Page 1 GATE EE - 2002 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V c (t), across the capacitor is given by (a) 5t (b) 5u(t) - C (c) 5 t C (d) ( ) 5u t C 1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is (a) ( ) ( ) ( ) 2 8 1 1 sin sin 3 sin 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (b) ( ) ( ) ( ) 2 8 1 1 sin cos 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K (c) ( ) ( ) ( ) 2 8 1 1 cos cos 3 cos 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (d) ( ) ( ) ( ) 2 8 1 1 cos sin 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K 1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by (a) B – N + 1 (b) B + N (c) N – B + 1 (d) N – 2B -1 1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode? (a) A circle of unit radius (b) An ellipse (c) A parabola (d) A straight line inclined at 45° with respect to the x-axis -1 0 f(t) 1 2 3 1 -1 Page 2 GATE EE - 2002 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V c (t), across the capacitor is given by (a) 5t (b) 5u(t) - C (c) 5 t C (d) ( ) 5u t C 1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is (a) ( ) ( ) ( ) 2 8 1 1 sin sin 3 sin 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (b) ( ) ( ) ( ) 2 8 1 1 sin cos 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K (c) ( ) ( ) ( ) 2 8 1 1 cos cos 3 cos 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (d) ( ) ( ) ( ) 2 8 1 1 cos sin 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K 1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by (a) B – N + 1 (b) B + N (c) N – B + 1 (d) N – 2B -1 1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode? (a) A circle of unit radius (b) An ellipse (c) A parabola (d) A straight line inclined at 45° with respect to the x-axis -1 0 f(t) 1 2 3 1 -1 GATE EE - 2002 1.5 Given a vector field , F r the divergence theorem states that (a) . . s v F dS FdV = ? ? ? r r ur r (b) . s v F dS FdV = ?× ? ? r r ur r (c) . s v F dS FdV × = ? ? ? r r ur r (d) . s v F dS FdV × = ? ? ? r r ur r 1.6 If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply? (a) reduces (b) increases (c) remains the same (d) increase or reduces depending upon the rotor resistance 1.7 A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve of Fig.1.7? (a) Curve A (b) Curve B (c) Curve C (d) Curve D 1.8 A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal? (a) Voltage induced across the low voltage winding (b) Core flux (c) Load current (d) Current drawn from the source 1.9 A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in Fig.1.9. The reading of the voltmeter, V, will be (a) 0 V (b) 400 V (c) 600 V (d) 800 V C B A D Torque Speed 400V 400:200:200 ~ V 50 Hz Page 3 GATE EE - 2002 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V c (t), across the capacitor is given by (a) 5t (b) 5u(t) - C (c) 5 t C (d) ( ) 5u t C 1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is (a) ( ) ( ) ( ) 2 8 1 1 sin sin 3 sin 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (b) ( ) ( ) ( ) 2 8 1 1 sin cos 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K (c) ( ) ( ) ( ) 2 8 1 1 cos cos 3 cos 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (d) ( ) ( ) ( ) 2 8 1 1 cos sin 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K 1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by (a) B – N + 1 (b) B + N (c) N – B + 1 (d) N – 2B -1 1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode? (a) A circle of unit radius (b) An ellipse (c) A parabola (d) A straight line inclined at 45° with respect to the x-axis -1 0 f(t) 1 2 3 1 -1 GATE EE - 2002 1.5 Given a vector field , F r the divergence theorem states that (a) . . s v F dS FdV = ? ? ? r r ur r (b) . s v F dS FdV = ?× ? ? r r ur r (c) . s v F dS FdV × = ? ? ? r r ur r (d) . s v F dS FdV × = ? ? ? r r ur r 1.6 If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply? (a) reduces (b) increases (c) remains the same (d) increase or reduces depending upon the rotor resistance 1.7 A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve of Fig.1.7? (a) Curve A (b) Curve B (c) Curve C (d) Curve D 1.8 A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal? (a) Voltage induced across the low voltage winding (b) Core flux (c) Load current (d) Current drawn from the source 1.9 A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in Fig.1.9. The reading of the voltmeter, V, will be (a) 0 V (b) 400 V (c) 600 V (d) 800 V C B A D Torque Speed 400V 400:200:200 ~ V 50 Hz GATE EE - 2002 1.10 The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in Fig.1.10 is 10 kHz. The frequency of the signal available at Q is (a) 10 kHz (b) 2.5 kHz (c) 20 kHz (d) 5 kHz 1.11 The forward resistance of the diode shown in Fig.1.11 is 5O and the remaining parameters are same as those of an ideal diode. The dc component of the source current is (a) 50 Vm p (b) 50 2 Vm p (c) 100 2 Vm p (d) 2 50 Vm p 1.12 The cut-in voltage of both Zener diode D z and diode D shown in Fig.1.12 is 0.7 V, while break down voltage of D z is 3.3 V and reverse breakdown voltage of D is 50 V. the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage (V 0 ) are (a) 3.3 V in the positive half cycle and 1.4 V in the negative half cycle (b) 4 V in the positive half cycle and 5 V in the negative half cycle (c) 3.3 V in both positive and negative half cycles (d) 4 V in both positive and negative half cycles 1.13 The line-to-line input voltage to the 3 phase, 50 Hz, ac circuit shown in Fig.1.13 is 100 V rms. Assuming that the phase sequence is RYB, the wattmeters would read. (a) W 1 = 886 W and W 2 = 886 W (b) W 1 = 500 W and W 2 = 500 W (c) W 1 = 0 W and W 2 = 1000 W (d) W 1 = 250 W and W 2 = 750 W D Q Q FF0 CLK 45O ~ V msin(?t) ?=314 rad/s 1kO ~ 10sin(?t) ?=314 rad/s D D Z V O I W 2 5?60°O 5?60°O 5?60°O R Y B W 1 Page 4 GATE EE - 2002 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V c (t), across the capacitor is given by (a) 5t (b) 5u(t) - C (c) 5 t C (d) ( ) 5u t C 1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is (a) ( ) ( ) ( ) 2 8 1 1 sin sin 3 sin 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (b) ( ) ( ) ( ) 2 8 1 1 sin cos 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K (c) ( ) ( ) ( ) 2 8 1 1 cos cos 3 cos 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (d) ( ) ( ) ( ) 2 8 1 1 cos sin 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K 1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by (a) B – N + 1 (b) B + N (c) N – B + 1 (d) N – 2B -1 1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode? (a) A circle of unit radius (b) An ellipse (c) A parabola (d) A straight line inclined at 45° with respect to the x-axis -1 0 f(t) 1 2 3 1 -1 GATE EE - 2002 1.5 Given a vector field , F r the divergence theorem states that (a) . . s v F dS FdV = ? ? ? r r ur r (b) . s v F dS FdV = ?× ? ? r r ur r (c) . s v F dS FdV × = ? ? ? r r ur r (d) . s v F dS FdV × = ? ? ? r r ur r 1.6 If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply? (a) reduces (b) increases (c) remains the same (d) increase or reduces depending upon the rotor resistance 1.7 A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve of Fig.1.7? (a) Curve A (b) Curve B (c) Curve C (d) Curve D 1.8 A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal? (a) Voltage induced across the low voltage winding (b) Core flux (c) Load current (d) Current drawn from the source 1.9 A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in Fig.1.9. The reading of the voltmeter, V, will be (a) 0 V (b) 400 V (c) 600 V (d) 800 V C B A D Torque Speed 400V 400:200:200 ~ V 50 Hz GATE EE - 2002 1.10 The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in Fig.1.10 is 10 kHz. The frequency of the signal available at Q is (a) 10 kHz (b) 2.5 kHz (c) 20 kHz (d) 5 kHz 1.11 The forward resistance of the diode shown in Fig.1.11 is 5O and the remaining parameters are same as those of an ideal diode. The dc component of the source current is (a) 50 Vm p (b) 50 2 Vm p (c) 100 2 Vm p (d) 2 50 Vm p 1.12 The cut-in voltage of both Zener diode D z and diode D shown in Fig.1.12 is 0.7 V, while break down voltage of D z is 3.3 V and reverse breakdown voltage of D is 50 V. the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage (V 0 ) are (a) 3.3 V in the positive half cycle and 1.4 V in the negative half cycle (b) 4 V in the positive half cycle and 5 V in the negative half cycle (c) 3.3 V in both positive and negative half cycles (d) 4 V in both positive and negative half cycles 1.13 The line-to-line input voltage to the 3 phase, 50 Hz, ac circuit shown in Fig.1.13 is 100 V rms. Assuming that the phase sequence is RYB, the wattmeters would read. (a) W 1 = 886 W and W 2 = 886 W (b) W 1 = 500 W and W 2 = 500 W (c) W 1 = 0 W and W 2 = 1000 W (d) W 1 = 250 W and W 2 = 750 W D Q Q FF0 CLK 45O ~ V msin(?t) ?=314 rad/s 1kO ~ 10sin(?t) ?=314 rad/s D D Z V O I W 2 5?60°O 5?60°O 5?60°O R Y B W 1 GATE EE - 2002 1.14 The logic circuit used to generate the active low chip select (CS) by an 8085 microprocessor to address a peripheral is shown in Fig.1.14. The peripheral will respond to addresses in the range. (a) E000-EFFF (b) 000E-FFFE (c) 1000-FFFF (d) 0001-FFF1 1.15 Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is 0.25 cm and the distance between their centers is 1m. If this distance is doubled, then the inductance per unit length (a) doubles (b) halves (c) increases but does not double (d) decreases but does not halve 1.16 Consider a power system with three identical generators. The transmission losses are negligible. One generator (G1) has a speed governor which maintains its speed constant at the rated value, while the other generators (G2 and G3) have governors with a droop of 5%. If the load of the system is increased, then in steady state. (a) generation of G2 and G3 is increased equally while generation of G1 is unchanged. (b) generation of G1 alone is increased while generation of G2 and G3 is unchanged. (c) generation of G1, G2 and G3 is increased equally. (d) generation of G1, G2 and G3 is increased in the ratio 0.5:0.25:0.25. 1.17 A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at (a) the upper surface of the conductor (b) the lower surface of the conductor (c) the ground surface (d) midway between the conductor and ground 1.18 Consider the problem of relay co-ordination for the distance relays R1 and R2 on adjacent lines of a transmission system (Fig.1.18). The Zone 1 and Zone 2 settings for both the relays are indicated on the diagram. Which of the following indicates the correct time setting for the Zone 2 of relays R1 and R2. (a) 1 2 2 0.6 , 2 0.3 R R TZ s TZ s = = (b) 1 2 2 0.3 , 2 0.6 R R TZ s TZ s = = (c) 1 2 2 0.3 , 2 0.3 R R TZ s TZ s = = (d) 1 2 2 0.1 , 2 0.3 R R TZ s TZ s = = CS A 15 A 14 A 13 A 12 Zone1 (R1) Zone2 (R1) Zone1 (R2) Zone2 (R2) R2 R1 Page 5 GATE EE - 2002 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 A current impulse, 5d(t), is forced through a capacitor C. The voltage, V c (t), across the capacitor is given by (a) 5t (b) 5u(t) - C (c) 5 t C (d) ( ) 5u t C 1.2 Fourier Series for the waveform, f(t) shown in Fig.1.2 is (a) ( ) ( ) ( ) 2 8 1 1 sin sin 3 sin 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (b) ( ) ( ) ( ) 2 8 1 1 sin cos 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K (c) ( ) ( ) ( ) 2 8 1 1 cos cos 3 cos 5 9 25 t t t p p p p ? ? + + + ? ? ? ? K (d) ( ) ( ) ( ) 2 8 1 1 cos sin 3 sin 5 9 25 t t t p p p p ? ? - + + ? ? ? ? K 1.3 The graph of an electrical network has N nodes and B branches. The number of links, L, with respect to the choice of a tree, is given by (a) B – N + 1 (b) B + N (c) N – B + 1 (d) N – 2B -1 1.4 Two in-phase, 50 Hz sinusoidal waveform of unit amplitude are fed into channel 1 and channel 2 respectively of an oscilloscope. Assuming that the voltage scale, time scale and other settings are exactly the same for both the channels, what would be observed if the oscilloscope is operated in X-Y mode? (a) A circle of unit radius (b) An ellipse (c) A parabola (d) A straight line inclined at 45° with respect to the x-axis -1 0 f(t) 1 2 3 1 -1 GATE EE - 2002 1.5 Given a vector field , F r the divergence theorem states that (a) . . s v F dS FdV = ? ? ? r r ur r (b) . s v F dS FdV = ?× ? ? r r ur r (c) . s v F dS FdV × = ? ? ? r r ur r (d) . s v F dS FdV × = ? ? ? r r ur r 1.6 If a 400V, 50 Hz, star connected, 3 phase squirrel cage induction motor is operated from a 400 V, 75 Hz supply, the torque that the motor can now provide while drawing rated current from the supply? (a) reduces (b) increases (c) remains the same (d) increase or reduces depending upon the rotor resistance 1.7 A dc series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque-speed characteristic of this motor will be approximately represented by which curve of Fig.1.7? (a) Curve A (b) Curve B (c) Curve C (d) Curve D 1.8 A 1 kVA, 230V/100V, single phase, 50 Hz transformer having negligible winding resistance and leakage inductance is operating under saturation, while 250 V, 50 Hz sinusoidal supply is connected to the high voltage winding. A resistive load is connected to the low voltage winding which draws rated current. Which one of the following quantities will not be sinusoidal? (a) Voltage induced across the low voltage winding (b) Core flux (c) Load current (d) Current drawn from the source 1.9 A 400V/200V/200V, 50 Hz three winding transformer is connected as shown in Fig.1.9. The reading of the voltmeter, V, will be (a) 0 V (b) 400 V (c) 600 V (d) 800 V C B A D Torque Speed 400V 400:200:200 ~ V 50 Hz GATE EE - 2002 1.10 The frequency of the clock signal applied to the rising edge triggered D flip-flop shown in Fig.1.10 is 10 kHz. The frequency of the signal available at Q is (a) 10 kHz (b) 2.5 kHz (c) 20 kHz (d) 5 kHz 1.11 The forward resistance of the diode shown in Fig.1.11 is 5O and the remaining parameters are same as those of an ideal diode. The dc component of the source current is (a) 50 Vm p (b) 50 2 Vm p (c) 100 2 Vm p (d) 2 50 Vm p 1.12 The cut-in voltage of both Zener diode D z and diode D shown in Fig.1.12 is 0.7 V, while break down voltage of D z is 3.3 V and reverse breakdown voltage of D is 50 V. the other parameters can be assumed to be the same as those of an ideal diode. The values of the peak output voltage (V 0 ) are (a) 3.3 V in the positive half cycle and 1.4 V in the negative half cycle (b) 4 V in the positive half cycle and 5 V in the negative half cycle (c) 3.3 V in both positive and negative half cycles (d) 4 V in both positive and negative half cycles 1.13 The line-to-line input voltage to the 3 phase, 50 Hz, ac circuit shown in Fig.1.13 is 100 V rms. Assuming that the phase sequence is RYB, the wattmeters would read. (a) W 1 = 886 W and W 2 = 886 W (b) W 1 = 500 W and W 2 = 500 W (c) W 1 = 0 W and W 2 = 1000 W (d) W 1 = 250 W and W 2 = 750 W D Q Q FF0 CLK 45O ~ V msin(?t) ?=314 rad/s 1kO ~ 10sin(?t) ?=314 rad/s D D Z V O I W 2 5?60°O 5?60°O 5?60°O R Y B W 1 GATE EE - 2002 1.14 The logic circuit used to generate the active low chip select (CS) by an 8085 microprocessor to address a peripheral is shown in Fig.1.14. The peripheral will respond to addresses in the range. (a) E000-EFFF (b) 000E-FFFE (c) 1000-FFFF (d) 0001-FFF1 1.15 Consider a long, two-wire line composed of solid round conductors. The radius of both conductors is 0.25 cm and the distance between their centers is 1m. If this distance is doubled, then the inductance per unit length (a) doubles (b) halves (c) increases but does not double (d) decreases but does not halve 1.16 Consider a power system with three identical generators. The transmission losses are negligible. One generator (G1) has a speed governor which maintains its speed constant at the rated value, while the other generators (G2 and G3) have governors with a droop of 5%. If the load of the system is increased, then in steady state. (a) generation of G2 and G3 is increased equally while generation of G1 is unchanged. (b) generation of G1 alone is increased while generation of G2 and G3 is unchanged. (c) generation of G1, G2 and G3 is increased equally. (d) generation of G1, G2 and G3 is increased in the ratio 0.5:0.25:0.25. 1.17 A long wire composed of a smooth round conductor runs above and parallel to the ground (assumed to be a large conducting plane). A high voltage exists between the conductor and the ground. The maximum electric stress occurs at (a) the upper surface of the conductor (b) the lower surface of the conductor (c) the ground surface (d) midway between the conductor and ground 1.18 Consider the problem of relay co-ordination for the distance relays R1 and R2 on adjacent lines of a transmission system (Fig.1.18). The Zone 1 and Zone 2 settings for both the relays are indicated on the diagram. Which of the following indicates the correct time setting for the Zone 2 of relays R1 and R2. (a) 1 2 2 0.6 , 2 0.3 R R TZ s TZ s = = (b) 1 2 2 0.3 , 2 0.6 R R TZ s TZ s = = (c) 1 2 2 0.3 , 2 0.3 R R TZ s TZ s = = (d) 1 2 2 0.1 , 2 0.3 R R TZ s TZ s = = CS A 15 A 14 A 13 A 12 Zone1 (R1) Zone2 (R1) Zone1 (R2) Zone2 (R2) R2 R1 GATE EE - 2002 1.19. Let s(t) be the step response of a linear system with zero initial conditions; then the response of this system to an input u(t) is (a) ( ) ( ) 0 t s t u d t t t - ? (b) ( ) ( ) 0 t d s t u d dt t t t ? ? ? ? - ? ? ? ? ? (c) ( ) ( ) 1 1 0 0 t t s t u d d t t t t ? ? ? ? - ? ? ? ? ? ? (d) ( ) ( ) 2 0 t s t u d t t t - ? 1.20. Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is (a) ( ) 0 lim s Y s ? (b) ( ) lim s Y s ?8 (c) ( ) 0 lim s sY s ? (d) ( ) lim s sY s ?8 1.21. The determinant of the matrix 1 0 0 0 100 1 0 0 100 200 1 0 100 200 300 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? is: (a) 100 (b) 200 (c) 1 (d) 300 1.22. The state transition matrix for the system X AX = & with initial state X(0) is (a) ( ) 1 sI A - - (b) ( ) 0 At e X (c) Laplace inverse of [( ) 1 sI A - - ] (d) Laplace inverse of [( ) 1 sI A - - X(0)] 1.23. A six pulse thyristor rectifier bridge is connected to a balanced 50 Hz three phase ac source. Assuming that the dc output current of the rectifier is constant, the lowest frequency harmonic component in the ac source line current is (a) 100 Hz (b) 150 Hz (c) 250 Hz (d) 300 Hz 1.24. What is the rms value of the voltage waveform shown in Fig.1.24? (a) 200 V p (b) 100 V p (c) 200 V (d) 100 V 100V ? p/3 -100V 2p/3 4p/3 5p/3 2p pRead More

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