Page 1 GATE EC - 1998 SECTION - A 1. For each of the following (1.1 â€“ 1.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or D) as appropriate, against the corresponding question number in the answer book. 1.1 A network has 7 nodes and 5 independent loops. The number of branches in the network is (a) 13 (b) 12 (c) 11 (d) 10 1.2 The eigen values of the matrix A = 0 1 1 0 ? ? ? ? ? ? are (a) 1,1 (b) -1,-1 (c) j,-j (d) 1,-1 1.3 If ( ) 2 2 , f t s ? ? = + then the value of ( ) lim t f t ?8 (a) cannot be determined (b) is zero (c) is unity (d) is infinite 1.4 The trigonometric Fourier series of a periodic time function can have only (a) cosine terms (b) sine terms (c) cosine and sine terms (d) d.c. and cosine terms 1.5 The nodal method of circuit analysis is based on (a) KVL and Ohmâ€™s law (b) KCL and Ohmâ€™s law (c) KCL and KVL (d) KCL, KVL and Ohmâ€™s law 1.6 Superposition theorem is NOT applicable to networks containing (a) nonlinear elements (b) dependent voltage sources (c) dependent current sources (d) transformers 1.7 The parallel RLC circuit shown in Fig.1.7 is in resonance. In this cicuit (a) 1 R I mA < (b) 1 R L I I mA + > (c) 1 R C I I mA + < (d) 1 R C I I mA + > 1mA RMS I R R I L I C L Page 2 GATE EC - 1998 SECTION - A 1. For each of the following (1.1 â€“ 1.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or D) as appropriate, against the corresponding question number in the answer book. 1.1 A network has 7 nodes and 5 independent loops. The number of branches in the network is (a) 13 (b) 12 (c) 11 (d) 10 1.2 The eigen values of the matrix A = 0 1 1 0 ? ? ? ? ? ? are (a) 1,1 (b) -1,-1 (c) j,-j (d) 1,-1 1.3 If ( ) 2 2 , f t s ? ? = + then the value of ( ) lim t f t ?8 (a) cannot be determined (b) is zero (c) is unity (d) is infinite 1.4 The trigonometric Fourier series of a periodic time function can have only (a) cosine terms (b) sine terms (c) cosine and sine terms (d) d.c. and cosine terms 1.5 The nodal method of circuit analysis is based on (a) KVL and Ohmâ€™s law (b) KCL and Ohmâ€™s law (c) KCL and KVL (d) KCL, KVL and Ohmâ€™s law 1.6 Superposition theorem is NOT applicable to networks containing (a) nonlinear elements (b) dependent voltage sources (c) dependent current sources (d) transformers 1.7 The parallel RLC circuit shown in Fig.1.7 is in resonance. In this cicuit (a) 1 R I mA < (b) 1 R L I I mA + > (c) 1 R C I I mA + < (d) 1 R C I I mA + > 1mA RMS I R R I L I C L GATE EC - 1998 1.8 A periodic signal x(t) of period o T is given by ( ) 1 1 1, 0, 2 o t T x t T T t ? < ? = ? < < ? ? The d.c. component of x(t) is (a) 1 0 T T (b) 1 0 2 T T (c) 1 0 2T T (d) 0 1 T T 1.9 The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation ( ), 0 at e u t a - > will be (a) at ae - (b) ( ) 1 1 at e a - ? ? - ? ? ? ? (c) ( ) 1 at a e - - (d) 1 at e - - 1.10 The short-circuit admittance matrix of a two-port network is 1 0 2 1 0 2 - ? ? ? ? ? ? ? ? ? ? ? ? The two port network is (a) non-reciprocal and passive (b) non-reciprocal and active (c) reciprocal and passive (d) reciprocal and active 1.11 The voltage across the terminals a and b in Fig.1.11 is (a) 0.5 V (b) 3.0 V (c) 3.5 V (d) 4.0 V 1.12 The electron and hole concentrations in a intrinsic semiconductor are n i and p i respectively. When doped with a p-type material, these change to n and p, respectively. Then (a) i i n p n p + = + (b) i i n n p p + = + (c) i i np np = (d) i i np np = 1.13 If T f of BJT is related to its , and m g C C p µ as follows: (a) T m C C f g p µ + = (b) ( ) T m e C C f g p µ p + = (c) m T g f C C p µ = + (d) ( ) 2 m T g f C C p µ p = + t + 2O 1O - 1H 3A 2O 1V a Page 3 GATE EC - 1998 SECTION - A 1. For each of the following (1.1 â€“ 1.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or D) as appropriate, against the corresponding question number in the answer book. 1.1 A network has 7 nodes and 5 independent loops. The number of branches in the network is (a) 13 (b) 12 (c) 11 (d) 10 1.2 The eigen values of the matrix A = 0 1 1 0 ? ? ? ? ? ? are (a) 1,1 (b) -1,-1 (c) j,-j (d) 1,-1 1.3 If ( ) 2 2 , f t s ? ? = + then the value of ( ) lim t f t ?8 (a) cannot be determined (b) is zero (c) is unity (d) is infinite 1.4 The trigonometric Fourier series of a periodic time function can have only (a) cosine terms (b) sine terms (c) cosine and sine terms (d) d.c. and cosine terms 1.5 The nodal method of circuit analysis is based on (a) KVL and Ohmâ€™s law (b) KCL and Ohmâ€™s law (c) KCL and KVL (d) KCL, KVL and Ohmâ€™s law 1.6 Superposition theorem is NOT applicable to networks containing (a) nonlinear elements (b) dependent voltage sources (c) dependent current sources (d) transformers 1.7 The parallel RLC circuit shown in Fig.1.7 is in resonance. In this cicuit (a) 1 R I mA < (b) 1 R L I I mA + > (c) 1 R C I I mA + < (d) 1 R C I I mA + > 1mA RMS I R R I L I C L GATE EC - 1998 1.8 A periodic signal x(t) of period o T is given by ( ) 1 1 1, 0, 2 o t T x t T T t ? < ? = ? < < ? ? The d.c. component of x(t) is (a) 1 0 T T (b) 1 0 2 T T (c) 1 0 2T T (d) 0 1 T T 1.9 The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation ( ), 0 at e u t a - > will be (a) at ae - (b) ( ) 1 1 at e a - ? ? - ? ? ? ? (c) ( ) 1 at a e - - (d) 1 at e - - 1.10 The short-circuit admittance matrix of a two-port network is 1 0 2 1 0 2 - ? ? ? ? ? ? ? ? ? ? ? ? The two port network is (a) non-reciprocal and passive (b) non-reciprocal and active (c) reciprocal and passive (d) reciprocal and active 1.11 The voltage across the terminals a and b in Fig.1.11 is (a) 0.5 V (b) 3.0 V (c) 3.5 V (d) 4.0 V 1.12 The electron and hole concentrations in a intrinsic semiconductor are n i and p i respectively. When doped with a p-type material, these change to n and p, respectively. Then (a) i i n p n p + = + (b) i i n n p p + = + (c) i i np np = (d) i i np np = 1.13 If T f of BJT is related to its , and m g C C p µ as follows: (a) T m C C f g p µ + = (b) ( ) T m e C C f g p µ p + = (c) m T g f C C p µ = + (d) ( ) 2 m T g f C C p µ p = + t + 2O 1O - 1H 3A 2O 1V a GATE EC - 1998 1.14 The static characteristic of an adequately forward biased p-n junction is a straight line, if the plot is of (a) log I vs. log V (b) log I vs. V (c) I vs. log V (d) I vs. V 1.15 A long specimen of p-type semiconductor material (a) is positively charged (b) is electrically neutral (c) has an electric field directed along its length (d) acts as a dipole 1.16 The Z-transform of the time function ( ) 0 k n k d 8 = - ? is (a) 1 Z Z - (b) 1 Z Z - (c) ( ) 2 1 Z Z - (d) ( ) 2 1 Z Z - 1.17 The number of roots of 3 2 5 7 3 0 s s s + + + = in the left half of the s-plane is (a) zero (b) one (c) two (d) three 1.18 The transfer function of a tachometer is of the form (a) Ks (b) K s (c) ( ) 1 K s + (d) ( ) 1 K s s + 1.19. Consider a unity feedback control system with open-loop transfer function ( ) ( ) . 1 K G s s s = + The steady state error of the system due to a unit step input is (a) zero (b) K (c) 1 K (d) infinite 1.20. The transfer function of a zero-order-hold system is (a) ( ) 1 1 sT e s - ? ? + ? ? ? ? (b) ( ) 1 1 sT e s - ? ? - ? ? ? ? (c) 1 1 sT e s - ? ? - ? ? ? ? (d) 1 1 sT e s - ? ? + ? ? ? ? 1.21. In the Bode-plot of a unity feedback control system, the value of phase of G(j?) at the gain cross over frequency is â€“125°. The phase margin of the system is (a) -125° (b) -55° (c) 55° (d) 125° Page 4 GATE EC - 1998 SECTION - A 1. For each of the following (1.1 â€“ 1.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or D) as appropriate, against the corresponding question number in the answer book. 1.1 A network has 7 nodes and 5 independent loops. The number of branches in the network is (a) 13 (b) 12 (c) 11 (d) 10 1.2 The eigen values of the matrix A = 0 1 1 0 ? ? ? ? ? ? are (a) 1,1 (b) -1,-1 (c) j,-j (d) 1,-1 1.3 If ( ) 2 2 , f t s ? ? = + then the value of ( ) lim t f t ?8 (a) cannot be determined (b) is zero (c) is unity (d) is infinite 1.4 The trigonometric Fourier series of a periodic time function can have only (a) cosine terms (b) sine terms (c) cosine and sine terms (d) d.c. and cosine terms 1.5 The nodal method of circuit analysis is based on (a) KVL and Ohmâ€™s law (b) KCL and Ohmâ€™s law (c) KCL and KVL (d) KCL, KVL and Ohmâ€™s law 1.6 Superposition theorem is NOT applicable to networks containing (a) nonlinear elements (b) dependent voltage sources (c) dependent current sources (d) transformers 1.7 The parallel RLC circuit shown in Fig.1.7 is in resonance. In this cicuit (a) 1 R I mA < (b) 1 R L I I mA + > (c) 1 R C I I mA + < (d) 1 R C I I mA + > 1mA RMS I R R I L I C L GATE EC - 1998 1.8 A periodic signal x(t) of period o T is given by ( ) 1 1 1, 0, 2 o t T x t T T t ? < ? = ? < < ? ? The d.c. component of x(t) is (a) 1 0 T T (b) 1 0 2 T T (c) 1 0 2T T (d) 0 1 T T 1.9 The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation ( ), 0 at e u t a - > will be (a) at ae - (b) ( ) 1 1 at e a - ? ? - ? ? ? ? (c) ( ) 1 at a e - - (d) 1 at e - - 1.10 The short-circuit admittance matrix of a two-port network is 1 0 2 1 0 2 - ? ? ? ? ? ? ? ? ? ? ? ? The two port network is (a) non-reciprocal and passive (b) non-reciprocal and active (c) reciprocal and passive (d) reciprocal and active 1.11 The voltage across the terminals a and b in Fig.1.11 is (a) 0.5 V (b) 3.0 V (c) 3.5 V (d) 4.0 V 1.12 The electron and hole concentrations in a intrinsic semiconductor are n i and p i respectively. When doped with a p-type material, these change to n and p, respectively. Then (a) i i n p n p + = + (b) i i n n p p + = + (c) i i np np = (d) i i np np = 1.13 If T f of BJT is related to its , and m g C C p µ as follows: (a) T m C C f g p µ + = (b) ( ) T m e C C f g p µ p + = (c) m T g f C C p µ = + (d) ( ) 2 m T g f C C p µ p = + t + 2O 1O - 1H 3A 2O 1V a GATE EC - 1998 1.14 The static characteristic of an adequately forward biased p-n junction is a straight line, if the plot is of (a) log I vs. log V (b) log I vs. V (c) I vs. log V (d) I vs. V 1.15 A long specimen of p-type semiconductor material (a) is positively charged (b) is electrically neutral (c) has an electric field directed along its length (d) acts as a dipole 1.16 The Z-transform of the time function ( ) 0 k n k d 8 = - ? is (a) 1 Z Z - (b) 1 Z Z - (c) ( ) 2 1 Z Z - (d) ( ) 2 1 Z Z - 1.17 The number of roots of 3 2 5 7 3 0 s s s + + + = in the left half of the s-plane is (a) zero (b) one (c) two (d) three 1.18 The transfer function of a tachometer is of the form (a) Ks (b) K s (c) ( ) 1 K s + (d) ( ) 1 K s s + 1.19. Consider a unity feedback control system with open-loop transfer function ( ) ( ) . 1 K G s s s = + The steady state error of the system due to a unit step input is (a) zero (b) K (c) 1 K (d) infinite 1.20. The transfer function of a zero-order-hold system is (a) ( ) 1 1 sT e s - ? ? + ? ? ? ? (b) ( ) 1 1 sT e s - ? ? - ? ? ? ? (c) 1 1 sT e s - ? ? - ? ? ? ? (d) 1 1 sT e s - ? ? + ? ? ? ? 1.21. In the Bode-plot of a unity feedback control system, the value of phase of G(j?) at the gain cross over frequency is â€“125°. The phase margin of the system is (a) -125° (b) -55° (c) 55° (d) 125° GATE EC - 1998 1.22. Consider a feedback control system with loop transfer fucntion ( ) ( ) ( ) ( )( ) 1 0.5 1 1 2 K s G s H s s s s + = + + The type of the closed loop system is (a) zero (b) one (c) two (d) three 1.23. The transfer function of a phase lead controller is 1 3 1 Ts Ts + + . The maximum value of phase provided by this controller is (a) 90° (b) 60° (c) 45° (d) 30° 1.24. The Nyquist plot of a phase transfer function g(j?) H(j?) of a system encloses the (-1,0) point. The gain margin of the system is (a) less than zero (b) zero (c) greater than zero (d) infinity 1.25 The transfer function of a system is ( ) ( ) 2 2 2 6 5 1 2 s s s s + + + + The characteristic equation of the system is (a) 2 2 6 5 0 s s + + = (b) ( ) ( ) 2 1 2 0 s s + + = (c) ( ) ( ) 2 2 2 6 5 1 2 0 s s s s + + + + + = (d) ( ) ( ) 2 2 2 6 5 1 2 0 s s s s + + - + + = 1.26 In a synchro error detector, the output voltage is proportional to ( ) , n t ? ? ? ? ? where ( ) t ? is the rotor velocity and n equals (a) -2 (b) -1 (c) 1 (d) 2 1.27 Two identical FETs, each characterissed by the parameters and m d g r are connected in parallel. The composite FET is then characterized by the parameters (a) and 2 2 m d g r (b) and 2 2 d m r g (c) 2 and 2 d m r g (d) 2 and 2 m d g r 1.28 The circuit of Fig.1.28 is an example of feedback of the following type (a) current series (b) current shunt (c) voltage series (d) voltage shunt V O ~ V i +V CC Page 5 GATE EC - 1998 SECTION - A 1. For each of the following (1.1 â€“ 1.40) four alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by writing (A, B, C or D) as appropriate, against the corresponding question number in the answer book. 1.1 A network has 7 nodes and 5 independent loops. The number of branches in the network is (a) 13 (b) 12 (c) 11 (d) 10 1.2 The eigen values of the matrix A = 0 1 1 0 ? ? ? ? ? ? are (a) 1,1 (b) -1,-1 (c) j,-j (d) 1,-1 1.3 If ( ) 2 2 , f t s ? ? = + then the value of ( ) lim t f t ?8 (a) cannot be determined (b) is zero (c) is unity (d) is infinite 1.4 The trigonometric Fourier series of a periodic time function can have only (a) cosine terms (b) sine terms (c) cosine and sine terms (d) d.c. and cosine terms 1.5 The nodal method of circuit analysis is based on (a) KVL and Ohmâ€™s law (b) KCL and Ohmâ€™s law (c) KCL and KVL (d) KCL, KVL and Ohmâ€™s law 1.6 Superposition theorem is NOT applicable to networks containing (a) nonlinear elements (b) dependent voltage sources (c) dependent current sources (d) transformers 1.7 The parallel RLC circuit shown in Fig.1.7 is in resonance. In this cicuit (a) 1 R I mA < (b) 1 R L I I mA + > (c) 1 R C I I mA + < (d) 1 R C I I mA + > 1mA RMS I R R I L I C L GATE EC - 1998 1.8 A periodic signal x(t) of period o T is given by ( ) 1 1 1, 0, 2 o t T x t T T t ? < ? = ? < < ? ? The d.c. component of x(t) is (a) 1 0 T T (b) 1 0 2 T T (c) 1 0 2T T (d) 0 1 T T 1.9 The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation ( ), 0 at e u t a - > will be (a) at ae - (b) ( ) 1 1 at e a - ? ? - ? ? ? ? (c) ( ) 1 at a e - - (d) 1 at e - - 1.10 The short-circuit admittance matrix of a two-port network is 1 0 2 1 0 2 - ? ? ? ? ? ? ? ? ? ? ? ? The two port network is (a) non-reciprocal and passive (b) non-reciprocal and active (c) reciprocal and passive (d) reciprocal and active 1.11 The voltage across the terminals a and b in Fig.1.11 is (a) 0.5 V (b) 3.0 V (c) 3.5 V (d) 4.0 V 1.12 The electron and hole concentrations in a intrinsic semiconductor are n i and p i respectively. When doped with a p-type material, these change to n and p, respectively. Then (a) i i n p n p + = + (b) i i n n p p + = + (c) i i np np = (d) i i np np = 1.13 If T f of BJT is related to its , and m g C C p µ as follows: (a) T m C C f g p µ + = (b) ( ) T m e C C f g p µ p + = (c) m T g f C C p µ = + (d) ( ) 2 m T g f C C p µ p = + t + 2O 1O - 1H 3A 2O 1V a GATE EC - 1998 1.14 The static characteristic of an adequately forward biased p-n junction is a straight line, if the plot is of (a) log I vs. log V (b) log I vs. V (c) I vs. log V (d) I vs. V 1.15 A long specimen of p-type semiconductor material (a) is positively charged (b) is electrically neutral (c) has an electric field directed along its length (d) acts as a dipole 1.16 The Z-transform of the time function ( ) 0 k n k d 8 = - ? is (a) 1 Z Z - (b) 1 Z Z - (c) ( ) 2 1 Z Z - (d) ( ) 2 1 Z Z - 1.17 The number of roots of 3 2 5 7 3 0 s s s + + + = in the left half of the s-plane is (a) zero (b) one (c) two (d) three 1.18 The transfer function of a tachometer is of the form (a) Ks (b) K s (c) ( ) 1 K s + (d) ( ) 1 K s s + 1.19. Consider a unity feedback control system with open-loop transfer function ( ) ( ) . 1 K G s s s = + The steady state error of the system due to a unit step input is (a) zero (b) K (c) 1 K (d) infinite 1.20. The transfer function of a zero-order-hold system is (a) ( ) 1 1 sT e s - ? ? + ? ? ? ? (b) ( ) 1 1 sT e s - ? ? - ? ? ? ? (c) 1 1 sT e s - ? ? - ? ? ? ? (d) 1 1 sT e s - ? ? + ? ? ? ? 1.21. In the Bode-plot of a unity feedback control system, the value of phase of G(j?) at the gain cross over frequency is â€“125°. The phase margin of the system is (a) -125° (b) -55° (c) 55° (d) 125° GATE EC - 1998 1.22. Consider a feedback control system with loop transfer fucntion ( ) ( ) ( ) ( )( ) 1 0.5 1 1 2 K s G s H s s s s + = + + The type of the closed loop system is (a) zero (b) one (c) two (d) three 1.23. The transfer function of a phase lead controller is 1 3 1 Ts Ts + + . The maximum value of phase provided by this controller is (a) 90° (b) 60° (c) 45° (d) 30° 1.24. The Nyquist plot of a phase transfer function g(j?) H(j?) of a system encloses the (-1,0) point. The gain margin of the system is (a) less than zero (b) zero (c) greater than zero (d) infinity 1.25 The transfer function of a system is ( ) ( ) 2 2 2 6 5 1 2 s s s s + + + + The characteristic equation of the system is (a) 2 2 6 5 0 s s + + = (b) ( ) ( ) 2 1 2 0 s s + + = (c) ( ) ( ) 2 2 2 6 5 1 2 0 s s s s + + + + + = (d) ( ) ( ) 2 2 2 6 5 1 2 0 s s s s + + - + + = 1.26 In a synchro error detector, the output voltage is proportional to ( ) , n t ? ? ? ? ? where ( ) t ? is the rotor velocity and n equals (a) -2 (b) -1 (c) 1 (d) 2 1.27 Two identical FETs, each characterissed by the parameters and m d g r are connected in parallel. The composite FET is then characterized by the parameters (a) and 2 2 m d g r (b) and 2 2 d m r g (c) 2 and 2 d m r g (d) 2 and 2 m d g r 1.28 The circuit of Fig.1.28 is an example of feedback of the following type (a) current series (b) current shunt (c) voltage series (d) voltage shunt V O ~ V i +V CC GATE EC - 1998 1.29 In a differential amplifier, CMRR can be improved by using an increased (a) emitter resistance (b) collector resistance (c) power supply voltages (d) source resistance 1.30 From a measurement of the rise time of the output pulse of an amplifier whose input is a small amplitude square wave, one can estimate the following parameter of the amplifier: (a) gain-bandwidth product (b) slow rate (c) upper 3-dB frequency (d) lower 3-dB frequency 1.31 A distorted sinusoidal has the amplitudes 1 2 3 , , A A A Kof the fundamental, second harmonic, third harmonic, Krespectively. The total harmonic distortion is (a) 2 3 1 A A A + +K (b) 2 2 2 3 1 A A A + +K (c) 2 2 2 3 2 2 2 1 2 3 A A A A A + + + + K K (d) 2 2 2 3 1 A A A ? ? + + ? ? ? ? ? ? K 1.32 The emitter coupled pair of BJTâ€™s gives a linear transfer relation between the differential output voltage and the differential input voltage id V only when the magnitude of id V is less a times the thermal voltage, where a is (a) 4 (b) 3 (c) 2 (d) 1 1.33 In a shunt-shunt negative feedback amplifier, as compared to the basic amplifier (a) both, input and output impedances, decrease (b) input impedance decreases but output impedance increases (c) input impedance increases but output impedance decreases (d) both, input and output impedances increase 1.34 A multistage amplifier has a low-pass response with three real poles at s = -? 1 , -? 2 and ? 3 . The approximate overall bandwidth B of the amplifier will be given by (a) 1 2 3 B ? ? ? = + + (b) 1 2 3 1 1 1 1 B ? ? ? = + + (c) ( ) 1 3 1 2 3 B ? ? ? = + + (d) 2 2 2 1 2 3 B ? ? ? = + +Read More

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