Page 1 EC? GATE Paper 2008 Q. 1 to 20 Carry One Mark Each 1. All the four entries of the 2×2 matrix 11 12 21 22 p p P p p ? ? = ? ? ? ? are nonzero, and one of its eigenvalues is zero. Which of the following statements is true? (A) 11 22 12 21 p p p p 1 - = (B) 11 22 12 21 p p p p 1 - = - (C) 11 22 12 21 p p p p 0 - = (D) 11 22 12 21 p p p p 0 + = 2. The system of linear equations 4x 2y 7 2x y 6 + = + = has (A) a unique solution (B) no solution (C) an infinite number of solutions (D) exactly two distinct solutions 3. The equation ( ) sin z 10has = (A) no real or complex solution (B) exactly two distinct complex solutions (C) a unique solution (D) an infinite number of complex solutions 4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + - (A) 2 (B) 1 (C) 0.5 (D) 0 5. Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x=0? (A) ( ) 3 sin x (B) ( ) 2 sin x (C) ( ) 3 cos x (D) ( ) 2 cos x 6. Which of the following is a solution to the differential equation ( ) ( ) dx t 3x t 0? dt + = (A) ( ) t x t 3e - = (B) ( ) 3t x t 2e - = (C) ( ) 2 3 x t t 2 = - (D) ( ) 2 x t 3t = 7. In the following graph, the number of trees (P) and the number of cut-sets (Q) are (A) P=2, Q=2 (B) P=2, Q=6 (C) P=4, Q=6 (D) P=4, Q=10 ( ) 4 ( ) 1 ( ) 2 ( ) 3 Page 2 EC? GATE Paper 2008 Q. 1 to 20 Carry One Mark Each 1. All the four entries of the 2×2 matrix 11 12 21 22 p p P p p ? ? = ? ? ? ? are nonzero, and one of its eigenvalues is zero. Which of the following statements is true? (A) 11 22 12 21 p p p p 1 - = (B) 11 22 12 21 p p p p 1 - = - (C) 11 22 12 21 p p p p 0 - = (D) 11 22 12 21 p p p p 0 + = 2. The system of linear equations 4x 2y 7 2x y 6 + = + = has (A) a unique solution (B) no solution (C) an infinite number of solutions (D) exactly two distinct solutions 3. The equation ( ) sin z 10has = (A) no real or complex solution (B) exactly two distinct complex solutions (C) a unique solution (D) an infinite number of complex solutions 4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + - (A) 2 (B) 1 (C) 0.5 (D) 0 5. Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x=0? (A) ( ) 3 sin x (B) ( ) 2 sin x (C) ( ) 3 cos x (D) ( ) 2 cos x 6. Which of the following is a solution to the differential equation ( ) ( ) dx t 3x t 0? dt + = (A) ( ) t x t 3e - = (B) ( ) 3t x t 2e - = (C) ( ) 2 3 x t t 2 = - (D) ( ) 2 x t 3t = 7. In the following graph, the number of trees (P) and the number of cut-sets (Q) are (A) P=2, Q=2 (B) P=2, Q=6 (C) P=4, Q=6 (D) P=4, Q=10 ( ) 4 ( ) 1 ( ) 2 ( ) 3 EC? GATE Paper 2008 8. In the following circuit, the switch S is closed at t=0. The rate of change of current ( ) di 0 dt + is given by (A) 0 (B) S S R I L (C) ( ) S S R R I L + (D) 8 9. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system? (A) ( ) ( ) ( ) y t x t 2 x t 4 = - + + (B) ( ) ( ) ( ) y t t 4 x t 1 = - + (C) ( ) ( ) ( ) y t t 4 x t 1 = + - (D) ( ) ( ) ( ) y t t 5 x t 5 = + + 10. The impulse response h(t) of a linear time-invariant continuous time system is described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß - where u(t) denotes the unit step function, and a and ß are real constants. This system is stable if (A) a is positive and ß is positive (B) a is negative and ß is negative (C) a is positive and ß is negative (D) a is negative and ß is positive 11. The pole-zero plot given below corresponds to a (A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter 12. Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems? S R ( ) i t L S R S I s j? O O X X Page 3 EC? GATE Paper 2008 Q. 1 to 20 Carry One Mark Each 1. All the four entries of the 2×2 matrix 11 12 21 22 p p P p p ? ? = ? ? ? ? are nonzero, and one of its eigenvalues is zero. Which of the following statements is true? (A) 11 22 12 21 p p p p 1 - = (B) 11 22 12 21 p p p p 1 - = - (C) 11 22 12 21 p p p p 0 - = (D) 11 22 12 21 p p p p 0 + = 2. The system of linear equations 4x 2y 7 2x y 6 + = + = has (A) a unique solution (B) no solution (C) an infinite number of solutions (D) exactly two distinct solutions 3. The equation ( ) sin z 10has = (A) no real or complex solution (B) exactly two distinct complex solutions (C) a unique solution (D) an infinite number of complex solutions 4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + - (A) 2 (B) 1 (C) 0.5 (D) 0 5. Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x=0? (A) ( ) 3 sin x (B) ( ) 2 sin x (C) ( ) 3 cos x (D) ( ) 2 cos x 6. Which of the following is a solution to the differential equation ( ) ( ) dx t 3x t 0? dt + = (A) ( ) t x t 3e - = (B) ( ) 3t x t 2e - = (C) ( ) 2 3 x t t 2 = - (D) ( ) 2 x t 3t = 7. In the following graph, the number of trees (P) and the number of cut-sets (Q) are (A) P=2, Q=2 (B) P=2, Q=6 (C) P=4, Q=6 (D) P=4, Q=10 ( ) 4 ( ) 1 ( ) 2 ( ) 3 EC? GATE Paper 2008 8. In the following circuit, the switch S is closed at t=0. The rate of change of current ( ) di 0 dt + is given by (A) 0 (B) S S R I L (C) ( ) S S R R I L + (D) 8 9. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system? (A) ( ) ( ) ( ) y t x t 2 x t 4 = - + + (B) ( ) ( ) ( ) y t t 4 x t 1 = - + (C) ( ) ( ) ( ) y t t 4 x t 1 = + - (D) ( ) ( ) ( ) y t t 5 x t 5 = + + 10. The impulse response h(t) of a linear time-invariant continuous time system is described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß - where u(t) denotes the unit step function, and a and ß are real constants. This system is stable if (A) a is positive and ß is positive (B) a is negative and ß is negative (C) a is positive and ß is negative (D) a is negative and ß is positive 11. The pole-zero plot given below corresponds to a (A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter 12. Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems? S R ( ) i t L S R S I s j? O O X X EC? GATE Paper 2008 (A) (B) (C) (D) 13. Which of the following is NOT associated with a p-n junction? (A) Junction capacitance (B) Charge Storage Capacitance (C) Depletion Capacitance (D) Channel Length Modulation 14. Which of the following is true? (A) A silicon wafer heavily doped with boron is a p + substrate (B) A silicon wafer lightly doped with boron is a p + substrate (C) A silicon wafer heavily doped with arsenic is a p + substrate (D) A silicon wafer lightly doped with arsenic is a p + substrate 15. For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is (A) 360º (B) 180º (C) 90º (D) 45º 16. For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of two of Maxwellâ€™s equations? (A) .E 0 B 0 ? = ? × = (B) .E 0 .B 0 ? = ? = (C) E 0 B 0 ? × = ? × = (D) E 0 .B 0 ? × = ? = s j? . . . . . . . . X X X X X X s j? · · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · s j? · · · · · · X X X . . . . X X X . . s j? X . X X X X X . . . . . . . . . . . Page 4 EC? GATE Paper 2008 Q. 1 to 20 Carry One Mark Each 1. All the four entries of the 2×2 matrix 11 12 21 22 p p P p p ? ? = ? ? ? ? are nonzero, and one of its eigenvalues is zero. Which of the following statements is true? (A) 11 22 12 21 p p p p 1 - = (B) 11 22 12 21 p p p p 1 - = - (C) 11 22 12 21 p p p p 0 - = (D) 11 22 12 21 p p p p 0 + = 2. The system of linear equations 4x 2y 7 2x y 6 + = + = has (A) a unique solution (B) no solution (C) an infinite number of solutions (D) exactly two distinct solutions 3. The equation ( ) sin z 10has = (A) no real or complex solution (B) exactly two distinct complex solutions (C) a unique solution (D) an infinite number of complex solutions 4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + - (A) 2 (B) 1 (C) 0.5 (D) 0 5. Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x=0? (A) ( ) 3 sin x (B) ( ) 2 sin x (C) ( ) 3 cos x (D) ( ) 2 cos x 6. Which of the following is a solution to the differential equation ( ) ( ) dx t 3x t 0? dt + = (A) ( ) t x t 3e - = (B) ( ) 3t x t 2e - = (C) ( ) 2 3 x t t 2 = - (D) ( ) 2 x t 3t = 7. In the following graph, the number of trees (P) and the number of cut-sets (Q) are (A) P=2, Q=2 (B) P=2, Q=6 (C) P=4, Q=6 (D) P=4, Q=10 ( ) 4 ( ) 1 ( ) 2 ( ) 3 EC? GATE Paper 2008 8. In the following circuit, the switch S is closed at t=0. The rate of change of current ( ) di 0 dt + is given by (A) 0 (B) S S R I L (C) ( ) S S R R I L + (D) 8 9. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system? (A) ( ) ( ) ( ) y t x t 2 x t 4 = - + + (B) ( ) ( ) ( ) y t t 4 x t 1 = - + (C) ( ) ( ) ( ) y t t 4 x t 1 = + - (D) ( ) ( ) ( ) y t t 5 x t 5 = + + 10. The impulse response h(t) of a linear time-invariant continuous time system is described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß - where u(t) denotes the unit step function, and a and ß are real constants. This system is stable if (A) a is positive and ß is positive (B) a is negative and ß is negative (C) a is positive and ß is negative (D) a is negative and ß is positive 11. The pole-zero plot given below corresponds to a (A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter 12. Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems? S R ( ) i t L S R S I s j? O O X X EC? GATE Paper 2008 (A) (B) (C) (D) 13. Which of the following is NOT associated with a p-n junction? (A) Junction capacitance (B) Charge Storage Capacitance (C) Depletion Capacitance (D) Channel Length Modulation 14. Which of the following is true? (A) A silicon wafer heavily doped with boron is a p + substrate (B) A silicon wafer lightly doped with boron is a p + substrate (C) A silicon wafer heavily doped with arsenic is a p + substrate (D) A silicon wafer lightly doped with arsenic is a p + substrate 15. For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is (A) 360º (B) 180º (C) 90º (D) 45º 16. For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of two of Maxwellâ€™s equations? (A) .E 0 B 0 ? = ? × = (B) .E 0 .B 0 ? = ? = (C) E 0 B 0 ? × = ? × = (D) E 0 .B 0 ? × = ? = s j? . . . . . . . . X X X X X X s j? · · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · s j? · · · · · · X X X . . . . X X X . . s j? X . X X X X X . . . . . . . . . . . EC? GATE Paper 2008 17. In the following limiter circuit, an input voltage i V 10sin100 t = p applied. Assume that the diode drop is 0.7V when it is forward biased. The Zener breakdown voltage is 6.8V. The maximum and minimum values of the output voltage respectively are (A) 6.1V, 0.7V - (B) 0.7V, 7.5V - (C) 7.5V, 0.7V - (D) 7.5V, 7.5V - 18. A silicon wafer has 100nm of oxide on it and is inserted in a furnace at a temperature above 1000ºC for further oxidation in dry oxygen. The oxidation rate (A) is independent of current oxide thickness and temperature (B) is independent of current oxide thickness but depends on temperature (C) slows down as the oxide grows (D) is zero as the existing oxide prevents further oxidation 19. The drain current of a MOSFET in saturation is given by ( ) 2 p GS r K V V = - l where K is a constant. The magnitude of the transconductance g m is (A) ( ) 2 GS T DS K V V V - (B) ( ) GS T 2K V V - (C) d GS DS I V V - (D) ( ) 2 GS T GS K V V V - 20. Consider the amplitude modulated (AM) signal C c m c A cos t 2cos t cos t. ? + ? ? For demodulating the signal using envelope detector, the minimum value of A c should be (A) 2 (B) 1 (C) 0.5 (D) 0 Q. 21 to 75 carry two Marks Each 21. The Thevenin equivalent impedance Z th between the nodes P and Q in the following circuit is (A) 1 (B) 1 1 s s + + (C) 1 2 s s + + (D) 2 2 s s 1 s 2s 1 + + + + 1K D1 0 D2 V 6.8V Z i V + - 1O 10V 1H 1 F 1O 1 A Q P Page 5 EC? GATE Paper 2008 Q. 1 to 20 Carry One Mark Each 1. All the four entries of the 2×2 matrix 11 12 21 22 p p P p p ? ? = ? ? ? ? are nonzero, and one of its eigenvalues is zero. Which of the following statements is true? (A) 11 22 12 21 p p p p 1 - = (B) 11 22 12 21 p p p p 1 - = - (C) 11 22 12 21 p p p p 0 - = (D) 11 22 12 21 p p p p 0 + = 2. The system of linear equations 4x 2y 7 2x y 6 + = + = has (A) a unique solution (B) no solution (C) an infinite number of solutions (D) exactly two distinct solutions 3. The equation ( ) sin z 10has = (A) no real or complex solution (B) exactly two distinct complex solutions (C) a unique solution (D) an infinite number of complex solutions 4. For real values of x, the minimum value of the function ( ) ( ) ( ) f x exp x exp x is = + - (A) 2 (B) 1 (C) 0.5 (D) 0 5. Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x=0? (A) ( ) 3 sin x (B) ( ) 2 sin x (C) ( ) 3 cos x (D) ( ) 2 cos x 6. Which of the following is a solution to the differential equation ( ) ( ) dx t 3x t 0? dt + = (A) ( ) t x t 3e - = (B) ( ) 3t x t 2e - = (C) ( ) 2 3 x t t 2 = - (D) ( ) 2 x t 3t = 7. In the following graph, the number of trees (P) and the number of cut-sets (Q) are (A) P=2, Q=2 (B) P=2, Q=6 (C) P=4, Q=6 (D) P=4, Q=10 ( ) 4 ( ) 1 ( ) 2 ( ) 3 EC? GATE Paper 2008 8. In the following circuit, the switch S is closed at t=0. The rate of change of current ( ) di 0 dt + is given by (A) 0 (B) S S R I L (C) ( ) S S R R I L + (D) 8 9. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system? (A) ( ) ( ) ( ) y t x t 2 x t 4 = - + + (B) ( ) ( ) ( ) y t t 4 x t 1 = - + (C) ( ) ( ) ( ) y t t 4 x t 1 = + - (D) ( ) ( ) ( ) y t t 5 x t 5 = + + 10. The impulse response h(t) of a linear time-invariant continuous time system is described by ( ) ( ) ( ) ( ) ( ) h t exp t u t exp t u t , = a + ß - where u(t) denotes the unit step function, and a and ß are real constants. This system is stable if (A) a is positive and ß is positive (B) a is negative and ß is negative (C) a is positive and ß is negative (D) a is negative and ß is positive 11. The pole-zero plot given below corresponds to a (A) Low pass filter (B) High pass filter (C) Band pass filter (D) Notch filter 12. Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems? S R ( ) i t L S R S I s j? O O X X EC? GATE Paper 2008 (A) (B) (C) (D) 13. Which of the following is NOT associated with a p-n junction? (A) Junction capacitance (B) Charge Storage Capacitance (C) Depletion Capacitance (D) Channel Length Modulation 14. Which of the following is true? (A) A silicon wafer heavily doped with boron is a p + substrate (B) A silicon wafer lightly doped with boron is a p + substrate (C) A silicon wafer heavily doped with arsenic is a p + substrate (D) A silicon wafer lightly doped with arsenic is a p + substrate 15. For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is (A) 360º (B) 180º (C) 90º (D) 45º 16. For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of two of Maxwellâ€™s equations? (A) .E 0 B 0 ? = ? × = (B) .E 0 .B 0 ? = ? = (C) E 0 B 0 ? × = ? × = (D) E 0 .B 0 ? × = ? = s j? . . . . . . . . X X X X X X s j? · · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · X X X · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · s j? · · · · · · X X X . . . . X X X . . s j? X . X X X X X . . . . . . . . . . . EC? GATE Paper 2008 17. In the following limiter circuit, an input voltage i V 10sin100 t = p applied. Assume that the diode drop is 0.7V when it is forward biased. The Zener breakdown voltage is 6.8V. The maximum and minimum values of the output voltage respectively are (A) 6.1V, 0.7V - (B) 0.7V, 7.5V - (C) 7.5V, 0.7V - (D) 7.5V, 7.5V - 18. A silicon wafer has 100nm of oxide on it and is inserted in a furnace at a temperature above 1000ºC for further oxidation in dry oxygen. The oxidation rate (A) is independent of current oxide thickness and temperature (B) is independent of current oxide thickness but depends on temperature (C) slows down as the oxide grows (D) is zero as the existing oxide prevents further oxidation 19. The drain current of a MOSFET in saturation is given by ( ) 2 p GS r K V V = - l where K is a constant. The magnitude of the transconductance g m is (A) ( ) 2 GS T DS K V V V - (B) ( ) GS T 2K V V - (C) d GS DS I V V - (D) ( ) 2 GS T GS K V V V - 20. Consider the amplitude modulated (AM) signal C c m c A cos t 2cos t cos t. ? + ? ? For demodulating the signal using envelope detector, the minimum value of A c should be (A) 2 (B) 1 (C) 0.5 (D) 0 Q. 21 to 75 carry two Marks Each 21. The Thevenin equivalent impedance Z th between the nodes P and Q in the following circuit is (A) 1 (B) 1 1 s s + + (C) 1 2 s s + + (D) 2 2 s s 1 s 2s 1 + + + + 1K D1 0 D2 V 6.8V Z i V + - 1O 10V 1H 1 F 1O 1 A Q P EC? GATE Paper 2008 22. The driving point impedance of the following network is given by ( ) 2 0.2s Z s . s 0.1s 2 = + + The component values are (A) L 5H, R 0.5 , C 0.1F = = O = (B) L 0.1H, R 0.5 , C 5F = = O = (C) L 5H, R 2 , C 0.1F = = O = (D) L 0.1H, R 2 , C 5F = = O = 23. The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The switches S1 and S2 are mechanically coupled and connected as follows ( ) ( ) ( ) ( ) ( ) For 2nT t 2n 1 T, n 0,1,2,... S1 to P1 and S2 to P2 For 2n 1 T t 2n 2 T, n 0,1,2,... S1 to Q1 and S2 to Q2 = < + = + = < + = Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function, the voltage V c (t) across the capacitor is given be (A) ( ) ( ) n n 0 1 tu t nT 8 = - - ? (B) ( ) ( ) ( ) n n 0 u t 2 1 u t nT 8 = + - - ? (C) ( ) ( ) ( ) ( ) n n 0 tu t 2 1 t nT u t nT 8 = + - - - ? (D) ( ) ( ) t 2nT t 2nT T n 0 0.5 e 0.5e 8 - - - - - = ? ? - + ? ? ? 24. The probability density function (PDF) of a random variable X is as shown below R ( ) Z s L O ( ) C V t + - 1A 1A 1F C 1O S2 S1 0.5O 1O Q1 P1 Q2 P2 1O 1 1 - 0 1 x PDFRead More

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