Page 1 GATE EC - 2000 + - + - - - + + + V 2 0V 2V 1V V 1 10V 4V 5V E=? SECTION â€“ A (75 marks) 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 In the circuit of Fig.P.11, the voltage v(t) is (a) at bt e e - (b) at bt e e + (c) at bt ae be - (d) at bt ae be + 1.2 In the circuit of Fig.P1.2, the value of the voltage source E is (a) -16 V (b) 4 V (c) -6V (d) 16 V 1.3 Given that ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 0 2 1 , , . 3 2 1 t s s L f t L f t h t f g t d s s s t t t + + ? ? ? ? = = = = - ? ? ? ? + + + ? ( ) L h t ? ? ? ? is (a) 2 1 3 s s + + (b) 1 3 s + (c) ( )( ) 2 2 1 2 3 2 1 s s s s s + + + + + + (d) None of the above 1.4 In the differential amplifier of Fig.P1.4, if the source resistance of the current source EE I is infinite, then the common-mode gain is (a) zero (b) infinite (c) indeterminate (d) 1 2 2 in in T V V V + + V(t) 1O 1O e at - 1H e bt R I EE R -V EE V CC V in1 V in2 Page 2 GATE EC - 2000 + - + - - - + + + V 2 0V 2V 1V V 1 10V 4V 5V E=? SECTION â€“ A (75 marks) 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 In the circuit of Fig.P.11, the voltage v(t) is (a) at bt e e - (b) at bt e e + (c) at bt ae be - (d) at bt ae be + 1.2 In the circuit of Fig.P1.2, the value of the voltage source E is (a) -16 V (b) 4 V (c) -6V (d) 16 V 1.3 Given that ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 0 2 1 , , . 3 2 1 t s s L f t L f t h t f g t d s s s t t t + + ? ? ? ? = = = = - ? ? ? ? + + + ? ( ) L h t ? ? ? ? is (a) 2 1 3 s s + + (b) 1 3 s + (c) ( )( ) 2 2 1 2 3 2 1 s s s s s + + + + + + (d) None of the above 1.4 In the differential amplifier of Fig.P1.4, if the source resistance of the current source EE I is infinite, then the common-mode gain is (a) zero (b) infinite (c) indeterminate (d) 1 2 2 in in T V V V + + V(t) 1O 1O e at - 1H e bt R I EE R -V EE V CC V in1 V in2 GATE EC - 2000 1.5 In the circuit of Fig.P.15, o V is (a) -1 V (b) 2 V (c) +1 V (d) +15 V 1.6 Introducing a resistor in the emitter of a common amplifier stabilizes the dc operating point against variations in (a) only the temperature (b) only the ß of the transistor (c) both temperature and ß (d) none of the above 1.7 The current gain of a bipolar transistor drops at high frequencies because of (a) transistor capacitances (b) high current effects in the base (c) parasitic inductive elements (d) the Early effect 1.8 An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The amplifier (a) will always be unstable at high frequencies (b) will be stable for all frequencies (c) may be unstable, depending on the feedback factor (d) will oscillate at low frequencies 1.9 If the op-amp in Fig.P.1.9, is ideal, then o v , is (a) zero (b) ( ) 1 2 sin V V t ? - (c) ( ) 1 2 sin V V t ? - + (d) ( ) 1 2 sin V V t ? + 1.10 The configuration of Fig.P.1.10 is a (a) precision integrator (b) Hartley oscillator (c) Butterworth highpass filter (d) Wien-bridge oscillator +15V + - -15V R R +1V V o + - V o C C C V 1 sin?t V 2 sin?t C R + - V o C R R 1 R 2 Page 3 GATE EC - 2000 + - + - - - + + + V 2 0V 2V 1V V 1 10V 4V 5V E=? SECTION â€“ A (75 marks) 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 In the circuit of Fig.P.11, the voltage v(t) is (a) at bt e e - (b) at bt e e + (c) at bt ae be - (d) at bt ae be + 1.2 In the circuit of Fig.P1.2, the value of the voltage source E is (a) -16 V (b) 4 V (c) -6V (d) 16 V 1.3 Given that ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 0 2 1 , , . 3 2 1 t s s L f t L f t h t f g t d s s s t t t + + ? ? ? ? = = = = - ? ? ? ? + + + ? ( ) L h t ? ? ? ? is (a) 2 1 3 s s + + (b) 1 3 s + (c) ( )( ) 2 2 1 2 3 2 1 s s s s s + + + + + + (d) None of the above 1.4 In the differential amplifier of Fig.P1.4, if the source resistance of the current source EE I is infinite, then the common-mode gain is (a) zero (b) infinite (c) indeterminate (d) 1 2 2 in in T V V V + + V(t) 1O 1O e at - 1H e bt R I EE R -V EE V CC V in1 V in2 GATE EC - 2000 1.5 In the circuit of Fig.P.15, o V is (a) -1 V (b) 2 V (c) +1 V (d) +15 V 1.6 Introducing a resistor in the emitter of a common amplifier stabilizes the dc operating point against variations in (a) only the temperature (b) only the ß of the transistor (c) both temperature and ß (d) none of the above 1.7 The current gain of a bipolar transistor drops at high frequencies because of (a) transistor capacitances (b) high current effects in the base (c) parasitic inductive elements (d) the Early effect 1.8 An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The amplifier (a) will always be unstable at high frequencies (b) will be stable for all frequencies (c) may be unstable, depending on the feedback factor (d) will oscillate at low frequencies 1.9 If the op-amp in Fig.P.1.9, is ideal, then o v , is (a) zero (b) ( ) 1 2 sin V V t ? - (c) ( ) 1 2 sin V V t ? - + (d) ( ) 1 2 sin V V t ? + 1.10 The configuration of Fig.P.1.10 is a (a) precision integrator (b) Hartley oscillator (c) Butterworth highpass filter (d) Wien-bridge oscillator +15V + - -15V R R +1V V o + - V o C C C V 1 sin?t V 2 sin?t C R + - V o C R R 1 R 2 GATE EC - 2000 1.11 Assume that the op-amp of Fig.P1.11 is ideal. If i v is a triangular wave, then o v will be (a) square wave (b) triangular wave (c) parabolic wave (d) sine wave 1.12 The Fourier Transform of the signal ( ) 2 3t x t e - = is of the following form, where A and B are constants: (a) Bf Ae - (b) Bf Ae - (c) 2 A B f + (d) Bf Ae - 1.13 A system with an input ( ) x t and output ( ) y t is described by the relation: ( ) ( ). y t tx t = This system is (a) linear and time-invariant (b) linear and time varying (c) non-linear and time-invariant (d) non-linear and time-varying 1.14 The amplitude modulated wave from ( ) ( ) 1 cos c a C s t A K m t t ? ? ? = + ? ? is fed to an ideal envelope detector. The maximum magnitude of ( ) 0 K m t is greater than 1. Which of the following could be the detector output? (a) ( ) c A m t (b) ( ) 2 2 1 c a A K m t ? ? + ? ? (c) ( ) 1 c a A K m t ? ? + ? ? (d) ( ) 2 1 c a A K m t ? ? + ? ? 1.15 An 8 bit successive approximation analog to digital converter has full scale reading of 2.55 V and its conversion time for an analog input of 1V is 20µs. The conversion for a 2V input will be (a) 10 µs (b) 20 µs (c) 40 µs (d) 50 µs 1.16 The number of hardware interrupts (which require an external signal to interrupt) present in an 8085 microprocessor are (a) 1 (b) 4 (c) 5 (d) 13 1.17 The most commonly used amplifier in sample and hold circuits is (a) a unity gain inverting amplifier (b) a unity gain non-inverting amplifier (c) an inverting amplifier with a gain of 10 (d) an inverting amplifier with a gain of 100 + - V o R C V o Page 4 GATE EC - 2000 + - + - - - + + + V 2 0V 2V 1V V 1 10V 4V 5V E=? SECTION â€“ A (75 marks) 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 In the circuit of Fig.P.11, the voltage v(t) is (a) at bt e e - (b) at bt e e + (c) at bt ae be - (d) at bt ae be + 1.2 In the circuit of Fig.P1.2, the value of the voltage source E is (a) -16 V (b) 4 V (c) -6V (d) 16 V 1.3 Given that ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 0 2 1 , , . 3 2 1 t s s L f t L f t h t f g t d s s s t t t + + ? ? ? ? = = = = - ? ? ? ? + + + ? ( ) L h t ? ? ? ? is (a) 2 1 3 s s + + (b) 1 3 s + (c) ( )( ) 2 2 1 2 3 2 1 s s s s s + + + + + + (d) None of the above 1.4 In the differential amplifier of Fig.P1.4, if the source resistance of the current source EE I is infinite, then the common-mode gain is (a) zero (b) infinite (c) indeterminate (d) 1 2 2 in in T V V V + + V(t) 1O 1O e at - 1H e bt R I EE R -V EE V CC V in1 V in2 GATE EC - 2000 1.5 In the circuit of Fig.P.15, o V is (a) -1 V (b) 2 V (c) +1 V (d) +15 V 1.6 Introducing a resistor in the emitter of a common amplifier stabilizes the dc operating point against variations in (a) only the temperature (b) only the ß of the transistor (c) both temperature and ß (d) none of the above 1.7 The current gain of a bipolar transistor drops at high frequencies because of (a) transistor capacitances (b) high current effects in the base (c) parasitic inductive elements (d) the Early effect 1.8 An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The amplifier (a) will always be unstable at high frequencies (b) will be stable for all frequencies (c) may be unstable, depending on the feedback factor (d) will oscillate at low frequencies 1.9 If the op-amp in Fig.P.1.9, is ideal, then o v , is (a) zero (b) ( ) 1 2 sin V V t ? - (c) ( ) 1 2 sin V V t ? - + (d) ( ) 1 2 sin V V t ? + 1.10 The configuration of Fig.P.1.10 is a (a) precision integrator (b) Hartley oscillator (c) Butterworth highpass filter (d) Wien-bridge oscillator +15V + - -15V R R +1V V o + - V o C C C V 1 sin?t V 2 sin?t C R + - V o C R R 1 R 2 GATE EC - 2000 1.11 Assume that the op-amp of Fig.P1.11 is ideal. If i v is a triangular wave, then o v will be (a) square wave (b) triangular wave (c) parabolic wave (d) sine wave 1.12 The Fourier Transform of the signal ( ) 2 3t x t e - = is of the following form, where A and B are constants: (a) Bf Ae - (b) Bf Ae - (c) 2 A B f + (d) Bf Ae - 1.13 A system with an input ( ) x t and output ( ) y t is described by the relation: ( ) ( ). y t tx t = This system is (a) linear and time-invariant (b) linear and time varying (c) non-linear and time-invariant (d) non-linear and time-varying 1.14 The amplitude modulated wave from ( ) ( ) 1 cos c a C s t A K m t t ? ? ? = + ? ? is fed to an ideal envelope detector. The maximum magnitude of ( ) 0 K m t is greater than 1. Which of the following could be the detector output? (a) ( ) c A m t (b) ( ) 2 2 1 c a A K m t ? ? + ? ? (c) ( ) 1 c a A K m t ? ? + ? ? (d) ( ) 2 1 c a A K m t ? ? + ? ? 1.15 An 8 bit successive approximation analog to digital converter has full scale reading of 2.55 V and its conversion time for an analog input of 1V is 20µs. The conversion for a 2V input will be (a) 10 µs (b) 20 µs (c) 40 µs (d) 50 µs 1.16 The number of hardware interrupts (which require an external signal to interrupt) present in an 8085 microprocessor are (a) 1 (b) 4 (c) 5 (d) 13 1.17 The most commonly used amplifier in sample and hold circuits is (a) a unity gain inverting amplifier (b) a unity gain non-inverting amplifier (c) an inverting amplifier with a gain of 10 (d) an inverting amplifier with a gain of 100 + - V o R C V o GATE EC - 2000 1.18 The number of comparators in a 4 bit flash ADC is (a) 4 (b) 5 (c) 15 (d) 16 1.19. For the logic circuit shown in Fig.P1.19, the required input condition (A,B,C) to make the output (X)=1 is (a) 1, 0, 1 (b) 0, 0, 1 (c) 1, 1, 1 (d) 0, 1, 1 1.20. In the 8085 microprocessor, the RST6 instruction transfers the program execution to the following location (a) 30 H (b) 24 H (c) 48 H (d) 60 H 1.21. The magnitudes of the open-circuit and short-circuit input impedances of a transmission line are 100O and 25O respectively. The characteristic impedance of the line is, (a) 25O (b) 50O (c) 75O (d) 100O 1.22. A TEM wave is incident normally upon a perfect conductor. The E and H fields at the boundary will be, respectively. (a) minimum and minimum (b) maximum and maximum (c) minimum and maximum (d) maximum and minimum 1.23. The frequency range for satellite communication is (a) 1 KHz to 100 KHz (b) 100 KHz to 10 KHz (c) 10 MHz to 30 MHz (d) 1 GHz to 30 GHz 1.24. If the diameter of a 2 ? dipole antenna is increased from to , 100 50 ? ? then its (a) bandwidth increases (b) bandwidth decreases (c) gain increases (d) gain decreases 1.25 The circuit of Fig.P1.25 represents a (a) low pass filter (b) high pass filter (c) band pass filter (d) band reject filter A B C x L 1 ~ R S V S C 2 C 1 L 2 R L V o Page 5 GATE EC - 2000 + - + - - - + + + V 2 0V 2V 1V V 1 10V 4V 5V E=? SECTION â€“ A (75 marks) 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the FIRST sheet of the answer book. 1.1 In the circuit of Fig.P.11, the voltage v(t) is (a) at bt e e - (b) at bt e e + (c) at bt ae be - (d) at bt ae be + 1.2 In the circuit of Fig.P1.2, the value of the voltage source E is (a) -16 V (b) 4 V (c) -6V (d) 16 V 1.3 Given that ( ) ( ) ( )( ) ( ) ( ) ( ) 2 2 0 2 1 , , . 3 2 1 t s s L f t L f t h t f g t d s s s t t t + + ? ? ? ? = = = = - ? ? ? ? + + + ? ( ) L h t ? ? ? ? is (a) 2 1 3 s s + + (b) 1 3 s + (c) ( )( ) 2 2 1 2 3 2 1 s s s s s + + + + + + (d) None of the above 1.4 In the differential amplifier of Fig.P1.4, if the source resistance of the current source EE I is infinite, then the common-mode gain is (a) zero (b) infinite (c) indeterminate (d) 1 2 2 in in T V V V + + V(t) 1O 1O e at - 1H e bt R I EE R -V EE V CC V in1 V in2 GATE EC - 2000 1.5 In the circuit of Fig.P.15, o V is (a) -1 V (b) 2 V (c) +1 V (d) +15 V 1.6 Introducing a resistor in the emitter of a common amplifier stabilizes the dc operating point against variations in (a) only the temperature (b) only the ß of the transistor (c) both temperature and ß (d) none of the above 1.7 The current gain of a bipolar transistor drops at high frequencies because of (a) transistor capacitances (b) high current effects in the base (c) parasitic inductive elements (d) the Early effect 1.8 An amplifier with resistive negative feedback has two left half-plane poles in its open-loop transfer function. The amplifier (a) will always be unstable at high frequencies (b) will be stable for all frequencies (c) may be unstable, depending on the feedback factor (d) will oscillate at low frequencies 1.9 If the op-amp in Fig.P.1.9, is ideal, then o v , is (a) zero (b) ( ) 1 2 sin V V t ? - (c) ( ) 1 2 sin V V t ? - + (d) ( ) 1 2 sin V V t ? + 1.10 The configuration of Fig.P.1.10 is a (a) precision integrator (b) Hartley oscillator (c) Butterworth highpass filter (d) Wien-bridge oscillator +15V + - -15V R R +1V V o + - V o C C C V 1 sin?t V 2 sin?t C R + - V o C R R 1 R 2 GATE EC - 2000 1.11 Assume that the op-amp of Fig.P1.11 is ideal. If i v is a triangular wave, then o v will be (a) square wave (b) triangular wave (c) parabolic wave (d) sine wave 1.12 The Fourier Transform of the signal ( ) 2 3t x t e - = is of the following form, where A and B are constants: (a) Bf Ae - (b) Bf Ae - (c) 2 A B f + (d) Bf Ae - 1.13 A system with an input ( ) x t and output ( ) y t is described by the relation: ( ) ( ). y t tx t = This system is (a) linear and time-invariant (b) linear and time varying (c) non-linear and time-invariant (d) non-linear and time-varying 1.14 The amplitude modulated wave from ( ) ( ) 1 cos c a C s t A K m t t ? ? ? = + ? ? is fed to an ideal envelope detector. The maximum magnitude of ( ) 0 K m t is greater than 1. Which of the following could be the detector output? (a) ( ) c A m t (b) ( ) 2 2 1 c a A K m t ? ? + ? ? (c) ( ) 1 c a A K m t ? ? + ? ? (d) ( ) 2 1 c a A K m t ? ? + ? ? 1.15 An 8 bit successive approximation analog to digital converter has full scale reading of 2.55 V and its conversion time for an analog input of 1V is 20µs. The conversion for a 2V input will be (a) 10 µs (b) 20 µs (c) 40 µs (d) 50 µs 1.16 The number of hardware interrupts (which require an external signal to interrupt) present in an 8085 microprocessor are (a) 1 (b) 4 (c) 5 (d) 13 1.17 The most commonly used amplifier in sample and hold circuits is (a) a unity gain inverting amplifier (b) a unity gain non-inverting amplifier (c) an inverting amplifier with a gain of 10 (d) an inverting amplifier with a gain of 100 + - V o R C V o GATE EC - 2000 1.18 The number of comparators in a 4 bit flash ADC is (a) 4 (b) 5 (c) 15 (d) 16 1.19. For the logic circuit shown in Fig.P1.19, the required input condition (A,B,C) to make the output (X)=1 is (a) 1, 0, 1 (b) 0, 0, 1 (c) 1, 1, 1 (d) 0, 1, 1 1.20. In the 8085 microprocessor, the RST6 instruction transfers the program execution to the following location (a) 30 H (b) 24 H (c) 48 H (d) 60 H 1.21. The magnitudes of the open-circuit and short-circuit input impedances of a transmission line are 100O and 25O respectively. The characteristic impedance of the line is, (a) 25O (b) 50O (c) 75O (d) 100O 1.22. A TEM wave is incident normally upon a perfect conductor. The E and H fields at the boundary will be, respectively. (a) minimum and minimum (b) maximum and maximum (c) minimum and maximum (d) maximum and minimum 1.23. The frequency range for satellite communication is (a) 1 KHz to 100 KHz (b) 100 KHz to 10 KHz (c) 10 MHz to 30 MHz (d) 1 GHz to 30 GHz 1.24. If the diameter of a 2 ? dipole antenna is increased from to , 100 50 ? ? then its (a) bandwidth increases (b) bandwidth decreases (c) gain increases (d) gain decreases 1.25 The circuit of Fig.P1.25 represents a (a) low pass filter (b) high pass filter (c) band pass filter (d) band reject filter A B C x L 1 ~ R S V S C 2 C 1 L 2 R L V o GATE EC - 2000 2. This question consists of TWENTY-FIVE sub-questions (2.1 â€“ 2.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answers in the boxes corresponding to the questions only on the SECOND sheet of the answer book. 2.1 The eigen values of the matrix 2 1 0 0 0 3 0 0 0 0 2 0 0 0 1 4 - ? ? ? ? ? ? ? ? - ? ? - ? ? ? ? are (a) 2, -2, 1, -1 (b) 2, 3, -2, 4 (c) 2, 3, 1, 4 (d) None of the above 2.2. Use the data of Fig.2(a). The current i in the circuit of Fig.(b) is (a) -2A (b) 2A (c) -4A (d) +4A 2.3. For the circuit in Fig.P2.3, the voltage o v is (a) 2V (b) 1V (c) -1V (d) None of the above 2.4. A linear time invariant system has an impulse response 2 , 0 t e t > . If the initial conditions are zero and the input is 3 , t e the output for t > 0 is (a) 3 2 t t e e - (b) 5t e (c) 3 2 t t e e + (d) None of the above 2.5. In the circuit of Fig.P2.5, assume that the transistor is in active region. It has a large ß and its base-emitter voltage is 0.7V. The value of c I is (a) Indeterminate since c R is not given (b) 1 mA (c) 5 mA (d) 10 mA 10V + R 2 R 1 R 3 R 4 2A 20V + R 2 R 1 R 3 R 4 I=? v o 2O 2O 4V + - - + 2V 2O - + 430O 15V R C 10kO I C 5kORead More

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