Q1. If A = - - - l éëêêê ùûúúú 0 1 2 1 0 3 2 2 is a singular matrix, then l is (A) 0 (B) -2 (C) 2 (D) -1 Q2. Let f x ex ( ) = in [0, 1]. Then, the value of c of the mean-value theorem is (A) 0.5 (B) ( ) e -1 (C) log ( ) e -1 (D) None Q3. If D u u u = + + xy yz zx x y z , then the value of A S × òò d is, where S is the surface of the cube defined by 0 1 £ £ x , 0 1 £ £ y , 0 1 £ £ z (A) 0.5 (B) 3 (C) 0 (D) 1.5 Q4. The gradient of field f y x xyz = + 2 is (A) y y z x y z xy x y z ( ) ( ) + + + + u u u 2 (B) y x z x x z xy x y z ( ) ( ) 2 + + + + u u u (C) y yx xy x y z 2 2 u u u + + (D) y y z x y z xy x y z ( ) ( ) 2 2 + + + + u u u Q5. In the circuit of fig. Q5 the value of R1 will be (A) 25W (B) 50W (C) 100W (D) 2000W 1 Paper-1 Questions Q1. to Q20. carry one mark each. 100 V R1 –+ 20 V –+ 70 V R2 60 W Fig Q5 PAPER -1 GATE ECE By R. K. Kanodia MCQs : The book contains only solved Multiple choice questions (MCQ) which is the main requirement of the GATE exam. Each and every problem has its complete solution. We understand the fact that theoretical studies should be done from the standard book, that one has studied for the semester exams and thus one should use the same material to understand the concepts of the same. We have deliberately excluded theoretical matter in the book so as not to mislead the students. However, wherever needed, satisfactory explanation of the formula has been included in the solution.Q6. The voltage v o in fig. Q6 is always equal to (A) 1 V (B) 5 V (C) 9 V (D) None of the above Q7. Epitaxial growth is used in integrated circuit (A) because it produces low parasitic capacitance (B) because it yields back-to-back isolating junctions (C) to grow single crystal n -doped silicon on a single-crystal p -type substrate (D) to grow selectively single-crystal p -doped silicon of one resistivity on p -type substrate of a different resistivity. Q8. The chemical reaction involved in epitaxial growth in IC chips takes place at a temperature of about (A) 500° C (B) 800° C (C) 1200° C (D) 2000° C Q9. In the circuit of fig. Q9 the output voltage v o is (A) 2.67 V (B) -2.67 V (C) -6.67 V (D) 6.67 V Q10. Assertion (A) In the self bias CE transistor amplifier a single battery is used. Reason (R) The collector base junction is forward biased by VCC . Chose the correct option: (A) Both A and R individually true and R is the correct explanation of A. (B) Both A and R individually true and but R is not the correct explanation of A. (C) A is true but R is false (D) A is false 2 Paper-1 20 kW 20 kW 40 kW 60 kW -1 V +0.5 V +2 V vo Fig Q9 GATE ECE By R. K. Kanodia Adherence to Pattern: All Multiple choice questions are strictly according to the GATE pattern. Every problem selected and included in the book is a model problem for the preparation of the exam which would thus prepare and equip the students better. Kindly note, that the standard of Multiple choice questions and their solution in every unit is much better than the ones available in a famous series of problems & solutions as far as GATE is concerned. –+vo 5 V 1 A 4 W Fig Q6Q11. The address bus width of a memory of size 1024 ´ 8 bits is (A) 10 bits (B) 13 bits (C) 8 bits (D) 18 bits Q12. Consider the TTL circuit in fig Q12. The value ofVH andVL are respectively (A) 5 V, 0 V (B) 4.8 V, 0 V (C) 4.8 V, 0.2 V (D) 5 V, 0.2 V Q13. Consider a discrete-time system S whose response to a complex exponential input e j n p 2 is specified as S e e j n j n : p p 2 3 2 Þ .The system is (A) definitely LTI (B) definitely not LTI (C) may be LTI (D) information is not sufficient. Q14. The DTFT of signal 2 4 2 d[ ] - n is (A) 2 2 e j - W (B) 2 2 e j W (C) 1 (D) None of the above Q15. Consider the List I and List II List I List II P. Derivative control 1. Improved overshoot response Q. Integral control 2. Less steady state errors R. Rate feed back control 3. Less stable S. Proportional control 4. More damping The correct match is P Q R S (A) 1 2 3 4 (B) 4 3 1 2 (C) 2 3 1 4 (D) 1 2 4 3 3 Paper-1 +5 V Vi Vo 2 kW 4 kW Fig Q12 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Q16. The pole–zero plot given in fig.Q16 is that of a (A) PID controller (B) PD controller (C) Integrator (D) Lag–lead compensating network Q17. In TDM non essential frequency components of the modulating signal are removed by (A) sampler (B) attenuator (C) pre-alias filter (C) modulator Q18. Coherent demodulation of FSK signal can be affected using (A) correlation receiver (B) bandpass filter and envelope detectors (C) discriminator detection (C) above all Q19. Two dissimilar antennas having their maximum directivities equal, (A) must have their beamwidths also equal. (B) can not have their beamwidths equal because they are dissimilar antenna. (C) may not necessarily have their maximum power gain equal. (D) must have their effective aperture areas ( capture areas) also equal. Q20. The dominant mode in a rectangular waveguide is TE10 because this mode has (A) no attenuation (B) no cut-off (C) no magnetic field component (D) the highest cut-off wavelength 4 Paper-1 s jw Fig Q16 Problem 10. v1 = ? (A) 6 V (B) 7 V (C) 8 V (D) 10 V 1 W 1 W 3 W 2 W 6 W 8 V v1 –+ 2 W 6 W 18 V Fig. P.1.4.10 Solution 10. (A) By changing the LHS and RHS in Thevenin equivalent v1 4 1 1 12 1 2 1 1 1 16 1 1 2 6 = + + + + + + + = V 4 V 12 V 1 W 1 W v1 –+ 2 W 6 W 1 W Fig. S1.4.10 Consider above problem and its solution from book GATE ECE by R. K. Kanodia ( chapter 1.4 Circuit Theorems). If problem is solved using mesh analysis or nodal gives 4 or 3 variables. The solution shown above has only one variable and require less calculation reducing time and errors as well. The trick in this book are not new but it equip students to think differently.Q21. If the rank of the matrix, A = - éëêêê ùûúúú 2 1 3 4 7 1 4 5l is 2, then the value of l is (A) -13 (B) 13 (C) 3 (D) None of these Q22. If u exyz = , then ¶ ¶ ¶ ¶ 3u x y z is equal to (A) e xyz x y z xyz [ ] 1 3 2 2 2 + + (B) e xyz x y z xyz [ ] 1 3 3 3 + + (C) e xyz x y z xyz [ ] 1 3 2 2 2 + + (D) e xyz x y z xyz [ ] 1 3 3 3 3 + + Q23. The value of e xx dx x 11 ++ æè çç öø ÷÷ ò sin cos is (A) e x c x tan 2 + (B) e x c x cot 2 + (C) e x c x tan + (D) e x c x cot + Q24. The solution of the differential equation ( ) x y dx xydy - + = 2 2 0 is (A) ye A x 2 = (B) xe A y x 2 = (C) xe A x y 2 = (D) ye A x y 2 = Q25. The Taylor’s series expansion of f z z ( ) sin = about z = p4 is (A) 12 1 4 1 2 4 2 + - æè ç öø ÷- - æè ç öø ÷- éë êê ùû úú z z p p ! ....... (B) 12 1 4 1 2 4 2 + - æè ç öø ÷+ - æè ç öø ÷+ éë êê ùû úú z z p p ! ....... (C) 12 1 4 1 2 4 2 - - æè ç öø ÷- - æè ç öø ÷- éë êê ùû úú z z p p ! ....... (D) None of the above 5 Paper-1 Questions Q21. to Q75. carry two marks each. All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Q26. Consider the following tableDiameter of heart (in mm) Number of persons 120 5 121 9 122 14 123 8 124 5 125 9 The median of the above frequency distribution is (A) 122 mm (B) 123 mm (C) 122.5 mm (D) 122.75 mm Q27. For dy dx x y = + 2 , given that y =0 at x =0, using Picard’s method up to third order of approximation the solution of the differential equation is (A) x x x x 2 5 8 11 2 40 480 1600 + + + (B) x x x x 2 5 8 11 2 20 160 4400 + + + (C) x x x x 2 5 8 11 2 20 160 2400 + + + (D) x x x x 2 5 8 11 2 40 480 2400 + + + Q28. The bilateral laplace transform of cos ( ) * ( ) 3t u t e u t t - - is (A) - + + s s s ( )( ) 1 9 2 , Re ( ) s >0 (B) - + + s s s ( )( ) 1 9 2 , - < 1 Re ( ) s < 0 (C) s s s ( )( ) + + 1 9 2 , - < 1 Re ( ) s < 0 (D) s s s ( )( ) + + 1 9 2 , Re ( ) s >0 6 Paper-1 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Q29. The z-transform of x n n [ ] | | =æè ç öø ÷ 23 is (A) - - - - < < - 5 2 3 3 2 32 23 z z z z ( )( ) , (B) - - - < < 5 2 3 3 2 23 32 z z z z ( )( ) , | | (C) 5 2 3 3 2 23 23 z z z z ( ) ( ) , | | - - < < (D) 5 2 3 3 2 32 23 z z z z ( )( ) , - - - < < - Q30. Consider the graph shown in fig. Q30 in which twigs are solid line and links are dotted line. A fundamental loop matrix for this tree is given as below BF = - - - éëêêê ùûúúú 1 0 0 1 0 1 0 1 0 1 1 0 0 0 1 0 1 1 The oriented graph will be (A) (B) (C) (D) 7 Paper-1 4 1 2 5 6 3 Fig Q30 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Q31. The value of the current measured by the ammeter in Fig. Q31 is (A) 23 A (B) 53 A (C) - 56 A (D) 29 A Q32. In the circuit of fig. Q32 the equivalent resistance seen by the capacitor is (A) -470W (B) 470W (C) -90W (D) vC ( ) 0 is required Q33. In the circuit of fig. Q33 switch is moved from position a to b at t =0. The i t L ( ) for t > 0 is (A) ( ) 4 6 4 - t e t A (B) ( ) 3 6 4 - - t e t A (C) ( ) 3 9 5 - - t e t A (D) ( ) 3 8 5 - - t e t A 8 Paper-1 14 W 0.02 F t=0 ba 2 W 12 V 4 A 6 W iL 2 H Fig Q33 120 W 70 W C 4ix vC –+ Fig Q32 2 A 3 A 6 W 4 W 7 W 5 W 2 W Ammeter Fig Q31 GATE ECE By R. K. Kanodia Unit Division: Each unit has been further sub-divided into separate chapters and not clustered together. Thus the non-combination of all the problems in a single unit makes the reader, to remain focused and able to manage his time during his preparation.Q34. In the circuit of fig. Q34 the i t ( ) will be (A) 2 2 5 77 sin ( . ) t + ° A (B) cos ( . ) 2 84 23 t - ° A (C) 2 2 5 77 sin ( . ) t - ° A (D) cos ( . ) 2 84 23 t + ° A Q35. In the circuit of fig. Q35 Leq will be (A) 1 H (B) 2 H (C) 3 H (D) 4 H Q36. The maximum voltage across capacitor would be (A) 3200 V (B) 3 V (C) -3V (D) 1600 V 9 Paper-1 GATE ECE By R. K. Kanodia Time Management: Time is a very important factor in any competitive exam and the same applies for GATE too. It has been observed and concluded that if students can manage time, they can get a better score in GATE. The solutions provided are extremely logical yet tricky so that they save time when the student solve them in the examination, as they have already been used to solving difficult and tricky problems. 10 W mF 14 25 W 0.105v1 3 V v1 + – ~ vC –+ 4 H Fig Q36 1 H1 H 2 H2 H 3 H Leq Fig Q35 1 W 4 W 0.25 F 4 H i 10cos 2 V t ~ Fig Q34Q37. Three scattering mechanism exist in a semiconductor. If only the first mechanism were present, the mobility would be 500 cm V s 2 - . If only the second mechanism were present, the mobility would be 750 cm V s 2 - . If only third mechanism were present, the mobility would be 1500 cm V s 2 - . The net mobility is (A) 2750 cm V s 2 - (B) 1114 cm V s 2 - (C) 818 cm V s 2 - (D) 250 cm V s 2 - Q38. In a silicon (ni = ´ - 15 1010 3 . cm , Dn =35 2 cm s) sample the electron concentration drops linearly from 1018 cm-3 to 1016 cm-3 over a length of 2.0 mm. The current density due to the electron diffusion current is (A) 93 104 . ´ A cm2 (B) 28 104 . ´ A cm2 (C) 93 109 . ´ A cm2 (D) 28 109 . ´ A cm2 Q39. A pn junction diode is operating in reverse bias region. The applied reverse voltage, at which the ideal reverse current reaches 90% of its reverse saturation current, is (A) -59.6 mV (B) 2.7 mV (C) 4.8 mV (D) 42.3 mV Q40. In bipolar transistor biased in the forward-active region the base current is I B =50mA and the collector currents is IC =2 7 . mA. The a is (A) 0.949 (B) 54 (C) 0.982 (D) 0.018 10 Paper-1 GATE ECE By R. K. Kanodia Variety: The book carries in it a large variety of problems. The words of one of the senior educators of a reputed coaching institute bear testimony to the fact wherein he comments that “We can’t expect so much variety of problems in a single book available in the market.”Q41. An n -channel silicon (ni = ´ - 15 1010 3 . cm ) JFET at T =300 K has doping concentration of Nd = ´ 8 1016 cm-3 and Na = ´ 3 1018 cm-3 . The channel thickness dimensions is a =05 . mm. If the undepleted channel has to be 0 2 . mm, the required gate voltage is (A) 2.73 V (B) -2.73 V (C) 4.66 V (D) -4.66 V Q42. In the circuit shown in fig. Q42 voltageVE = 4 V. The value of a and b are respectively (A) 0.943, 17.54 (B) 0.914, 17.54 (C) 0.914, 10.63 (D) 0.914, 11.63 Q43. In the current mirror circuit of fig. Q43 the transistor parameters areVBE =0 7 . V, b =50 and the Early voltage is infinite. Assume transistor are matched. The output current I o is (A) 1.04 mA (B) 1.68 mA (C) 962 mA (D) 432 mA 11 Paper-1 GATE ECE By R. K. Kanodia Includes Previous Exam Questions: This books contain questions on earlier IES, IAS & GATE exams that might be relevant to learn some concepts but we have purposely not mentioned them in our book. We believe and strongly advocate that every year GATE contains new and unique problems. Io +5 V 1 mA Fig Q43 -5 V VE 2 kW 8 kW 100 kW +5 V Fig Q42Q44. The parameter of the transistor in fig. Q44 areVTN =12 . mA /V2 , Kn =0 5 . mA /V2 , and l =0. The voltageVDS is (A) 2.83 V (B) 6.52 V (C) 3.48 V (D) 4.98 V Q45. In the circuit shown in fig. Q45 the op-amp is ideal. If transistor has b =60, then the total current supplied by the 15 V source is (A) 123.1 mA (B) 98.3 mA (C) 49.4 mA (D) 168 mA Q46. Consider the statements below: 1. If the output waveform from an OR gate is the same as the waveform at one of its inputs, the other input is being held permanently LOW. 2. If the output waveform from an OR gate is always HIGH, one of its input is being held permanently HIGH. The statement, which is always true, is (A) Both 1 and 2 (B) Only 1 (C) Only 2 (D) None of the above 12 Paper-1 47 kW+15 V 100 W Vz = 5 V vo Fig Q45 50 A m +5 V -5 V Fig Q44 GATE ECE By R. K. Kanodia Levels of MCQs: The Multiple choice questions included in the book are in a conceptually evolving method, allowing the student to progress from one level of complexity to another but always aiding in understanding the basic foundation of the subject. Thus, the MCQs gradually and scientifically advance from the basic level to a more complex level, helping in the systematic understanding of the problem rather than an abrupt one.Q47. A logic circuit consist of two 2 4 ´ decoder as shown in fig. Q47. The output of decoder are as follow D0 1 = when A A 0 1 0 0 = = , D1 1 = when A A 0 1 1 0 = = , D2 1 = when A A 0 1 0 1 = = , D3 1 = when A A 0 1 1 1 = = , The value of f x y z ( , , ) is (A) 0 (B) z (C) z (D) 1 Q48. The circuit shown in fig. Q48 implements the function (A) ABC ABC + (B ) ABC A B C + + + ( ) (C) ABC A B C + + + ( ) (D) None of the above 13 Paper-1 GATE ECE By R. K. Kanodia Less Erroneous: The book has very few errors [less than 5%] compared to the other books available in the market which have upto 40% errors. This puts the students in a better and more comfortable situation as all the errors are traceable due to availability of the complete solution and moreover, the errors are never conceptual but data or typo mistakes. Kindly note that, all the errata will be soon available at our website www.nodia.co.in +VDD +VDD Y A A B B C C A B C ABC Fig Q48 xy A1 A0 D1 D2 D0 D3 f z A0 A1 D1 D2 D0 D3 Fig Q47Q49. Consider the following 8085 assembly program MVI A, DATA1 MOV B, A SUI 51H JC DLT MOV A, B SUI 82H JC DSPLY DLT : XRA A OUT PORT1 HLT DSPLY : MOV A, B OUT PORT2 HLT This program will display (A) the bytes from 51H to 82H at PORT2 (B) 00H AT PORT1 (C) all byte at PORT1 (D) the bytes from 52H to 81H at PORT 2 Q50. Consider the following program MVI A, BYTE1 RRC RRC If BYTE1 =32H, the contents of A after the execution of program will be (A) 08H (B) 8CH (C) 12H (D) None of the above Q51. The response of a system S to a complex input x t e j t ( ) = 5 is specified as y t te j t ( ) = 5 . The system (A) is definitely LTI (B) is definitely not LTI (C) may be LTI (D) information is insufficient 14 Paper-1 GATE ECE By R. K. Kanodia Attractive Format: We understand student psychology and the fact that if the book is in an attractive format, the student would feel good in reading the book. This fact also heightens the interest to study in a student. Thus the style of the book is so designed that it appeals to its readers, yet is expressive and detailed.Q52. The following input output pairs have been observed during the operation of a time invariant system : x n y n x n y SS 1 1 2 1 0 2 0 1 2 0 0 3 [ ] { , , } [ ] { , , } [ ] { , , } = ¬ ® ¾ = = ¬ ® ¾ 2 3 3 0 1 0 2 0 0 0 1 1 2 1 [ ] { , , , } [ ] { , , , } [ ] { , , } n x n y n S = = ¬ ® ¾ = The conclusion regarding the linearity of the system is (A) System is linear (B) System is not linear (C) One more observation is required. (D) Conclusion cannot be drawn from observation. Q53. The transfer function H s ( ) of a stable system is H s s s s s s ( ) ( )( ) = + - + - + 2 25 9 1 2 10 The impulse response is (A) - + + - e u t e t e t u t t t t ( ) ( sin cos ) ( ) 3 2 3 (B) - - + - - e u t e t e t u t t t t ( ) ( sin cos ) ( ) 3 2 3 (C) - - + - e u t e t e t u t t t t ( ) ( sin cos ) ( ) 3 2 3 (D) - + + - - e u t e t e t u t t t t ( ) ( sin cos ) ( ) 3 2 3 Q54. The frequency response which has nonlinear phase is (A) 1 1 jw+ (B) 1 1 2 ( ) jw+ (C) 1 1 2 ( )( ) j j w w + + (D) All above 15 Paper-1 GATE ECE By R. K. Kanodia Aim : The aim of the book is to provide quality material, a fact which can easily be seen in books available for the preparation of IIT-JEE, AIEEE, CPMT & CAT, but till date never observed in the material available GATE preparation. In other words, we want to provide ELITE material but which is also economical. E : Expressive L : Less Erroneous I : Individualistic T : Targeted approach E : Exhaustive contentQ55. Consider a discrete-time periodic signalx n n n [ ] sin sin = æè ç öø ÷ æè ç öø ÷ 11 20 20p p with a fundamental period N =20. The Fourier series coefficients of this function are (A) 1 20 5 6 ( [ ] [ ]) u k u k + - - , | | k £10 (B) 1 20 5 5 ( [ ] [ ]) u k u k + - - , | | k £10 (C) ( [ ] [ ]) u k u k + - + 5 6 , | | k £10 (D) ( [ ] [ ]) u k u k + - - 5 6 , | | k £10 Q56. A feedback control system shown in fig. Q56 is subjected to noise N s ( ). The noise transfer function C s N s N ( ) ( ) is (A) G G G G H 1 2 1 2 1+ (B) GG H 21 1+ (C) GG H 22 1+ (D) None of the above Q57. For the block diagram shown in the fig. Q57 the limiting value of K for stability of inner loop is found to be X K Y < < . The over all system will be stable if and only if (A) 4 4 X K Y < < (B) X K Y 2 2 < < (C) 2 2 X K Y < < (D) X K Y < < 16 Paper-1 K ( -)( + 3 )( + 4 ) s a s a s a R s ( ) C s ( ) + + Fig Q57 N s ( ) + G1 G2 H2 ++ R s ( ) C s ( ) Fig Q56 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Q58. The transfer function of a ufb system is G s s s s s s s a s ( ) ( )( )( ) ( )( )( ) = + + + + + + 10 3 10 20 25 30 5 The value of a to yield velocity error constant Kv =104 is (A) 4 (B) 0 (C) 8 (D) 16 Q59. The forward-path transfer function of a ufb system is G s K s s s s ( ) ( )( ) ( ) = + + - a 3 1 2 . The root-loci for K >0 with a =5 is (A) (B) (C) (D) Q60. Consider the asymptotic Bode plot of a minimum phase linear system given in fig. Q60. The transfer function is (A) 8 2 5 10 s s s s ( ) ( )( ) + + + (B) 4 5 2 10 ( ) ( )( ) s s s + + + (C) 4 2 5 10 ( ) ( )( ) s s s s + + + (D) 8 5 2 10 s s s s ( ) ( )( ) + + + 17 Paper-1 -20 dB/dec -20 dB/dec -40 dB/dec dB w 6 0.1 w1 w2 10 32 Fig Q60 s jw -1 -3 -5 1 s jw -1 -3 -5 1 s jw -1 -3 -5 1 s jw -1 -3 -5 1 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Q61. The joint PDF of random variable x and y is shown in fig. Q61. The value of A is (A) 1 (B) 2 (C) 4 (D) None of the above Q62. The probability density function of a random variable X is given as f x X ( ). A random variable Y is defined as y ax b = + where a< 0. The PDF of random variable Y is (A) bf y b a X - æè ç öø ÷(B) af y b a X - æè ç öø ÷ (C) 1a f y b a X - æè ç öø ÷(D) 1b f y b a X - æè ç öø ÷ Q63. A carrier is amplitude modulate to 100 % by a polar rectangular signal as shown in fig. Q62. The percentage increase in signal power is (A) 83.3 % (B) 100 % (C) 50 % (D) None of the above Q64. In a AM signal the received signal power is10 10 - W with a maximum modulating signal of 5 kHz. The noise spectral density at the receiver input is10 18 - W Hz. If the noise power is restricted to the message signal bandwidth only, the signals-to-noise ratio at the input to the receiver is (A) 43 dB (B) 66 dB (C) 56 dB (D) 33 dB 18 Paper-1 m t ( ) 1 t -1 Fig Q62 A 1 1 x y P x y XY ( , ) Fig Q61 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Q65. Fig. Q65 shows a PCM signals in which amplitude level of +1 volt and -1 volt are used to represent binary symbol 1 and 0 respectively. The code word used consists of three bits. The sampled version of analog signal from which this PCM signal is derived is (A) 4 5 2 1 3 (B) 8 4 3 1 2 (C) 6 4 3 1 7 (D) 1 2 3 4 5 Q66. The flux of D u u = f + f f r r 2 2 3 cos sin over the closed surface of the cylinder 0 3 3 £ < = z , r is (A) 324 (B) 81p (C) 81 (D) 64p Q67. In a certain region J u u u = + + ( ) sin ( ) 4 2 10 3 4 y xz z t x y z A m. If volume charge density rv in z =0 plane is zero, then rv is (A) 3 10 2 4 z t cos ( )mC m3 (B) 03 10 2 4 . cos ( ) z t mC m3 (C) -3 10 2 4 z t cos ( )mC m3 (D) -03 10 2 4 . cos ( ) z t mC m3 Q68. Twol 4 transformer in tandem are to connect a 50Wline to a 75Wload as shown in fig. Q68. If Zo 2 30 = W and there is no reflected wave to the left of A, then the characteristic impedance Zo1 is (A) 28W (B) 56W (C) 49W (D) 24.5W 19 Paper-1 l/4 Z = o 50 W Zo1 75 W Zo2 l/4 Fig Q68 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same. Fig Q65Q69. The cross section of a waveguide is shown in fig. Q69. It has dielectric discontinuity as shown in fig. If the guide operate at 8 GHz in the dominant mode, the standing wave ratio is (A) -3.911 (B) 2.468 (C) 1.564 (D) 4.389 Q70. An antenna consists of 4 identical Hertizian dipoles uniformly located along the z–axis and polarized in the z-direction. The spacing between the dipole is l4 . The group pattern function is (A) 4 4 2 cos cos cos cos p q p q æè ç öø ÷ æè ç öø ÷(B) 4 4 8 cos cos cos cos p q p q æè ç öø ÷ æè ç öø ÷ (C) 4 4 2 cos cos sin cos p q p q æè ç öø ÷ æè ç öø ÷(D) 4 4 8 cos cos sin cos p q p q æè ç öø ÷ æè ç öø ÷ Common Data Questions Common Data for Questions Q71-73: In the voltage regulator circuit in fig. Q71-73 the Zener diode current is to be limited to the range 5 100 £ £ iz mA. Q71. The range of possible load current is (A) 5 130 £ £ iL mA (B) 25 120 £ £ iL mA (C)10 110 £ £ iL mA (D) None of the above Q72. The range of possible load resistance is (A) 60 372 £ £ RL W (B) 60 200 £ £ RL W (C) 40 192 £ £ RL W (D) 40 360 £ £ RL W Q73. The power rating required for the load resistor is (A) 576 mW (B) 360 mW (C) 480 mW (D) 75 mW 20 Paper-1 12 W 6.3 V Vz = 4.8 V RL iL Rz = 0 iz Fig Q71-73 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same. y x 5 cm 2.5 cm m e o o , m e o o , 2.25 z Fig Q69Common Data for Questions Q74-75: The state-space representation of a system is given by & ( ) ( ) ( ) x A x B u t t t = × + × , where A = - éë ê ùû ú 0 2 2 0 , B = éë ê ùû ú 01 If x( ) 0 is the initial state vector, and the component of the input vector u( ) t are all unit step function, then the state transition equation is given by & ( ) ( ) x x t t t = + F( ) ( ) 0 q , whereF( ) t is a state transition matrix and q( ) t is a vector matrix. Q74. TheF( ) t is (A) cos sin sin cos 2 2 2 2 t t t t - éë ê ùû ú(B) cos sin sin cos 2 2 2 2 t t t t - éë ê ùû ú (C) sin cos cos sin 2 2 2 2 t t t t - éë ê ùû ú(D) sin cos cos sin 2 2 2 2 t t t t - éë ê ùû ú Q75. The q( ) t is (A) 05 1 2 05 2 . ( sin ) . cos - éë ê ùû ú t t (B) sin cos22tt éë ê ùû ú (C) 05 1 2 05 2 . ( cos ) . sin - éë ê ùû ú t t (D) cos sin 22tt éë ê ùû ú Statement for Linked Answer Questions: Q76. and Q77: A silicon Hall device at T =300 K has the geometry d = - 10 3 cm , W = - 10 2 cm, L = - 10 1 cm. The following parameters are measured: I x =0 75 . mA, Vx =15 V, VH = +58 . mV, Bz =01. tesla. Q76. The majority carrier concentration is (A) 8 1015 ´ cm-3 , n -type (B) 8 1015 ´ cm-3 , p -type (C) 4 1015 ´ cm-3 , n -type (D) 4 1015 ´ cm-3 , p -type Q77. The majority carrier mobility is (A) 430 cm V s 2 - (B) 215 cm V s 2 - (C) 390 cm V s 2 - (D) 195 cm V s 2 - 21 Paper-1 Linked Answer Questions: Q76. to Q85. carry two marks each. All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Statement for Linked Answer Questions: Q78 and Q79: Consider the circuit shown in fig. Q78-79. Q78. The expression for the next state Q+ is (A) xQ B) xQ (C) x Q Å (D) x Q u Q79. Let the clock pulses be numbered 1, 2, 3... after the point at which the FF is reset (Q0 0 = ). The circuit is a (A) even parity checker (B) odd parity generator (C) Both A and B (D) None of the above Statement for Linked Answer Questions: Q80 and Q81: A causal and stable LTI system has the property that 23 23 æè ç öø ÷Þ æè ç öø ÷ n n u n n u n [ ] [ ]. Q80. The frequency response H e j ( ) W for this system is (A) 2 2 3 e ej j W W - (B) 2 2 3 e ej j - - - W W (C) 2 3 2 e ej j W W - (D) 2 3 2 e ej j - - WW Q81. The difference equation for this system relating any input x n [ ] and the corresponding output y n [ ] is (A) 3 2 1 2 y n y n x n [ ] [ ] [ ] - - = (B) 3 2 1 2 1 y n y n x n [ ] [ ] [ ] - - = - (C) 3 2 1 2 1 y n y n x n [ ] [ ] [ ] - + = + (D) 3 2 1 2 y n y x n [ ] [ ] [ ] - + = 22 Paper-1 S Q CLK R x Fig Q78-79 All questions are drawn from the book GATE ECE by R. K. Kanodia published by NODIA & COMPANY. For full solution refer the same.Statement for Linked Answer Questions: Q82 and Q83: In a certain frequency–modulation experiment conducted with f m =1kHz and increasing amplitude (starting from 0 V), it is found that the carrier component of the FM signal is reduced to zero for the first time when Am = 2 V. Given that Bessel function J x 0 ( ) is zero for x =2 44 . , 5.52, 8.65, 11.8 and so on. Q82. The frequency sensitivity of the modulator is (A) 1.38 kHz V (B) 0.61 kHz V (C) 2.76 kHz V (D) 1.22 kHz V Q83. The carrier components is reduced to zero for the second time for the value of Am (A) 4.52 V (B) 3.38 V (C) 2.68 V (D) 1.39 V Statement for Linked Answer Questions: Q84 and Q85: The amplitude of a wave traveling through a lossy nonmagnetic medium reduces by 18% every meter. The wave operates at 10 MHz and the electric field leads the magnetic field by 24°. Q84. The propagation constant is (A) 0198 0 448 . . + j per meter `(B) 0346 0 713 . . + j per meter (C) 0 448 0198 . . + j per meter (D) 0 713 0346 . . + j per meter Q85. The skin depth is (A) 2.52 m (B) 5.05 m (C) 8.46 m (D) 4.23 m 23 Paper-1 Mul t ipl e Cho i c e Que s t i ons GATE Electronics & Communications By R. K. Kanodia Price 425.00 Pages 602 Published by NODIA & COMPANY For previous years papers & sample chapters of book please visit www.nodia.co.in Feel free to call at 09350292376 for any enquiry about book.Answers Paper-1 1. (B) 2. (C) 3. (D) 4. (A) 5. (C) 6. (D) 7. (C) 8. (C) 9. (B) 10. (A) 11. (A) 12. (D) 13. (B) 14. (A) 15. (D) 16. (D) 17. (C) 18. (A) 19. (C) 20. (D) 21. (B) 22. (C) 23. (A) 24. (B) 25. (A) 26. (A) 27. (B) 28. (B) 29. (B) 30. (D) 31. (C) 32. (B) 33. (C) 34. (B) 35. (D) 36. (A) 37. (D) 38. (B) 39. (A) 40. (C) 41. (D) 42. (C) 43. (C) 44. (B) 45. (C) 46. (D) 47. (D) 48. (B) 49. (A) 50. (B) 51. (B) 52. (B) 53. (D) 54. (D) 55. (A) 56. (A) 57. (B) 58. (A) 59. (A) 60. (C) 61. (B) 62. (C) 63. (B) 64. (A) 65. (D) 66. (B) 67. (B) 68. (D) 69. (C) 70. (A) 71. (B) 72. (C) 73. (A) 74. (A) 75. (C) 76. (B) 77. (C) 78. (C) 79. (D) 80. (D) 81. (B) 82. (D) 83. (A) 84. (A) 85. (B)24 Paper-1 Vision of NODIA & COMPANY 1. Highly Competitive: To be able to provide, the student, with the best quality material for the targeted exam and the best production quality books. The books published by us would be accurate and precise in content, well-targeted in approach, expressive in style and available at an affordable price.We take pride in stating that our first publication GATE-ECE by RK Kanodia has been a great success last year, on all aspects. Everyone who got through, due to this book, has given excellent feedback. Reviews can be read at our website www.nodia.co.in. 2. Avoid Student exploitation: We are aware that setting a high MRP, giving discounts to students&incentives to retailers, to sell a book is unethical and in a way exploits students as far as money is concerned. We respect the publishing field&do not want to employ gimmicks to increase our sales. The true appreciation of our work lies if the student can be pickup our book for its quality not because the retailer is promoting it in lieu of incentive. 3. Social Responsibility: To help improve the socio-economic conditions of the grass-root level with the earning from this endeavor. Rs.10, from every book sold, is contributed to the NGOs/Govt. Organizations working for the education of child labour.MCQ GATE-ECE by RK Kanodia Kindly note that our publication GATE-ECE by RK Kanodia, has the following features that make it an excellent study material in comparison to other books available on the GATE exam: 1. MCQs: The book contains only solved Multiple choice questions (MCQ) which is the main requirement of the GATE exam. Each and every problem has its complete solution. We understand that theoretical studies should be done from the standard book, that one has studied for the semester exams and thus one should use the same material to understand the concepts of the same. We have deliberately excluded theoretical matter in the guide book so as not to mislead the students. However, wherever needed, satisfactory explanation of the formula has been included in the solution. 2. Adherence to Pattern: All Multiple choice questions are strictly according to the GATE pattern. Every problem selected and included in the book is a model problem for the preparation of the exam which would thus prepare and equip the students better. Kindly note, that the standard of Multiple choice questions and their solution in every unit is much better than the ones available in a famous series of problems & solutions as far as GATE is concerned. 3. Levels of MCQs: The Multiple choice questions included in this book are in a conceptually evolving method, allowing the student to progress from one level of complexity to another but always aiding in understanding the basic foundation of the subject. Thus, the MCQs gradually and scientifically advance from the basic level to a more complex level, helping in the systematic understanding of the problem rather than an abrupt one. 4. Unit Division: Each unit has been further sub-divided into separate chapters and not clustered together. Thus the non-combination of all the problems in a single unit makes the reader, to remain focused and able to manage his time during his preparation. 5. Time Management: Time is a very important factor in any competitive exam and the same applies for GATE too. It has been observed and concluded that if students can manage time, they can get a better score in GATE. The solutions provided are extremely logical yet tricky so that they save time when the student solve them in the examination, as they have already been used to solving difficult and tricky problems. 6. Variety: The book carries in it a large variety of problems. The words of one of the senior educators of a reputed coaching institute bear testimony to the fact wherein he comments that “We can’t expect so much variety of problems in a single book available in the market.” 7. Includes Previous Exam Questions: This book contains questions on earlier IES, IAS & GATE exams that might be relevant to learn some concepts but we have purposely not mentioned them in our book. We believe and strongly advocate that every year GATE contains new and unique problems. 8. Less Erroneous: The book has very few errors [less than 5%] compared to the other books available in the market which have upto 40% errors. This puts the students in a better and more comfortable situation as all the errors are traceable due to availability of the complete solution and moreover, the errors are never conceptual but data or typo mistakes. Kindly note that, all the errata will be soon available at our website www.nodia.co.in 9. Attractive Format: We understand student psychology and the fact that if the book is in an attractive format, the student would feel good in reading the book. This fact also heightens the interest to study in a student. Thus the style of the book is so designed that it appeals to its readers, yet is expressive and detailed. 10. Aim : The aim of the book is to provide quality material, a fact which can easily be seen in books available for the preparation of IIT-JEE, AIEEE, CPMT & CAT, but till date never observed in the material available GATE preparation. In other words, we want to provide ELITE material but which is also economical. E : Expressive L : Less Erroneous I : Individualistic T : Targeted approach E : Exhaustive content We have received feedback, which state that the book fulfills more than what is stated above and thus it has been a great success last year, on all aspects. Everyone who got through, due to this book, has given excellent feedback. Reviews can be read at our website www.nodia.co.in. However, nothing in the world can be achieved without the help of constructive criticism and thus we would be obliged if you can send across your feedback to make our book, a GUIDE in true sense of the word. Feel free to mail or call at following for any enquiry about book: NODIA & COMPANY 09350292376 pk.goel@nodia.co.in 25 Paper-1Dear Student, We are a Delhi based publishing organization by the name of NODIA & COMPANY, conceptualized in June 2005, for providing competitive exam books in the field of Engineering. The company has been started with following AIM: 1. Highly Competitive: To be able to provide, the student, with the best quality material for the targeted exam and the best production quality books. The books published by us would be accurate and precise in content, well-targeted in approach, expressive in style and available at an affordable price.We take pride in stating that our first publication GATE-ECE by RK Kanodia has been a great success last year, on all aspects. Everyone who got through, due to this book, has given excellent feedback. Reviews can be read at our website www.nodia.co.in. 2. Avoid Student exploitation: We are aware that setting a high MRP, giving high discounts to students & incentives to retailers, to sell a book is unethical and in a way exploits students as far as money is concerned. We respect the publishing field & do not want to employ gimmicks to increase our sales. The true appreciation of our work lies if the student can be pickup our book for its quality not because the retailer is promoting it in lieu of incentive. 3. Social Responsibility: To help improve the socio-economic conditions of the grass-root level with the earning from this endeavor. Rs.10, from every book sold, is contributed to the NGOs/Govt. Organizations working for the education of child labour. A Concern: Regret to infer that, survival has been difficult keeping in mind the ethics. Publishers, who claim to be the partners in the progress of students, use cheap tactics to sell their material to them. A publisher, famous for providing books on GATE, which are incidentally also erroneous & copied, has also imitated our book this year. They have gone to the extent this year and introduced a revised edition of their book on GATE on Elect. & Comm., which also includes new large number of Multiple Choice Questions [MCQ]. All the MCQ’s&their solutions have been copied from our book [GATE by RK Kanodia]. This is condemnable act of plagiarism. They are trying to restrict our book from reaching the students, by giving high incentives to retailers & distributors. They are using all possible unfair means of the publishing field, to make money and monetary exploit students, yet the book fails to reach the students. An Appeal: We would like to make this Appeal to you against plagiarism and exploitation, keeping in mind the interest of students & publishing field, to support us in our fight. Our company has been started with very few resources and but have large vision. The greatest challenge for us is to reach every part of India. We realize that educators are busy people in times of change and thus they are not able to rate the books given to them, to be able to suggest the same to the students. Thus students, who are dependent on such educators for the knowledge of books, are not able to use the resources available to the maximum. The restriction of erroneous and plagiarized work, in reaching the hands of students thus becomes a huge task. Therefore, we request and ask for your support against this condemnable act of plagiarism. NODIA & COMPANY 26 Paper-1