GATE 2018 [Afternoon Session]

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2 GATE 08 [Aternoon Session].General Aptitude. Since 004 Question Q. to Q.5 carry one mark each ( k ) For what values o k given below is an integer? k 3 (A) 4, 8, 8 (B) 4, 0, 6 (C) 4, 8, 8 (D) 8, 6, 8 Ans. (C) Question Since you have gone o the the sand is likely to damage the car. The words that best ill the blanks in the above sentence are (A) course, coarse (B) course, course (C) coarse, course (D) coarse, coarse Ans. (A) Question 3 A common misconception among writers is that sentence structure mirrors thought, the more the structure, the more complicated the ideas. The words that best ill the blanks in the above sentence are (A) detailed (B) simple (C) clear (D) convoluted Ans. (D) Question 4 Functions Fab (, ) and Ga (, b ) are deined as ollows : Fab (, ) ( a b) and (, ) Ga b a b, where x represents the absolute value o x. What would be the value o GF ( (, 3), G (, 3))? (A) (B) 4 (C) 6 (D) 36 Ans. (A) Question 5 The three roots o the equation ( x) 0 are x {, 0, 3}. What are the three values o x or which ( x3) 0? (A) 5, 3, 0 (B), 0, 3 (C) 0, 6, 8 (D), 3, 6 Ans. (D) Q.6 to Q.0 carry two marks each Question 6 An password must contain three characters. The password has to contain one numeral rom 0 to 9, one upper and one lower case character rom the English alphabet. How many distinct passwords are possible? (A) 6,760 (B) 3,50 (C) 40,560 (D),05,456 Ans. (C) More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

3 GATE 08 [Aternoon Session] Since 004 Question 7 In a certain code, AMCF is written as EQGJ and NKUF is written as ROYJ. How will DHLP be written in that code? (A) RSTN (B) TLPH (C) HLPT (D) XSVR Ans. (C) Question 8 A class o twelve children has two more boys than girls. A group o three children are randomly picked rom this class to accompany the teacher on a ield trip. What is the probability that the group accompanying the teacher contains more girls than boys? (A) 0 (B) (C) Ans. (*) 4/ Question 9 P, Q, R and S crossed a lake in a boat that can hold a maximum o two persons, with only one set o oars. The ollowing additional acts are available. (i) The boat held two persons on each o the three orward trips across the lake and one person on each o the two return trips. (ii) P is unable to row when someone else is in the boat. (iii) Q is unable to row with anyone else except R. (iv) Each person rowed or at least one trip (v) Only one person can row during a trip Who rowed twice? (A) P (B) Q (C) R (D) S Ans. (C) Question 0 A designer uses marbles o our dierent colours or his designs. The cost o each marble is the same, irrespective o the colour. The table below shows the percentage o marbles o each colour used in the current design. The cost o each marble increased by 5%. Thereore, the designer decided to reduce equal numbers o marbles o each colour to keep the total cost unchanged. What is the percentage o blue marbles in the new design? Ans. Blue Black Red Yellow 40% 5% 0% 5% (A) (B) 40.5 (C) (D) 46.5 (C) (D) 5 Copyright Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

4 3 GATE 08 [Aternoon Session].Technical Section. Since 004 Q. to Q.5 carry one mark each Question (Digital Electronics) In the logic circuit shown in the igure, Y is given by A B C D (A) Y ABCD (B) Y ( AB)( C D) (C) Y ABC D (D) Y AB CD Ans. (D) Question (Power Electronics) The waveorm o the current drawn by a semi-converter rom a sinusoidal AC voltage source is shown in the igure. I I 0 0 A, the rms value o undamental component o the current is A (up to decimal places). Voltage and current Vm sin( t) Y 30 0 I Ans Question 3 (Signals & Systems) Let be the real valued unction o a real variable deined ( x) x [ x], where [ x ] denotes the largest.5 integer less than or equal to x. The value o ( xdx ) is (up to decimal plces). 0.5 Ans. 0.5 Question 4 (Network Theory) V In the two-port network shown, the h parameter (where, h when V 0 ) in ohms is (up I to decimal places). I 0 I t I I V V Ans. 0.5 More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

5 4 GATE 08 [Aternoon Session] Since 004 Question 5 (Power System) A bus admittance matrix or an electric power system has 8000 non zero elements. The minimum number o branches (transmission lines and transormers) in this power system are (up to decimal places). Ans Question 6 (Signals & Systems) A continuous time input signal x() t is an eigen unction o an LTI system, i the output is (A) kx() t, where k is an eigen value jt (B) ke x() t, where k is an eigen value and (C) x() te j t, where j t e j t e is a complex exponential signal is a complex exponential signal (D) kh( ), where k is an eigen value and H ( ) is a requency response o the system. Ans. (A) Question 7 (Engineering Mathematics) Let be a real valued unction o a real variable deined as ( x) x or x 0 x 0. Which o the ollowing statement is true? (A) ( x ) is discontinuous at x 0 (B) ( x ) is continuous but not dierentiable at x 0 (C) ( x) is dierentiable but its irst derivative is not continuous at x 0 (D) ( x ) is dierentiable but its irst derivative is not dierentiable at x 0., and ( x) x or Ans. (D) Question 8 (Control System) Consider a unity eedback system with orward transer unction is given by, Gs () ( s)( s) The steady state error in the output o the system or a unit-step input is (up to decimal places). Ans Question 9 (Power System) In the igure, the voltages are V( t) 00cos( t), V( t) 00cos( t /8) and V 3 ( t ) 00cos( t / 36). The circuit is in sinusoidal steady state, and R L, P, P and P 3 are the average power outputs. Which one o the ollowing statements is true? R L R L P v () t v () t v () t P P 3 3 Copyright Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

6 5 GATE 08 [Aternoon Session] Since 004 (A) P P P 3 0 (B) P 0, P 0, P 3 0 (C) P 0, P 0, P 3 0 (D) P 0, P 0, P 3 0 Ans. (C) Question 0 (Engineering Mathematics) z The value o the integral dz in counter clockwise direction around a circle C o radius with C z 4 center at the point z is i (A) (B) i Ans. (A) Question (Analog Electronics) vin The op-amp shown in the igure is ideal. The input impedance i Z (C) i (D) i in is given by V in ~ I in R V 0 R R R R (A) Z (B) Z (C) Z (D) Z R R R R Ans. (B) Question (Electrical & Electronics Measurement) Two wattmeter method is used or measurement o power in a balanced three-phase load supplied rom a balanced three-phase system. I one o the wattmeters reads hal o the other (both positive), then the power actor o the load is (A) 0.53 (B) 0.63 (C) (D) Ans. (D) Question 3 (Electrical Machine) Ans. In a salient pole synchronous motor, the developed reluctance torque attains the maximum value when the load angle in electrical degrees is (A) 0 (B) 45 (C) 60 (D) 90 (B) More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

7 6 GATE 08 [Aternoon Session] Since 004 Question 4 (Power Electronics) Four power semiconductor devices are shown in the igure along with their relevant terminals. The device (s) that can carry dc current continuously in the direction shown when gated appropriately is (are) (A) Triac only (B) Triac and MOSFET (C) Triac and GTO (D) Thyristor and triac Ans. (A) Question 5 (Network Theory) The graph o a network has 8 nodes and 5 independent loops. The number o branches o the graph is (A) (B) (C) 3 (D) 4 Ans. (B) Question 6 (Power System) The series impedance matrix o a short three-phase transmission line in phase coordinates is Zs Zm Zm Zm Zs Z m. I the positive sequence impedance is ( j0) and the zero sequence is (4 j 3), Z m Zm Z s then the imaginary part o Ans. 7 Question 7 (Power Electronics) G A k I G I MT MT G k I Thyristor Triac GTO MOSFET Z m (in ) is (up to decimal places). A single phase ully controlled rectiier is supplying a load with an anti-parallel diode as shown in the igure. All switches and diodes are ideal. Which one o the ollowing is true or instantaneous load voltage and current? A G D s I L o a d i 0 + v 0 Ans. (A) v0 0 and i 0 0 (B) v0 0 and i 0 0 (C) v0 0 and i 0 0 (D) v0 0 and i 0 0 (C) Copyright Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

8 7 GATE 08 [Aternoon Session] Since 004 Question 8 (Engineering Mathematics) The value o the directional derivative o the unction ( x, y, z) xy yz zx at the point (,, ) in the direction o the vector p ij k is (A) (B) 0.95 (C) 0.93 (D) 0.9 Ans. (A) Question 9 (Power System) The positive negative and zero sequence impedances o a 5 MVA, three-phase, 5.5 kv, star-grounded, 50 Hz generator are j 0.pu, j 0.05 pu and j 0.0 pu respectively on the machine rating base. The machine is unloaded and working at the rated terminal voltage. I the grounding impedance o the generator is j 0.0 pu, then the magnitude o ault current or a b-phase to ground ault (in ka) is (up to decimal places). Ans Question 0 (Control System) Match the transer unctions o the second-order systems with the nature o the systems given below. Transer unctions Nature o system P. 5 s 5s5. Over damped Q. 5 s 0s5 II. Critically damped R. 35 s 8s35 III. Underdamped (A) P-I, Q-II, R-III (B) P-II, Q-I, R-III (C) P-III, Q-II, R-I (D) P-III, Q-I, R-II Ans. (C) Question (Engineering Mathematics) Consider a non-singular square matrix A. I trace (A) = 4 and trace ( A ) = 5. The determinant o the matrix A is (up to decimal place). Ans. 5.5 Question (Electrical Machine) A separately excited dc motor has an armature resistance Ra The ield excitation is kept constant. At an armature voltage o 00 V, the motor produces a torque o 500 Nm at zero speed. Neglecting all mechanical losses, the no-load speed o the motor (in radians/sec) or an armature voltage o 50 V is (up to decimal places.) Ans. 600 Question 3 (Power System) Consider a lossy transmission line with V and V as the sending and receiving end voltages, respectively. Z and X are the series impedance and reactance o the line, respectively. The steady-state stability limit or the transmission line will be More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

9 8 GATE 08 [Aternoon Session] VV (A) greater than X VV (B) less than X Since 004 VV (C) equal to X VV (D) equal to Z Ans. (B) Question 4 (Electromagnetic Field) A positive charge o nc is placed at (0, 0, 0.) where all dimensions are in metres. Consider the x-y plane to be a conducting ground plane. Take F/m. The Z component o the E ield at (0, 0, 0.) is closest to (A) V/m (B) V/m (C) V/m (D) V/m Ans. (B) Question 5 (Electrical Machine) A single-phase 00 kva. 000 V/00 V. 50 Hz transormer has a voltage drop o 5% across its series impedance at ull load. O this, 3% is due to resistance. The percentage regulation o the transormer at ull load with 0.8 lagging power actor is (A) 4.8 (B) 6.8 (C) 8.8 (D) 0.8 Ans. (A) Q.6 to Q.55 carry two marks each Question 6 (Power System) The positive, negative and zero sequence impedances o a three phase generator are Z, Z and Z 0 respectively. For a line-to-line ault with ault impedance Z, the ault current is I ki, where I is the ault current with zero ault impedance. The relation between Z and k is ( ZZ)( k) ( Z Z)( k) (A) Z (B) Z k k ( Z Z) k ( Z Z) k (C) Z (D) Z k k Ans. (A) Question 7 (Signal & Systems) Consider the two continuous-time signals deined below : t, t t, t x() t, x() t 0, otherwise 0, otherwise These signals are sampled with a sampling period o T = 0.5 seconds to obtain discrete-time signals x [ n] Ans. and x [ ] n, respectively. Which one o the ollowing statements is true? (A) The energy o x [ n ] is greater than the energy o x [ n ] (B) The energy o x [ n ] is greater than the energy o x [ n ]. (C) x [ n ] and x [ ] n have equal energies. (D) Neither x [ n ] nor x [ ] n is a inite-energy signal. (A) Copyright Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

10 9 GATE 08 [Aternoon Session] Since 004 Question 8 (Power Electronics) A phase controlled single phase rectiier, supplied by an AC source, eeds power to an R-L-E load as shown in the igure. The rectiier output voltage has an average value given V 0 (3 cos ), where V 80 volts and is the iring angle. I the power delivered to the lossless battery is 600 W, in m degree is (up to decimal places). V m Vm sin( t) V 0 0 mh 80 V Battery Ans. 90 Question 9 (Electrical & Electronics Measurement) A 0- Ampere moving iron ammeter has an internal resistance o 50 m and inductance o 0. mh. A shunt coil is connected to extend its range to 0-0 Ampere or all operating requencies. The time constant in milliseconds and resistance in m o the shunt coil respectively are (A) (B). (C) (D)., Ans. (A) Question 30 (Power System) Consider the two bus power system network with given loads as shown in the igure. All the values shown in the igure are in per unit. The reactive power supplied by generator G and G are Q G and Q G respectively. The per unit values o Q G, QG and line reactive power loss ( Q loss ) respectively are G 0 jqg.0 5 j5 j0. Q loss.00 0 j.0 G 5 jqg (A) 5.00,.68,.68 (B) 6.34, 0.00,.34 (C) 6.34,.34,.68 (D) 5.00,.34,.34 Ans. (C) More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

11 0 GATE 08 [Aternoon Session] Since 004 Question 3 (Power Electronics) The igure shows two buck converters connected in parallel. The common input dc voltage or the converters has value o 00 V. The converters have inductors o identical value. The load resistance is. The capacitor voltage has negligible rippel. Both converters operate in the continuous conduction mode. The switching requency is khz, and the switch control signals are as shown. The circuit operates in the steady state. Assume that the converters share the load equally, the average value o i, the current o switch S (in ampere), is (up to decimal places). s i s L S 00 V + C Switch control signals S L S t S 0.5 ms ms t Ans. 5 Question 3 (Electrical Machine) A 00 V DC series motor, when operating rom rated voltage while driving a certain load, draws 0 A current and runs at 000 rpm. The total series resistance is. The magnetic circuit is assumed to be linear. At the same supply voltage, the load torque is increased by 44%. The speed o the motor in rpm (rounded to the nearest integer) is. Ans. 85 Question 33 (Analog Electronics) In the circuit shown in the igure, the bipolar junction transistor (BJT) has a current gain 00. The base-emitter voltage drop is a constant, VBE 0.7 V. The value o the Thevenin equivalent resistance R Th (in ) as shown in the igure is (up to decimal places). 0 5 V 0 k k RTh 0.7 V Ans. 000 Copyright Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

13 GATE 08 [Aternoon Session] Since 004 Question 34 (Network Theory) The voltage v(t) across the terminals a and b as shown in the igure, is a sinusoidal voltage having a requency = 00 radian/s. When the inductor current i(t) is in phase with the voltage v(t), the magnitude o the impedance Z (in ) seen between the terminals a and b is (up to decimal places). vt () a it () L Z 00 F 00 b Ans. 50 Question 35 (Digital Electronics) Which one o the ollowing statements is true about the digital circuit shown in the igure. D Q D Q D Q out C C C in (A) It can be used or dividing the input requency by 3. (B) It can be used or dividing the input requency by 5. (C) It can be used or dividing the input requency by 7. (D) It cannot be reliably used as a requency divider due to disjoint internal cycles. Ans. (B) Question 36 (Network Theory) The voltages across the circuit in the igure, and the current through it are given that the ollowing expressions : Vi ( t) 5 0cos( t60) V and ii () t 5 X cos( t) A where 00 rad/sec I the average power delivered to the circuit is zero then the value o X (in Amp) is (upto two decimal places) + it i( ) Vt i( ) Electric Circuit Ans. 0 More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

14 GATE 08 [Aternoon Session] Question 37 (Engineering Mathematics) Since Let A 0 3 and B A A 4A 5I where, I is the 33identity matrix. The determinant o 0 0 B is.(upto one decimal places) Ans. Question 38 (Signals & Systems) The signal energy o the continuous time signal xt ( ) ( t) ut ( ) ( t) ut ( ) ( t3) ut ( 3) ( t4) ut ( 4) is (A) 3 (B) 7 3 (C) 3 (D) 5 3 Ans. (D) Question 39 (Power System) Ans. The per unit power output o a salient pole generator which is connected to an ininite bus is given by the expression, P.4sin 0.5sin, where is the load angle. Netwton Raphson method is used to calculate the value o or the irst iteration is 0 (A) 5 (B) (C) Question 40 (Control System) P 0.8 pu. I the initial guess is (C) 0 30, then its value (in degree) at the end o (D) The unit step response y(t) o a unity eedback system with open loop transer unction K GsHs () () is shown in the igure. The value o K is (up to decimal places). ( s) ( s) yt () Ans. 8 Copyright 0. 0 t (sec) Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

15 3 GATE 08 [Aternoon Session] Since 004 Question 4 (Network Theory) The equivalent impedance Z eq or the ininite ladder circuit shown in the igure is j9 j9 Z eq j5 j j5 j (A) j (B) j (C) j3 (D) 3 Ans. (A) Question 4 (Control System) The number o roots o the polynomial, o the complex plane is s s s s s s s , in the open let hal (A) 3 (B) 4 (C) 5 (D) 6 Ans. (A) Question 43 (Engineering Mathematics) I C is a circle z = 4 and z ( z) ( z 3z), then ( z) dz is C (A) (B) 0 (C) (D) Ans. (B) Question 44 (Electromagnetic Field) The capacitance o an air-illed parallel-plate capacitor is 60 pf. When a dielectric slab whose thickness is hal the distance between the plates, is placed on one o the plates covering it entirely, the capacitance becomes 86 pf. Neglecting the ringing eects, the relative permittivity o the dielectric is (up to decimal places). Ans..53 Question 45 (Power Electronics) A dc to dc converter shown in the igure is charging a battery bank, B whose voltage is constant at 50 V. B is another battery bank whose voltage is constant at 50 V. The value o the inductor. L is 5 mh and the ideal switch. S is operated with a switching requency o 5 khz with a duty ratio o 0.4. Once the circuit has attained steady state and assuming the diode D to be ideal, the power transerred rom B to B (in Watt) is (up to decimal places). More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

16 4 GATE 08 [Aternoon Session] Since 004 i L 5mH D B 50V B 50V Ans. Question 46 (Digital Electronics) Digital input signals A, B, C with A as the MSB and C as the LSB are used to realize the Boolean unction F m0 m m3m5 m7, where m i denotes the i th minterm. In addition. F has a don't care or m. The simpliied expression or F is given by (A) ACBC AC (B) A C (C) C A (D) ACBC AC Ans. (B) Question 47 (Electrical Machine) A transormer with toroidal core o permeability is shown in the igure. Assuming uniorm lux density across the circular core cross - section o radius o r R, and neglecting any leakage lux, the best estimate or the mean radius R is i Isin t p r i 0 s ~ v Vcost NP p R NS vs Vr N (A) P (B) I V Ans. (D) Question 48 (Engineering Mathematics) Ir NN P S (C) Vr N P I (D) Ir N P V 3 Let ( x) 3x 7x 5x 6. The maximum value o ( x ) over the interval [0, ] is (upto one decimal place) Ans. Question 49 (Electrical Machine) A 3-phase 900 kva, 3 kv/ 3kV ( /Y). 50 Hz transormer has primary (high voltage side) resistance per phase o 0.3 and secondary (low voltage side) resistance per phase o 0.0. Iron loss o the transormer is 00 kw. The ull load % eiciency o the transormer operated at unity power actor is (up to decimal places). Ans Copyright Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

17 5 GATE 08 [Aternoon Session] Since 004 Question 50 (Signal & System) Ans. 0 The Fourier transorm o a continuous-time signal x() t is given by X ( ),, where (0 j ) j and denotes requency. Then the value o ln x ( t) at t is (up to decimal place). (ln denotes the logarithm to base e). Question 5 (Electrical Machine) The equivalent circuit o a single phase induction motor is shown in the igure, where the parameters are R R' Xl Xl', X m 40 and s is the slip. At no-load, the motor speed can be approximated to be the synchronous speed. The no-load lagging power actor o the motor is (up to 3 decimal places). R jx l 0 V 0 X j M X j M R ' s X ' j l R ' ( s) X ' j l Ans Question 5 (Network Theory) A DC voltage source is connected to a series L-C circuit by turning on the switch S at time t = 0 as shown in the igure. Assume i(0) 0, v(0) 0. Which one o the ollowing circular loci represents the plot o i(t) versus v(t)? S it () 5V t 0 L H + C F vt () More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

18 6 GATE 08 [Aternoon Session] Since 004 (A) it () (B) it () vt () 5 vt () 5 (C) it () (D) it () 5 vt () 5 vt () Ans. (B) Question 53 (Control system) Consider a system governed by the ollowing equations dx () t x() t x() t dt dx() t x() t x() t dt The initial conditions are such that x(0) x(0). Let x lim x( t) and x lim x( t). Which one o the ollowing is true? (A) x x (B) x x (C) x x (D) x x Ans. (C) Question 54 (Engineering Mathematics) As shown in the igure, C is the arc rom the point (3, 0) to the point (0, 3) on the circle x t t y 9. The value o the integral ( y xy) dx ( x xy) dy is (up to decimal places). C y (3, 0) (3, 0) x Ans. 0 Copyright Head Oice : A/4-5, Smriti Nagar, Bhilai (C.G.), Contact : , Branch Oice : Raipur, : , Bhopal, : , Indore, :

19 7 GATE 08 [Aternoon Session] Since 004 Question 55 (Network Theory) A three-phase load is connected to a three-phase balanced supply as shown in the igure I Van 00 0 V, Vbn 000 V and Vcn V (angles are considered positive in the anti-clockwise direction), the value o R or zero current in the neutral wire is (up to decimal places). a R n c b j0 j0 Ans Answer Keys : General Aptitude. C. A 3. D 4. A 5. D 6. C 7. C 8. * (4/) 9. C 0. C Technical Part. D A 7. D C 0. A. B. D 3. B 4. A 5. B C 8. A C B 4. B 5. A 6. A 7. A A 30. D B D 39. C A 4. A 43. B B 47. D B 53. C More questions and video solutions o GATE - 08 are available in the Facebook group GATE ACADEMY (EE/EC/IN). To join click here

Q. 1 Q. 5 carry one mark each.

Q. 1 Q. 5 carry one mark each. GATE 08 General Aptitude (GA) Set6 Q. Q. 5 carry one mark each. Q. Since you have gone off the, the sand is likely to damage the car. The words that best fill the blanks in the above sentence are (A) course,