Page 1 GATE EC - 2006 Q.1 – Q.20 Carry One Mark Each. 1. The rank of the matrix 1 1 1 1 1 0 1 1 1 ? ? ? ? - ? ? ? ? ? ? is: (A) 0 (B) 1 (C) 2 (D) 3 2. , where P P ?×?× is a vector, is equal to (A) 2 P P P ×?× -? (B) ( ) 2 P P ? +? ?• (C) 2 P P ? +?× (D) ( ) 2 P P ? ?• -? 3. ( ) , P ds ?× • ?? where P is a vector, is equal to (A) P dl • ? (B) P dl ?×?× • ? (C) P dl ?× • ? (D) Pd? ?• ??? 4. A probability density function is of the form ( ) ( ) , , . x p x Ke x a - = ? -8 8 The value of K is (A) 0.5 (B) 1 (C) 0.5a (D) a 5. A solution for the differential equation ( ) ( ) ( ) 2 x t x t t d + = & with initial condition ( ) 0 0 x - = is: Page 2 GATE EC - 2006 Q.1 – Q.20 Carry One Mark Each. 1. The rank of the matrix 1 1 1 1 1 0 1 1 1 ? ? ? ? - ? ? ? ? ? ? is: (A) 0 (B) 1 (C) 2 (D) 3 2. , where P P ?×?× is a vector, is equal to (A) 2 P P P ×?× -? (B) ( ) 2 P P ? +? ?• (C) 2 P P ? +?× (D) ( ) 2 P P ? ?• -? 3. ( ) , P ds ?× • ?? where P is a vector, is equal to (A) P dl • ? (B) P dl ?×?× • ? (C) P dl ?× • ? (D) Pd? ?• ??? 4. A probability density function is of the form ( ) ( ) , , . x p x Ke x a - = ? -8 8 The value of K is (A) 0.5 (B) 1 (C) 0.5a (D) a 5. A solution for the differential equation ( ) ( ) ( ) 2 x t x t t d + = & with initial condition ( ) 0 0 x - = is: GATE EC - 2006 (A) ( ) 2t e u t - (B) ( ) 2t e u t (C) ( ) t e u t - (D) ( ) t e u t 6. A low-pass filter having a frequency response ( ) ( ) ( ) j H j A e f ? ? ? = does not produce any phase distortion if (A) ( ) ( ) 2 3 , A C k ? ? f ? ? = = (B) ( ) ( ) 2 , A C k ? ? f ? ? = = (C) ( ) ( ) 2 , A C k ? ? f ? ? = = (D) ( ) ( ) 1 , A C k ? f ? ? - = = 7. The values of voltage ( ) D V across a tunnel-diode corresponding to peak and valley currents are and P V V V respectively. The range of tunnel-diode voltage D V for which the slope of its D I V - characteristics is negative would be (A) 0 D V < (B) 0 D P V V = < (C) P D V V V V = < (D) D V V V = 8. The concentration of minority carriers in an extrinsic semiconductor under equilibrium is: (A) directly proportional to the doping concentration (B) inversely proportional to the doping concentration (C) directly proportional to the intrinsic concentration (D) inversely proportional to the intrinsic concentration 9. Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the (A) diffusion current (B) drift current (C) recombination current (D) induced current Page 3 GATE EC - 2006 Q.1 – Q.20 Carry One Mark Each. 1. The rank of the matrix 1 1 1 1 1 0 1 1 1 ? ? ? ? - ? ? ? ? ? ? is: (A) 0 (B) 1 (C) 2 (D) 3 2. , where P P ?×?× is a vector, is equal to (A) 2 P P P ×?× -? (B) ( ) 2 P P ? +? ?• (C) 2 P P ? +?× (D) ( ) 2 P P ? ?• -? 3. ( ) , P ds ?× • ?? where P is a vector, is equal to (A) P dl • ? (B) P dl ?×?× • ? (C) P dl ?× • ? (D) Pd? ?• ??? 4. A probability density function is of the form ( ) ( ) , , . x p x Ke x a - = ? -8 8 The value of K is (A) 0.5 (B) 1 (C) 0.5a (D) a 5. A solution for the differential equation ( ) ( ) ( ) 2 x t x t t d + = & with initial condition ( ) 0 0 x - = is: GATE EC - 2006 (A) ( ) 2t e u t - (B) ( ) 2t e u t (C) ( ) t e u t - (D) ( ) t e u t 6. A low-pass filter having a frequency response ( ) ( ) ( ) j H j A e f ? ? ? = does not produce any phase distortion if (A) ( ) ( ) 2 3 , A C k ? ? f ? ? = = (B) ( ) ( ) 2 , A C k ? ? f ? ? = = (C) ( ) ( ) 2 , A C k ? ? f ? ? = = (D) ( ) ( ) 1 , A C k ? f ? ? - = = 7. The values of voltage ( ) D V across a tunnel-diode corresponding to peak and valley currents are and P V V V respectively. The range of tunnel-diode voltage D V for which the slope of its D I V - characteristics is negative would be (A) 0 D V < (B) 0 D P V V = < (C) P D V V V V = < (D) D V V V = 8. The concentration of minority carriers in an extrinsic semiconductor under equilibrium is: (A) directly proportional to the doping concentration (B) inversely proportional to the doping concentration (C) directly proportional to the intrinsic concentration (D) inversely proportional to the intrinsic concentration 9. Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the (A) diffusion current (B) drift current (C) recombination current (D) induced current GATE EC - 2006 10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a reduction of the effective base-width caused by (A) electron-hole recombination at the base (B) the reverse biasing of the base-collector junction (C) the forward biasing of emitter-base junction (D) the early removal of stored base charge during saturation-to-cutoff switching. 11. The input impedance ( ) i Z and the output impedance ( ) 0 Z of an ideal trans- conductance (voltage controlled current source) amplifier are (A) 0 0, 0 i Z Z = = (B) 0 0, i Z Z = = 8 (C) 0 , 0 i Z Z = 8 = (D) 0 , i Z Z = 8 = 8 12. An n-channel depletion MOSFET has following two points on its D GS I V - curve: (i) 0 at 12 GS D V I mA = = and (ii) 6 Volts at 0 GS D V I = - = Which of the following Q-points will give the highest trans-conductance gain for small signals? (A) 6 Volts GS V = - (B) 3 Volts GS V = - (C) 0 Volts GS V = (D) 3 Volts GS V = 13. The number of product terms in the minimized sum-of-product expression obtained through the following K-map is (where “d” denotes don’t care states) 1 0 0 1 0 d 0 0 0 0 d 1 1 0 0 1 (A) 2 (B) 3 (C) 4 (D) 5 Page 4 GATE EC - 2006 Q.1 – Q.20 Carry One Mark Each. 1. The rank of the matrix 1 1 1 1 1 0 1 1 1 ? ? ? ? - ? ? ? ? ? ? is: (A) 0 (B) 1 (C) 2 (D) 3 2. , where P P ?×?× is a vector, is equal to (A) 2 P P P ×?× -? (B) ( ) 2 P P ? +? ?• (C) 2 P P ? +?× (D) ( ) 2 P P ? ?• -? 3. ( ) , P ds ?× • ?? where P is a vector, is equal to (A) P dl • ? (B) P dl ?×?× • ? (C) P dl ?× • ? (D) Pd? ?• ??? 4. A probability density function is of the form ( ) ( ) , , . x p x Ke x a - = ? -8 8 The value of K is (A) 0.5 (B) 1 (C) 0.5a (D) a 5. A solution for the differential equation ( ) ( ) ( ) 2 x t x t t d + = & with initial condition ( ) 0 0 x - = is: GATE EC - 2006 (A) ( ) 2t e u t - (B) ( ) 2t e u t (C) ( ) t e u t - (D) ( ) t e u t 6. A low-pass filter having a frequency response ( ) ( ) ( ) j H j A e f ? ? ? = does not produce any phase distortion if (A) ( ) ( ) 2 3 , A C k ? ? f ? ? = = (B) ( ) ( ) 2 , A C k ? ? f ? ? = = (C) ( ) ( ) 2 , A C k ? ? f ? ? = = (D) ( ) ( ) 1 , A C k ? f ? ? - = = 7. The values of voltage ( ) D V across a tunnel-diode corresponding to peak and valley currents are and P V V V respectively. The range of tunnel-diode voltage D V for which the slope of its D I V - characteristics is negative would be (A) 0 D V < (B) 0 D P V V = < (C) P D V V V V = < (D) D V V V = 8. The concentration of minority carriers in an extrinsic semiconductor under equilibrium is: (A) directly proportional to the doping concentration (B) inversely proportional to the doping concentration (C) directly proportional to the intrinsic concentration (D) inversely proportional to the intrinsic concentration 9. Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the (A) diffusion current (B) drift current (C) recombination current (D) induced current GATE EC - 2006 10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a reduction of the effective base-width caused by (A) electron-hole recombination at the base (B) the reverse biasing of the base-collector junction (C) the forward biasing of emitter-base junction (D) the early removal of stored base charge during saturation-to-cutoff switching. 11. The input impedance ( ) i Z and the output impedance ( ) 0 Z of an ideal trans- conductance (voltage controlled current source) amplifier are (A) 0 0, 0 i Z Z = = (B) 0 0, i Z Z = = 8 (C) 0 , 0 i Z Z = 8 = (D) 0 , i Z Z = 8 = 8 12. An n-channel depletion MOSFET has following two points on its D GS I V - curve: (i) 0 at 12 GS D V I mA = = and (ii) 6 Volts at 0 GS D V I = - = Which of the following Q-points will give the highest trans-conductance gain for small signals? (A) 6 Volts GS V = - (B) 3 Volts GS V = - (C) 0 Volts GS V = (D) 3 Volts GS V = 13. The number of product terms in the minimized sum-of-product expression obtained through the following K-map is (where “d” denotes don’t care states) 1 0 0 1 0 d 0 0 0 0 d 1 1 0 0 1 (A) 2 (B) 3 (C) 4 (D) 5 GATE EC - 2006 14. Let ( ) ( ) x t X j? ? be Fourier Transform pair. The Fourier Transform of the signal ( ) 5 3 x t - in terms of ( ) X j? is given as (A) 3 5 1 5 5 j j e X ? ? - ? ? ? ? ? ? (B) 3 5 1 5 5 j j e X ? ? ? ? ? ? ? ? (C) 3 1 5 5 j j e X ? ? - ? ? ? ? ? ? (D) 3 1 5 5 j j e X ? ? ? ? ? ? ? ? 15. The Dirac delta function ( ) t d is defined as (A) ( ) 1 0 0 otherwise t t d = ? = ? ? (B) ( ) 0 0 otherwise t t d 8 = ? = ? ? (C) ( ) ( ) 1 0 and 1 0 otherwise t t t dt d d 8 -8 = ? = = ? ? ? (D) ( ) ( ) 0 and 1 0 otherwise t t t dt d d 8 -8 8 = ? = = ? ? ? 16. If the region of convergence of 1 2 x n x n + ? ? ? ? ? ? ? ? is 1 2 , 3 3 z < < then the region of convergence of 2 n x n x n - ? ? ? ? ? ? ? ? includes (A) 1 3 3 z < < (B) 2 3 3 z < < (C) 3 3 2 z < < (D) 1 2 3 3 z < < 17. The open-loop transfer function of a unity-gain feedback control system is given by Page 5 GATE EC - 2006 Q.1 – Q.20 Carry One Mark Each. 1. The rank of the matrix 1 1 1 1 1 0 1 1 1 ? ? ? ? - ? ? ? ? ? ? is: (A) 0 (B) 1 (C) 2 (D) 3 2. , where P P ?×?× is a vector, is equal to (A) 2 P P P ×?× -? (B) ( ) 2 P P ? +? ?• (C) 2 P P ? +?× (D) ( ) 2 P P ? ?• -? 3. ( ) , P ds ?× • ?? where P is a vector, is equal to (A) P dl • ? (B) P dl ?×?× • ? (C) P dl ?× • ? (D) Pd? ?• ??? 4. A probability density function is of the form ( ) ( ) , , . x p x Ke x a - = ? -8 8 The value of K is (A) 0.5 (B) 1 (C) 0.5a (D) a 5. A solution for the differential equation ( ) ( ) ( ) 2 x t x t t d + = & with initial condition ( ) 0 0 x - = is: GATE EC - 2006 (A) ( ) 2t e u t - (B) ( ) 2t e u t (C) ( ) t e u t - (D) ( ) t e u t 6. A low-pass filter having a frequency response ( ) ( ) ( ) j H j A e f ? ? ? = does not produce any phase distortion if (A) ( ) ( ) 2 3 , A C k ? ? f ? ? = = (B) ( ) ( ) 2 , A C k ? ? f ? ? = = (C) ( ) ( ) 2 , A C k ? ? f ? ? = = (D) ( ) ( ) 1 , A C k ? f ? ? - = = 7. The values of voltage ( ) D V across a tunnel-diode corresponding to peak and valley currents are and P V V V respectively. The range of tunnel-diode voltage D V for which the slope of its D I V - characteristics is negative would be (A) 0 D V < (B) 0 D P V V = < (C) P D V V V V = < (D) D V V V = 8. The concentration of minority carriers in an extrinsic semiconductor under equilibrium is: (A) directly proportional to the doping concentration (B) inversely proportional to the doping concentration (C) directly proportional to the intrinsic concentration (D) inversely proportional to the intrinsic concentration 9. Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the (A) diffusion current (B) drift current (C) recombination current (D) induced current GATE EC - 2006 10. The phenomenon known as “Early Effect” in a bipolar transistor refers to a reduction of the effective base-width caused by (A) electron-hole recombination at the base (B) the reverse biasing of the base-collector junction (C) the forward biasing of emitter-base junction (D) the early removal of stored base charge during saturation-to-cutoff switching. 11. The input impedance ( ) i Z and the output impedance ( ) 0 Z of an ideal trans- conductance (voltage controlled current source) amplifier are (A) 0 0, 0 i Z Z = = (B) 0 0, i Z Z = = 8 (C) 0 , 0 i Z Z = 8 = (D) 0 , i Z Z = 8 = 8 12. An n-channel depletion MOSFET has following two points on its D GS I V - curve: (i) 0 at 12 GS D V I mA = = and (ii) 6 Volts at 0 GS D V I = - = Which of the following Q-points will give the highest trans-conductance gain for small signals? (A) 6 Volts GS V = - (B) 3 Volts GS V = - (C) 0 Volts GS V = (D) 3 Volts GS V = 13. The number of product terms in the minimized sum-of-product expression obtained through the following K-map is (where “d” denotes don’t care states) 1 0 0 1 0 d 0 0 0 0 d 1 1 0 0 1 (A) 2 (B) 3 (C) 4 (D) 5 GATE EC - 2006 14. Let ( ) ( ) x t X j? ? be Fourier Transform pair. The Fourier Transform of the signal ( ) 5 3 x t - in terms of ( ) X j? is given as (A) 3 5 1 5 5 j j e X ? ? - ? ? ? ? ? ? (B) 3 5 1 5 5 j j e X ? ? ? ? ? ? ? ? (C) 3 1 5 5 j j e X ? ? - ? ? ? ? ? ? (D) 3 1 5 5 j j e X ? ? ? ? ? ? ? ? 15. The Dirac delta function ( ) t d is defined as (A) ( ) 1 0 0 otherwise t t d = ? = ? ? (B) ( ) 0 0 otherwise t t d 8 = ? = ? ? (C) ( ) ( ) 1 0 and 1 0 otherwise t t t dt d d 8 -8 = ? = = ? ? ? (D) ( ) ( ) 0 and 1 0 otherwise t t t dt d d 8 -8 8 = ? = = ? ? ? 16. If the region of convergence of 1 2 x n x n + ? ? ? ? ? ? ? ? is 1 2 , 3 3 z < < then the region of convergence of 2 n x n x n - ? ? ? ? ? ? ? ? includes (A) 1 3 3 z < < (B) 2 3 3 z < < (C) 3 3 2 z < < (D) 1 2 3 3 z < < 17. The open-loop transfer function of a unity-gain feedback control system is given by GATE EC - 2006 ( ) ( )( ) . 1 2 K G s s s = + + The gain margin of the system in dB is given by (A) 0 (B) 1 (C) 20 (D) 8 18. In the system shown below, ( ) ( ) ( ) sin . x t t u t = In steady-sate, the response ( ) y t will be: (A) 1 sin 4 2 t p ? ? - ? ? ? ? (B) 1 sin 4 2 t p ? ? + ? ? ? ? (C) 1 sin 2 t e t - (D) sin cos t t - 19. The electric field of an electromagnetic wave propagating in the positive z- direction is given by $ ( ) $ sin sin . 2 x y E a t z a t z p ? ß ? ß ? ? = - + - + ? ? ? ? The wave is (A) linearly polarized in the z-direction (B) elliptically polarized (C) left-hand circularly polarized (D) right-hand circularly polarized 20. A transmission line is feeding 1 Watt of power to a horn antenna having a gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is: (A) 10 Watts ( ) x t ( ) y t 1 1 s+Read More

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

380 docs|127 tests

- Electronics and Communication Engineering (EC) 2005 GATE Paper without solution
- Electronics and Communication Engineering (EC) 2004 GATE Paper without solution
- Electronics and Communication Engineering (EC) 2003 GATE Paper without solution
- Electronics and Communication Engineering (EC) 2002 GATE Paper without solution
- Electronics and Communication Engineering (EC) 2001 GATE Paper without solution
- Electronics and Communication Engineering (EC) 1993 GATE Paper without solution