (D) qr qr 3. The impulse response of a continuous time system is given by h t = δ t δ t 3. The value of the step response at t = is ( ) ( ) ( ) 0 (B) (D) 3 (B) 33. The signal flow graph for a system is given below. The Transfer function, for the system is ( ) ( ) Y s U s s s U( s ) Y ( s) 7
EE-GATE-03 PAPER s 5s 6s s (B) s 6s s s s (D) 5s 6s 3. In the circuit shown below the op-amps are ideal. Then V out in Volts is V kω kω kω V 5V 5V kω 5V 5V kω V out (B) 6 8 (D) 0 35. In the circuit shown below, Q has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If V cc is 5V, X and Y are digital signals with 0V as logic 0 and Voc as logic, then the Boolean expression for Z is V cc R Z X R Q Diode Y : (B) XY (B) XY XY (D) XY 36. The clock frequency applied to the digital circuit shown in the figure below is khz. If the initial state of the output of the flip-flop is 0, then the frequency of the output waveform Q in khz is 0.5 (B) 0.5 X T Q Q (D) : (B) Clk Q Q 8
EE-GATE-03 PAPER 37. : z dz evaluated anticlockwise around the circle z i =, where i =, is z π (B) 0 π (D) i 38. A Matrix has eigenvalues - and -. The corresponding eigenvectors are and respectively. The matrix is 0 (B) (D) 0 0 3 : (D) 39. A dielectric slab with 500mm x 500mm cross-section is 0.m long. The slab is subjected to a uniform electric field of E = 6ax 8aykV /mm. The relative permittivity of the dielectric material is equal to. The value of constant ε 0 is 8.85 0 F /m. The energy stored in the dielectric in Joules is : (B) 8.85 0 (B) 8.85 0 5 88.5 (D) 885 0. For a power system network with n nodes, Z 33 of its bus impedance matrix is j0.5 per unit. The voltage at node 3 is.3 0º per unit. If a capacitor having : (D) reactance of j3.5 per unit is now added to the network between node 3 and the reference node, the current drawn by the capacitor per unit is 0.35 00º (B) 0.35 80º 0.37 00º (D) 0.3380º. The separately excited dc motor in the figure below has a rated armature current of 0A and a rated armature voltage of 50V. An ideal chopper switching at 5 khz is used to control the armature voltage. If La = 0.mH, Ra = Ω, neglecting armature reaction, the duty ratio of the chopper to obtain 50% of the rated torque at the rated speed and the rated field current is 00V L,R a a : (D) 0. (B) 0.5 0.6 (D) 0.7 9
EE-GATE-03 PAPER. A voltage 000 sin ω t Volts is applied across YZ. Assuming ideal diodes, the voltage measured across WX in Volts is kω W Y X Z : (D) A sinω t (B) ( ω ω ) ( sin ωt sin ω t ) / (D) 0 for all t kω sin t sin t / 3. Three capacitors C, C, and C 3 whose values are 0µ F, 5µ F and µ F respectively, have breakdown voltages of 0V, 5V and V respectively. For the interconnection shown, the maximum safe voltage in Volts that can be applied across the combination and the corresponding total charge in µ C stored in the effective capacitance across the terminals are respectively C C 3.8 and 36 (B) 7 and 9.8 and 3 (D) 7 and 80 C. In the circuit shown below, if the source voltage Vs = 00 53.3º V, then the Thevenin s equivalent voltage in volts as seen by the load resistance RL is 3Ω jω j6ω 5Ω V s V L j0i I 0V L I RL = 0Ω 00 90º (B) 800 0º 800 90º (D) 00 60º 5. The open loop transfer function of a dc motor is given as a ( ) ( ) ω s 0 =. When V s 0s connected in feedback as shown below, the approximate value of K a that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open loop system is 0
EE-GATE-03 PAPER R ( s) Ka Va ( s) 0 0s ω( s) (B) 5 0 (D) 00 6. In the circuit shown below, the knee current of the ideal Zener diode is 0mA. To maintain 5V across R L, the minimum value of R L in Ω and the minimum power rating of the Zener diode in mw respectively are 0V 00Ω I Load Vz = 5V R L 5 and 5 (B) 5 and 50 50 and 5 (D) 50 and 50 : (B) 7. A strain gauge forms one arm of the bridge shown in the figure below and has a nominal resistance without any load as Rs = 300Ω. Other bridge resistances are R = R = R3 = 300Ω. The maximum permissible current through the strain gauge is 0mA. During certain measurement when the bridge is excited by maximum permissible voltage and the strain gauge resistance is increased by % over the nominal value, the output voltage V o in mv is V i Rs R V o R 3 R : 56.0 (B) 0.83 9.85 (D) 0.0
EE-GATE-03 PAPER Common Data Questions: 8 & 9 The state variable formulation of a system is given as. x x. x x 0 = u 0 x = = x 0 0, x 0 0 and y= 0 x, ( ) ( ) 8. The response y ( t ) to the unit step input is e t (B) t t e e e t t e (D) e t : 9. The system is controllable but not observable (B) not controllable but observable both controllable and observable (D) both not controllable and not observable : Common Data Questions: 50 & 5 In the figure shown below, the chopper feeds a resistive load from a battery source. MOSFET Q is switched at 50 khz, with a duty ratio of 0.. All elements of the circuit are assumed to be ideal 00µ H V Q 70µ F 0Ω 50. The Peak to Peak source current ripple in amps is : 0.96 (B) 0. 0.9 (D) 0.88 5. The average source current in Amps in steady-state is : (B) 3/ (B) 5/3 5/ (D) 5/
EE-GATE-03 PAPER Linked Questions: Q.5 to Q.55 Carry Two Marks Each Statement for Linked Questions: 5 & 53 In the following network, the voltage magnitudes at all buses are equal to pu, the voltage phase angles are very small, and the line resistances are negligible. All the line reactances are equal to j Ω ( ) Bus slack jω Bus P = 0. pu jω jω Bus 3 P3 = 0. pu 5. The voltage phase angles in rad at buses and 3 are θ = 0., θ 3 = 0. (B) θ = 0, θ 3 = 0. : θ = 0., θ 3 = 0. (D) θ = 0., θ 3 = 0. 53. If the base impedance and the line-to line base voltage are 00 ohms and 00kV respectively, then the real power in MW delivered by the generator connected at the slack bus is -0 (B) 0 0 (D) 0 : Statement for Linked Questions: 5 & 55 The Voltage Source Inverter (VSI) shown in the figure below is switched to provide a 50Hz, square wave ac output voltage v o across an RL load. Reference polarity of v o and reference direction of the output current i o are indicated in the figure. It is given that R = 3 ohms, L = 9.55mH. Q D Q 3 D 3 L V dc v o i o R Q Q D D 3
EE-GATE-03 PAPER 5. In the interval when vo < 0 and io > 0 the pair of devices which conducts the load current is : (D) Q, Q (B) Q 3, Q D, D (D) D 3, D 55. Appropriate transition i.e., Zero Voltage Switching (ZVS) / Zero Current Switching (ZCS) of the IGBTs during turn-on / turn-off is : (D) ZVS during turn off ZCS during turn off (B) ZVS during turn-on (D) ZCS during turn-on Q. No. 56 60 Carry One Mark Each 56. Choose the grammatically CORRECT sentence: Two and two add four (B) Two and two become four Two and two are four (D) Two and two make four : (D) 57. Statement: You can always give me a ring whenever you need. : Which one of the following is the best inference from the above statement? Because I have a nice caller tune (B) Because I have a better telephone facility Because a friend in need in a friend indeed (D) Because you need not pay towards the telephone bills when you give me a ring 58. In the summer of 0, in New Delhi, the mean temperature of Monday to Wednesday was ºC and of Tuesday to Thursday was 3ºC. If the temperature on Thursday was 5% higher than that of Monday, then the temperature in ºC on Thursday was : 0 (B) 3 6 (D) 9 Explanations:- Let the temperature of Monday be T M Sum of temperatures of Tuesday and Wednesday = T and Temperature of Thursday =T Th Now, T T = 3 = 3 th m & T T = 3 3 = 9 T T = 6, Also T =.5T Th m Th m 0.5T = 6 T = 0 m m Temperature of thursday = 0 6 = 6 C O
EE-GATE-03 PAPER 59. Complete the sentence: Dare mistakes. commit (B) to commit committed (D) committing : (B) 60. They were requested not to quarrel with others. Which one of the following options is the closest in meaning to the word quarrel? make out (B) call out dig out (D) fall out : (D) Q. No. 6 65 Carry Two Marks Each 6. A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 6km in the third quarter. The average speed of the car in km per hour over the entire journey is : 30 (B) 36 0 (D) Explanations:-Average speed = 8 6 6 = = 0km / hr Total distance Total time 6. Find the sum to n terms of the series 0 8 73 n ( ) 9 9 0 (B) n ( ) 9 9 8 n ( ) 9 9 8 ( ) n 9 9 n (D) 8 : (D) Explanations:-Using the answer options, substitute n =. The sum should add up to 9 n 63. Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on. : (D) Which one of the following is the best inference from the above statement? The emergence of nationalism in colonial India led to our Independence (B) Nationalism in India emerged in the context of colonialism Nationalism in India is homogeneous (D) Nationalism in India is heterogeneous 3x x p p = 0 6. The set of values of p for which the roots of the equation ( ) : (B) are of opposite sign is (,0) (B) ( 0, ) (, ) (D) ( 0, ) 5
EE-GATE-03 PAPER 65. What is the chance that a leap year, selected at random, will contain 53 Sundays? : /7 (B) 3/7 /7 (D) 5/7 Explanations:-There are 5 complete weeks in a calendar year Number of days in a leap year = 366 85 7 = 36days Probability of 53 Saturdays = 7 6