Page 1 GATE EC - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The voltage e 0 in figure 1.1 is (a) 2V (b) 4 3 V (c) 4V (d) 8V 1.2. If each branch of a Delta circuit has impedance 3 , Z then each branch of the equivalent Wye circuit has impedance. (a) 3 Z (b) 3Z (c) 3 3Z (d) 3 Z 1.3. The transfer function of a system is given by ( ) ( ) 2 1 . 2 H s s s = - The impulse response of the system is: (* denotes convolution, and U(t) is unit step function) (a) (t 2 * e -2t )U(t) (b) (t * e 2t )U(t) (c) (te -2 t)U(t) (d) (te -2t )U(t) 1.4. The admittance parameter Y 12 in the 2-port network in Figure 1.4 is (a) -0.2 mho (b) 0.1 mho (c) -0.05 mho (d) 0.05 mho 1.5. The region of convergence of the z-transform of a unit step function is (a) 1 z > (b) 1 z < (c) (Real part of z) > 0 (d) (Real part of z) < 0 4O 2O 4O 12V 2O e O + - 20O 10O 5O E 1 I 1 - E 2 I 2 Page 2 GATE EC - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The voltage e 0 in figure 1.1 is (a) 2V (b) 4 3 V (c) 4V (d) 8V 1.2. If each branch of a Delta circuit has impedance 3 , Z then each branch of the equivalent Wye circuit has impedance. (a) 3 Z (b) 3Z (c) 3 3Z (d) 3 Z 1.3. The transfer function of a system is given by ( ) ( ) 2 1 . 2 H s s s = - The impulse response of the system is: (* denotes convolution, and U(t) is unit step function) (a) (t 2 * e -2t )U(t) (b) (t * e 2t )U(t) (c) (te -2 t)U(t) (d) (te -2t )U(t) 1.4. The admittance parameter Y 12 in the 2-port network in Figure 1.4 is (a) -0.2 mho (b) 0.1 mho (c) -0.05 mho (d) 0.05 mho 1.5. The region of convergence of the z-transform of a unit step function is (a) 1 z > (b) 1 z < (c) (Real part of z) > 0 (d) (Real part of z) < 0 4O 2O 4O 12V 2O e O + - 20O 10O 5O E 1 I 1 - E 2 I 2 GATE EC - 2001 1.6. The current gain of a BJT is (a) g m r 0 (b) m o g r (c) g m r p (d) m g r p 1.7. MOSFET can be used as a (a) current controlled capacitor (b) voltage controlled capacitor (c) current controlled inductor (d) voltage controlled inductor 1.8. The effective channel length of a MOSFET in saturation decreases with increase in (a) gate voltage (b) drain voltage (c) source voltage (d) body voltage 1.9. The ideal OP-AMP has the following characteristics. (a) 0 , , 0 i R A R = 8 = 8 = (b) 0 0, , 0 i R A R = = 8 = (c) 0 , , i R A R = 8 = 8 = 8 (d) 0 0, , i R A R = = 8 = 8 1.10. The 2’s complement representation of –17 is (a) 01110 (b) 01111 (c) 11110 (d) 10001 1.11. Consider the following two statements: Statement 1: A stable multi-vibrator can be used for generating square wave. Statement 2: B stable multi-vibrator can be used for storing binary information. (a) Only statement 1 is correct (b) Only statement 2 is correct (c) Both the statements 1 and 2 are correct (d) Both the statements 1 and 2 are incorrect 1.12. For the ring oscillator shown in Figure 1.12, the propagation delay of each inverter is 100 pico second. What is the fundamental frequency of the oscillator output? (a) 10 MHz (b) 100 MHz (c) 1 GHz (d) 2 GHz 1.13. An 8085 microprocessor based system uses a 4K × 8-bit RAM whose starting address is AA00. The address of the last byte in this RAM is (a) 0FFFH (b) 1000 H (c) B9FF H (d) BA00 H V 0 Page 3 GATE EC - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The voltage e 0 in figure 1.1 is (a) 2V (b) 4 3 V (c) 4V (d) 8V 1.2. If each branch of a Delta circuit has impedance 3 , Z then each branch of the equivalent Wye circuit has impedance. (a) 3 Z (b) 3Z (c) 3 3Z (d) 3 Z 1.3. The transfer function of a system is given by ( ) ( ) 2 1 . 2 H s s s = - The impulse response of the system is: (* denotes convolution, and U(t) is unit step function) (a) (t 2 * e -2t )U(t) (b) (t * e 2t )U(t) (c) (te -2 t)U(t) (d) (te -2t )U(t) 1.4. The admittance parameter Y 12 in the 2-port network in Figure 1.4 is (a) -0.2 mho (b) 0.1 mho (c) -0.05 mho (d) 0.05 mho 1.5. The region of convergence of the z-transform of a unit step function is (a) 1 z > (b) 1 z < (c) (Real part of z) > 0 (d) (Real part of z) < 0 4O 2O 4O 12V 2O e O + - 20O 10O 5O E 1 I 1 - E 2 I 2 GATE EC - 2001 1.6. The current gain of a BJT is (a) g m r 0 (b) m o g r (c) g m r p (d) m g r p 1.7. MOSFET can be used as a (a) current controlled capacitor (b) voltage controlled capacitor (c) current controlled inductor (d) voltage controlled inductor 1.8. The effective channel length of a MOSFET in saturation decreases with increase in (a) gate voltage (b) drain voltage (c) source voltage (d) body voltage 1.9. The ideal OP-AMP has the following characteristics. (a) 0 , , 0 i R A R = 8 = 8 = (b) 0 0, , 0 i R A R = = 8 = (c) 0 , , i R A R = 8 = 8 = 8 (d) 0 0, , i R A R = = 8 = 8 1.10. The 2’s complement representation of –17 is (a) 01110 (b) 01111 (c) 11110 (d) 10001 1.11. Consider the following two statements: Statement 1: A stable multi-vibrator can be used for generating square wave. Statement 2: B stable multi-vibrator can be used for storing binary information. (a) Only statement 1 is correct (b) Only statement 2 is correct (c) Both the statements 1 and 2 are correct (d) Both the statements 1 and 2 are incorrect 1.12. For the ring oscillator shown in Figure 1.12, the propagation delay of each inverter is 100 pico second. What is the fundamental frequency of the oscillator output? (a) 10 MHz (b) 100 MHz (c) 1 GHz (d) 2 GHz 1.13. An 8085 microprocessor based system uses a 4K × 8-bit RAM whose starting address is AA00. The address of the last byte in this RAM is (a) 0FFFH (b) 1000 H (c) B9FF H (d) BA00 H V 0 GATE EC - 2001 s x x j? K=0 K=0 K=5 8 K K=1 -3 -2 K=8 -1 1.14. The equivalent of the block diagram in Figure 1.14 is given in (a) (b) (c) (d) 15. If the characteristic equation of a closed-loop system is 2 2 2 0 s s + + = , then the system is (a) over damped (b) critically damped (c) underdamped (d) undamped 1.16. The root-locus diagram for a closed loop feedback system is shown in Figure 1.16. The system is overdamped. (a) only if 0 =K = 1 (b) only if 1 < K < 5 (c) only if K > 5 (d) if 0 =K < 1 or K > 5 E F G 1 G 2 H C E F G 1 H/G 2 C E F G 1G 2 HG 2 C E F G 1 HG 2 C E F G 1G 2 H/G 2 C Page 4 GATE EC - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The voltage e 0 in figure 1.1 is (a) 2V (b) 4 3 V (c) 4V (d) 8V 1.2. If each branch of a Delta circuit has impedance 3 , Z then each branch of the equivalent Wye circuit has impedance. (a) 3 Z (b) 3Z (c) 3 3Z (d) 3 Z 1.3. The transfer function of a system is given by ( ) ( ) 2 1 . 2 H s s s = - The impulse response of the system is: (* denotes convolution, and U(t) is unit step function) (a) (t 2 * e -2t )U(t) (b) (t * e 2t )U(t) (c) (te -2 t)U(t) (d) (te -2t )U(t) 1.4. The admittance parameter Y 12 in the 2-port network in Figure 1.4 is (a) -0.2 mho (b) 0.1 mho (c) -0.05 mho (d) 0.05 mho 1.5. The region of convergence of the z-transform of a unit step function is (a) 1 z > (b) 1 z < (c) (Real part of z) > 0 (d) (Real part of z) < 0 4O 2O 4O 12V 2O e O + - 20O 10O 5O E 1 I 1 - E 2 I 2 GATE EC - 2001 1.6. The current gain of a BJT is (a) g m r 0 (b) m o g r (c) g m r p (d) m g r p 1.7. MOSFET can be used as a (a) current controlled capacitor (b) voltage controlled capacitor (c) current controlled inductor (d) voltage controlled inductor 1.8. The effective channel length of a MOSFET in saturation decreases with increase in (a) gate voltage (b) drain voltage (c) source voltage (d) body voltage 1.9. The ideal OP-AMP has the following characteristics. (a) 0 , , 0 i R A R = 8 = 8 = (b) 0 0, , 0 i R A R = = 8 = (c) 0 , , i R A R = 8 = 8 = 8 (d) 0 0, , i R A R = = 8 = 8 1.10. The 2’s complement representation of –17 is (a) 01110 (b) 01111 (c) 11110 (d) 10001 1.11. Consider the following two statements: Statement 1: A stable multi-vibrator can be used for generating square wave. Statement 2: B stable multi-vibrator can be used for storing binary information. (a) Only statement 1 is correct (b) Only statement 2 is correct (c) Both the statements 1 and 2 are correct (d) Both the statements 1 and 2 are incorrect 1.12. For the ring oscillator shown in Figure 1.12, the propagation delay of each inverter is 100 pico second. What is the fundamental frequency of the oscillator output? (a) 10 MHz (b) 100 MHz (c) 1 GHz (d) 2 GHz 1.13. An 8085 microprocessor based system uses a 4K × 8-bit RAM whose starting address is AA00. The address of the last byte in this RAM is (a) 0FFFH (b) 1000 H (c) B9FF H (d) BA00 H V 0 GATE EC - 2001 s x x j? K=0 K=0 K=5 8 K K=1 -3 -2 K=8 -1 1.14. The equivalent of the block diagram in Figure 1.14 is given in (a) (b) (c) (d) 15. If the characteristic equation of a closed-loop system is 2 2 2 0 s s + + = , then the system is (a) over damped (b) critically damped (c) underdamped (d) undamped 1.16. The root-locus diagram for a closed loop feedback system is shown in Figure 1.16. The system is overdamped. (a) only if 0 =K = 1 (b) only if 1 < K < 5 (c) only if K > 5 (d) if 0 =K < 1 or K > 5 E F G 1 G 2 H C E F G 1 H/G 2 C E F G 1G 2 HG 2 C E F G 1 HG 2 C E F G 1G 2 H/G 2 C GATE EC - 2001 1.17. The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure 1.17 if G(s) has no pole in the right half of s- plane, the number of roots of the system characteristic equation in the right half of s-plane is (a) 0 (b) 1 (c) 2 (d) 3 1.18. Let d(t) denote the delta function. The value of the integral ( ) 3 cos 2 t t dt d 8 -8 ? ? ? ? ? ? ? is (a) 1 (b) -1 (c) 0 (d) 2 p 1.19. A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through (a) an RC filter (b) an envelope detector (c) a PLL (d) an ideal low-pass filter with appropriate bandwidth 1.20. The PDF of a Gaussian random variable X is given by ( ) ( ) 2 4 18 1 3 2 x x P x e p - - = . The probability of the event {X = 4} is (a) 1 2 (b) 1 3 2p (c) 0 (d) 1 4 1.21. If a signal f(t) has energy E, the energy of the signal f(2t) is equal to (a) E (b) 2 E (c) 2E (d) 4E 1.22. A transmission line is distortion-less if (a) 1 RL GC = (b) RL = GC (c) LG = RC (d) RG = LC -1 I m(s) G(s)-Plane R e(s) Page 5 GATE EC - 2001 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 The voltage e 0 in figure 1.1 is (a) 2V (b) 4 3 V (c) 4V (d) 8V 1.2. If each branch of a Delta circuit has impedance 3 , Z then each branch of the equivalent Wye circuit has impedance. (a) 3 Z (b) 3Z (c) 3 3Z (d) 3 Z 1.3. The transfer function of a system is given by ( ) ( ) 2 1 . 2 H s s s = - The impulse response of the system is: (* denotes convolution, and U(t) is unit step function) (a) (t 2 * e -2t )U(t) (b) (t * e 2t )U(t) (c) (te -2 t)U(t) (d) (te -2t )U(t) 1.4. The admittance parameter Y 12 in the 2-port network in Figure 1.4 is (a) -0.2 mho (b) 0.1 mho (c) -0.05 mho (d) 0.05 mho 1.5. The region of convergence of the z-transform of a unit step function is (a) 1 z > (b) 1 z < (c) (Real part of z) > 0 (d) (Real part of z) < 0 4O 2O 4O 12V 2O e O + - 20O 10O 5O E 1 I 1 - E 2 I 2 GATE EC - 2001 1.6. The current gain of a BJT is (a) g m r 0 (b) m o g r (c) g m r p (d) m g r p 1.7. MOSFET can be used as a (a) current controlled capacitor (b) voltage controlled capacitor (c) current controlled inductor (d) voltage controlled inductor 1.8. The effective channel length of a MOSFET in saturation decreases with increase in (a) gate voltage (b) drain voltage (c) source voltage (d) body voltage 1.9. The ideal OP-AMP has the following characteristics. (a) 0 , , 0 i R A R = 8 = 8 = (b) 0 0, , 0 i R A R = = 8 = (c) 0 , , i R A R = 8 = 8 = 8 (d) 0 0, , i R A R = = 8 = 8 1.10. The 2’s complement representation of –17 is (a) 01110 (b) 01111 (c) 11110 (d) 10001 1.11. Consider the following two statements: Statement 1: A stable multi-vibrator can be used for generating square wave. Statement 2: B stable multi-vibrator can be used for storing binary information. (a) Only statement 1 is correct (b) Only statement 2 is correct (c) Both the statements 1 and 2 are correct (d) Both the statements 1 and 2 are incorrect 1.12. For the ring oscillator shown in Figure 1.12, the propagation delay of each inverter is 100 pico second. What is the fundamental frequency of the oscillator output? (a) 10 MHz (b) 100 MHz (c) 1 GHz (d) 2 GHz 1.13. An 8085 microprocessor based system uses a 4K × 8-bit RAM whose starting address is AA00. The address of the last byte in this RAM is (a) 0FFFH (b) 1000 H (c) B9FF H (d) BA00 H V 0 GATE EC - 2001 s x x j? K=0 K=0 K=5 8 K K=1 -3 -2 K=8 -1 1.14. The equivalent of the block diagram in Figure 1.14 is given in (a) (b) (c) (d) 15. If the characteristic equation of a closed-loop system is 2 2 2 0 s s + + = , then the system is (a) over damped (b) critically damped (c) underdamped (d) undamped 1.16. The root-locus diagram for a closed loop feedback system is shown in Figure 1.16. The system is overdamped. (a) only if 0 =K = 1 (b) only if 1 < K < 5 (c) only if K > 5 (d) if 0 =K < 1 or K > 5 E F G 1 G 2 H C E F G 1 H/G 2 C E F G 1G 2 HG 2 C E F G 1 HG 2 C E F G 1G 2 H/G 2 C GATE EC - 2001 1.17. The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure 1.17 if G(s) has no pole in the right half of s- plane, the number of roots of the system characteristic equation in the right half of s-plane is (a) 0 (b) 1 (c) 2 (d) 3 1.18. Let d(t) denote the delta function. The value of the integral ( ) 3 cos 2 t t dt d 8 -8 ? ? ? ? ? ? ? is (a) 1 (b) -1 (c) 0 (d) 2 p 1.19. A band limited signal is sampled at the Nyquist rate. The signal can be recovered by passing the samples through (a) an RC filter (b) an envelope detector (c) a PLL (d) an ideal low-pass filter with appropriate bandwidth 1.20. The PDF of a Gaussian random variable X is given by ( ) ( ) 2 4 18 1 3 2 x x P x e p - - = . The probability of the event {X = 4} is (a) 1 2 (b) 1 3 2p (c) 0 (d) 1 4 1.21. If a signal f(t) has energy E, the energy of the signal f(2t) is equal to (a) E (b) 2 E (c) 2E (d) 4E 1.22. A transmission line is distortion-less if (a) 1 RL GC = (b) RL = GC (c) LG = RC (d) RG = LC -1 I m(s) G(s)-Plane R e(s) GATE EC - 2001 1.23. If a plane electromagnetic wave satisfies the equation 2 2 2 2 2 , x x E E c x t ? ? = ? ? the wave propagates in the (a) x-direction (b) z-direction (c) y-direction (d) xy plane at an angle of 45° between the x and z directions 1.24. The phase velocity of waves propagating in a hollow metal waveguide is (a) greater than the velocity of light in free space. (b) less than the velocity of light in free space. (c) equal to the velocity of light in free space. (d) equal to the group velocity. 1.25. The dominant mode in a rectangular waveguide is TE 10 , because this mode has (a) no attenuation (b) no cut-off (c) no magnetic field component (d) the highest cut-off wavelength 2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks 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 answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 2.1 The voltage e 0 in figure 2.1 is (a) 48 V (b) 24 V (c) 36 V (d) 28 V 2.2. In figure 2.2, the value of the load resistor R which maximizes the power delivered to it is (a) 14.14O (b) 10O (c) 200O (d) 28.28O 10O 8A 2O e 0 16V 6O 12O + - R 1H 10O ~ E mcos10tRead More

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