EC-Objective-Paper-I (Set-D)

Transcription

1 EC-Objective-Paper-I (Set-D). Consider an LTI system representing a passive electrical network. If the input is a sinusoidal signal, then the steady-state output of the network is (A) Sinusoidal with the same amplitude, frequency and phase Sinusoidal with the same frequency, but possibly different amplitude and phase Non-sinusoidal (D) Sinusoidal with a different frequency. A series R-L circuit ( R4 and L = 0.0) is excited by a voltage (in volt) V(t) = 8sin (00t + 90 o ). The current in the circuit will be o (A) 40sin 00t 5. A o 40sin5. A o (D) 40 sin 00t 5. A o 40 sin5. A Laplace of Desired Response Is Exp : s Y s Laplace of Excitation V s Hs Z s R sl R jl L H tan t an R R L Since the network is LTI, so when the input is sinusoidal output is also sinusoidal with same frequency with possible change in its magnitude and phase which it obtained from H(s). So to obtain the response we have to multiply the magnitude and add the phase to the excitation sin 00t 5. o i t 8sin 00t sin 00t H o 8 sin 00t 90 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

2 . An inductor L and 5 and 0 resistors are all connected in series across a voltage source Vt 50cos t volt. If the power consumed by the 5 resistor is 0 W, then the power factor of the circuit is (A) (D) 0.8 P 5 0W I 5 0W I A rms rms Power in a circuit is consumed only by resistance So total power consumed is P I 5 0 0W total rms Also we know that in a circuit P V I cos total rms rms 50 0W cos cos 0.6 lagging L cos t 4. A graph in which at least one path (disregarding orientation) exists between any two nodes of the graph is a (A) Connected graph Directed graph Sub-graph (D) Fundamental graph (A) 5. If Q t and Q l be the sub-matrices of Q f (fundamental cut-set matrix) corresponding to twigs and links of a connected graph respectively, then. Q t is an identity matrix.. Q l is a rectangular matrix. Q f is of rank (n ) Which of the above are correct? (A) and only and only and only (4), and EXP: Q t is a unitary matrix Q l is a may be rectangula or square matrix..it depends upon a tree fundamental cut-set matrix : n- ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

3 6. Tellegen s theorem (as applicable to any lumped d.c. network, regardless of the elements being linear or non-linear, time-varying or time-invariant) implies that (A) Sum of the voltage drops across each network element is equal to the total voltage applied to the network. Sum of the powers taken by all elements, in the network, within the constants imposed by KCL and KVL is zero. Sum of the currents meeting at any node is not the same as the current in that mesh. (D) It is applicable to a branch which is not coupled to other branches of the network. 7. For the two-port network shown in the figure the transmission parameter C is I I Z a V Z b V Za (A) Z a Z b (D) Z (D) The T parameter is V AV BI I CV DI I C V I 0 i.e., output port open circuit I V IZb C V Zb b Z a V Z b Z b V ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

4 8. Two identical two-port network having transmission matrix be the resultant transmission matrix of the cascade? A B (A) C D A C B D A C B D are cascaded. What will AC CD BC D A BC AB BD A (D) C B D When two networks are in cascade, the overall, transmission parameter is obtained by multiplying the individual T-matrix T A B A B A BC AB BD C D C D AC CD BC D overall 9. The unit impulse response of a system is t t 4e 6e. The step response of the same system for t 0 is t t Ae Be C, where A, B and C are respectively. (A) 4, and + +4, and -4, and (D) +4, and + t t h(t) 4e 6e Step response = s(t) h(t)dt t t s(t) 4e 6e dt t t e e 4 6 K ( ) ( ) A=4, B=- s(0) = 4-+K s(0) = +K Considering system with no memory s(0) = 0; K = C = - 0. The network function, H(s) is equal to ys (A) x s (A) x s ys xs ys (D) xs ys ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 4

5 The network function is ratio of L.T. of output and L.T. of input considering y(s) as output and x(s) an input Hs ys xs. The driving-point impedance of the network shown in the figure has a zero at 4 and poles at j5. R L C If Z(0) =, the values of R, L and C are respectively (A) 4,and 4 9 4, and 4 9 4, and 9 4 (D), and 9 According to the data given Zs Zs K s 4 K s 4 s j5 s j5 s 4s 9 sl R sc R sl Y s s LC scr s R C L R s s L LC Zs R L C R So, K, u and 9 C L LC 4k 9 Since Z0 K C F, 9 L H 9 LC 9C 4 R and 4 L F 4L 4 So, R, L H & C F 4 9 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 5

6 . If Zs s 4s 9 s s 6 (A) R-C impedance L-C impedance (D) is a driving point impedance, it represents an R-L impedance (D) R-L-C impedance The pole zero pattern of Z(s) is as shown. The properties are networks are as follows - RC impedance: Pole and zero are alternate and pole is near to origin RL impedance: Pole and zero are alternate but zero is near to origin LC impedance: Pole and zero are alternate and i.e., on j axis Zs All the above properties are not satisfied with the given Z(s), so it is a RLC impedance function.. The numerical value of the ratio of electric field intensity E and magnetic field intensity H is (A) (D) 5 E H 0 4. Consider a long line charge of coulomb/metre perpendicular to the plane of a paper. The electrical field lines and equipotential surfaces are respectively. (A) Radial, radial concentric with line charge Cylindrical concentric with line charge, radial Radial, radial but opposite in direction (D) Concentric with line charge, parallel to line charge (A) Q Electric field lines are radial. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 6

7 r r The potential at a distance r from the conductor along the length of the conductor is constant; those surfaces are called equipotential surfaces. So, equipotential surfaces are cylindrical concentric with the line charge. 5. Which of the following statements about electric field lines associated with electric charges is false? (A) Electric field line and can be either straight or curved Electric field lines form closed loops Electric field lines begin on positive charges and end on negative charges. (D) Electric field lines do not intersect For incase of Electric field.d v v.e From the above equation, we can conclude that electric field is a divergency field; it s not a circulating field. So, electric field lines never form closed path. 6. Which of the following represents Maxwell s divergence equation for static electric field? (A). B 0 H 0.B (D) H (A).D v.b0 Maxwell's equations E0 for static fields H J 7. A current of 5 A passes along the axis of a cylinder of 5 cm radius. The flux density at the surface of the cylinder is (A) T 0 T ) 00 T (D) 000 T ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 7

8 7 I B 0 T R Maxwell s major contribution to EM theory was to assert (A) That an electric field varying with time in free space gives rise to a current That a magnetic field varying with time gives rise to an electric field That a magnetic field varying with space gives rise to an electric field (D) That energy density due to an electric field is (A) E E H t The time varying electric field will produce a space varying orthogonal magnetic field. 9. Consider the following statements regarding Maxwell s equation in differential form:. For free space H j E. For free space,.d. For steady current, H J 4. For static electric field, 6 Which of the above statements are correct? (A) and and and 4 (D) 4 and For free space, the Maxwell s equations are: For static case.. D 0..D v. B E t. E 0. D H t. H J 4.. B 0 4..B 0 0. The equation which states the non-existence of isolated magnetic pole is (A).D.B 0.J (D) H J t ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 8

9 ..D v Gauss law. B E t Faraday's law. D H J Ampere's law t 4.. B0 non-existance of isolated magnetic pole. A periodic function satisfies Dirichlet s condition. This implies that the function (A) is non-linear is not absolutely integrable guarantees that Fourier series representation of the function exists (D) has infinite number of maxima and minima within a period. Consider Fourier representation of continuous and discrete-time systems. The complex exponentials (i.e., signals), which arise in such representation, have (A) Same properties always Different properties always Non-specific properties (D) Mostly same properties (A). If a dipole antenna has a radiation resistance of 7 the loss resistance of 7 and the power gain is 6, then the directivity is (A) 7.5 db 4.7 db 40 db (D) 4.6 db (D) P rad r Gd R rad R G R GP D Gd D in db 0log D.4dB Nearest approximation is Option D 4. An LTI system is causal if an only if (A) h(t) = 0 for t < 0 h(t) is finite for 0 t h(t) is finite for t < 0 (A) (D) h(t) is non-zero for all t ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 9

10 5. Let u[n] be the unit-step signal and xn un un n convergence of z-transform of x[n] is (A) z z z (D) z n xn un un n n xn u n n xnz X z n n0 n n n z n n. The region of n n z z n0 n0 n0 n0 n z z n o z z z z z z ROC : z ;ROC : z ROC : z ;ROC : z Common ROC z ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 0

11 6. If the z-transform of a sequence x[n] = {,,, ] is X[z], then the value of (A) (D) 5-9 (Not matching with given options) X is n X z X z x n z n xnz n0 o X z z z z z X n 9 7. If the z-transform of a system is given by Hz ROC: z, then the system is z where is real-valued,, z (A) A low-pass filter An all-pass filter A band-pass filter (D) A high-pass filter 8. Consider a discrete random variable assuming finitely many values. The cumulative distribution function of such a random variable is (A) Non-increasing function Non-decreasing function with finitely many discontinuities and assuming values less than one Non-decreasing function without discontinuities (D) Non-decreasing function assuming values larger than one. 9. A continuous random variable X has uncountably many values in the interval [a, b]. If C is a value in the interval [a, b], then P{X = C}. (A) is zero is strictly non-zero depends on the limits {a, b} (D) is less than one, but non-zero (A) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

12 0. In the case of a random variable dealing with non-deterministic signals. (A) It is a function from space of outcomes to the real/complex numbers It is a function with the probabilities of outcomes as random numbers The values assumed by signals are always deterministic (D) Sometimes the events associated with random variable are deterministic (A). The correlation function of a wide sense stationary random process representing a nondeterministic signal is (A) Not a deterministic function Deterministic, but not symmetric function Sometimes non-deterministic function (D) Always deterministic and symmetric function (D). What is an advantage of MOS transistor structure in integrated circuits? (A) Faster switching Less capacitance Higher component density and lower cost (D) Lower resistance. An LTI system has a wide-sense stationary (WSS) input signal with zero mean. Its output is (A) Non-zero mean and non-wss signal Zero mean and WSS signal Non-zero mean and WSS signal (D) Zero mean and non-wss signal 4. Which of the following statement are correct in association with the superposition theorem?. It is applicable to networks having more than one source.. It is used to determine the current in a branch or voltage across branch.. It is applicable to direct current circuits only. 4. It is applicable to networks having linear and bilateral elements. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

13 Select the correct answer using the code given below. (a), and (b), and 4 (c), and 4 (d), and 4 5. A network N consists of resistors, dependent and independent voltage and current sources. If the current in one particular resistance is I A, it will be doubled if the values of all the (a) Independent voltage sources are doubled. (b) Independent current sources are doubled (c) Dependent and independent voltage and current sources are doubled (d) Independent voltage and current sources are doubled (D) From the superposition theorem we know that the response across a particular element is the sum of response of the independent voltage and current source present in network there is not contribution of dependent source on it. And by homogeneity if a source it multiplied by K, response will also be multiplied by K. So if current is doubled i.e., the response is doubled then all the excitations (independent sources) will also be doubled. 6. The reactance of a 0 F capacitor at f=0hz (d.c) and f=50 Hz are respectively. (A) and and 8.47 and.84 (D) 0.0and.84 (A) X C C fc When f 0 X & When f 50 X 8.47 C C 7. Consider the following statements: Any element is redundant if connected in. Series with an ideal current source. Parallel with an ideal current source. Series with an ideal voltage source 4. Parallel with an ideal voltage source Which of the above statements are correct? (A) and and 4 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

14 and (D) and 4 R Is V L RL V R S I L RL a b From figure (a), observe that if we keep or remove R the load voltage and current are same so R is redundant here From figure (b), observe that if we keep or remove R, V L & I L is same and hence R is redundant Note that in figure (a) R can t be and in figure (b) R can t be 0, as it will result in violation of Kirchoff s law 8. Inductive reactance X is a function of inductance L and frequency f. The value of X increases when (A) Both L and f increase Both L and f decrease (A) XL L fl X L and X f L So, X L increases when both f and L increases. L increases and f decreases (D) L decreases and f increases 9. An alternating voltage is given by the equation v 8.84sin 77t 6 What are the values of r.m.s voltage, frequency and time period? (A) 0V, 60 Hz and s 00 V, 50 Hz and 0.0 s 00 V, 60 Hz and s (D) 0 V, 50 Hz and s ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 4

15 The standard form of A.C. voltage is Vt V sin ft Vt 8.84sin 77t 6 Comparing the above equation Vm 8.84 Vrms 00V T sec 77 f 60Hz T m 40. If a capacitor is energized by a symmetrical square-wave current source, then the steady-state voltage across the capacitor will be (A) A square wave A triangular wave A step function (D) An impulse function In a capacitor V idt t C Since integration of square wave is always a triangular wave, voltage in steady state across capacitor will always be a triangular wave. 4. The electric field in an electromagnetic wave (in vacuum) is described by E E sin kx t max where E 00N / C and K 0 m max 7 Speed of light is 8 0 m / s. What is the amplitude of the corresponding magnetic wave? (A) T 7. 0 T (D) T Given E E sin kx t E m m 00 N / C E H ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 5

16 E 00 H A / m 0 7 B 0H 40 Tesla 7 B.0 T For transverse electric waves between parallel plates, the lowest value of m, without making all the field components zero, is equal to (A) (D) 0 For transverse electric wave the lowest value of m is TE TE m When m 0, all the components will become zero m 4. A 0 db directional coupler is shown in the figure. 4 0 db The power output at port will be (A) 0 mw mw 5 mw (D) mw P Coupling factor = 0 =0 log P P P 00mW 00 P mw P mw 44. A loss-less transmission line of length l is open-circuited and has characteristic impedance Z o. The input impedance is (A) jzo tan l jzo tan l jzocot l (D) jzocot l The input impedance at the open circuited lossless transmission line is Zin jz0cot l ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 6

17 45. Conditions for a transmission line to be of low loss are (A) R L, G C R L, G C R L, G C (D) R L, G C Condition for low loss, R G L C R L G C 46. In a waveguide, attenuation near the cut-off frequency is (A) Low High Very high (D) Zero Near the cut off frequency, attenuation is almost infinite. So, attenuation is very high. 47. The phase velocity of waves propagating in a hollow metal waveguide is (A) Equal to the group velocity Equal to the velocity of light in free space Less than the velocity light in free space (D) Greater than the velocity of light in free space (D) Phase velocity of waves propagating in a hollow metal waveguide is greater than the free space velocity. V V P ; Always, V p V f fc 48. Compensation theorem applicable to antennas is also called as (A) Millman s theorem Superposition theorem Substitution theorem (D) Power transfer theorem ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 7

18 49. An isotropic radiator is one which radiates energy. (A) In a well defined direction uniformly in all directions Inside a hollow space (D) uniformly in horizontal plane Isotropic radiator, which radiates energy uniformly in all directions. 50. The effective length of an antenna is a measure of (A) Length of the antenna neglecting fringe effects Effectiveness of the antenna as a radiator/collector of electromagnetic energy Power consumed by the antenna (D) Range of the antenna Effective length of an antenna means, effectiveness of the antenna as a radiator of electromagnetic energy. 5. For a dipole antenna (A) The radiation intensity is maximum along the normal to the dipole axis The current distribution along its length is uniform irrespective of the length The effective length equals its physical length (D) The input impedance is independent of the location of the feed-point (A) For a dipole antenna, the radiation intensity is maximum along the normal to the dipole axis. 5. An ideal voltage source and an ideal voltmeter have internal impedances respectively (A) Zero, zero Zero, infinite Infinite, zero (D) Infinite, infinite In the voltage source (ideal), if R s =0 then only load voltage is independent of current drawn. In voltmeter internal impedance should be infinity, to avoid loading effect. 5. The current in a circuit is measured as 5 A and the accuracy of measurement is 0.5%. This current passes through a resistor 5k 0.%. The voltage is estimated to be 8. V. The error in the estimation would be (A) 0.06V 0.04V 0.06V (D) 0.V ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 8

19 (A) I 5A 0.5% R 5k 0.% V IR V 8.5 Volts %V %V 0.7% V V 00 V Volts 54. The full-scale deflecting torque of a 0A moving-iron ammeter is N m. What is the rate of change of self-inductance with respect to the deflection of the pointer of the ammeter at full scale? (A) 0.5 H / rad 0. H / rad. H / rad (D) 0. H / rad (D) For Moving Iron Ammeter, I dl T def. d 5 Given Tdef 60 N m and I 0A i.e., rate of change of self-inductance w.r.t. deflection 5 dl Tdef 60 0.H / rad d I The expected value of the voltage across a resistor is 80 V. However, the voltmeter reads 79V. The absolute error in the measurement is (A) 0.875V 0.5V.00V (D).5V Absolute error = Measured value True value Volt 56. A current of 0.5% A passes through a resistor of 00 0.%. The limiting error in the computation of power will be (A) 0.7% 0.9%.% (D).5% ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 9

20 I 0.5% A R 00 0.% P I R Watts %P % 57. A voltmeter reads 40 V on its 00 V range and an ammeter reads 75 ma on its 50 ma range in a circuit. Both the instruments are guaranteed % accuracy on FSD. The limiting error on the measured power is (A) 4% 5% 9% (D) % Measured value Full scale Accuracy V 40V 00V % I 75mA 50mA % 00 % 50 % %Error in V 5% ; %Error in I 4% % Error in P 5 4 9% 58. A voltmeter, having a guaranteed accuracy of % reads 9 V on a 0V to 50V range full scale reading. The percentage limiting error is (A) 0.67%.67% 6.7% (D) 0.067% 0 50 V Guaranteed accuracy of % 50 % % Limiting Error 6.67% A moving coil instrument has a resistance of 0 and gives a full scale deflection when carrying a current of 50 ma. What external resistance should be connected so that the instrument can be used to measure current up to 50 A? (A) 0 in parallel 00 in series 0.00 in parallel (D) 8.7 in series ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 0

21 Given, R 0 m I fs 50mA I 50A 0 Rsh A current of.0 A passes through a cell of e.m.f.5v having internal resistance of 0.5. The potential difference across the terminals of the cell is (A).5 V.50 V.00 V (D).0 V (D) By KVL, V 0 V.5 0. V.0 Volts.5V 0.5 A V 6. The atomic packing factor for face centered cubic (FCC) crystal structure is (A) (D) 6. A 4r B a C AC 4r From the triangle ABC, AC AB BC AC a a AC a AC a ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

22 v Atomic Packing Factor, APF N v atom unitcell Where'N'isno.of atomsin theunit cell V atom V a 4r (Volume of an atom) 44r APF a a Substituting r, we get 4 a 44 4 APF 0.74 a Thus, 74 percent of the volume of the FCC unit cell is occupied by atoms and the remaining 6 percent volume of the unit cell is vacant or void space. 6. Drift velocity in a metal is (A) Inversely proportional to the force on an electron due to applied electric field Directly proportional to the mass of an electron Proportional to the mobility of an electron (D) Inversely proportional to the strength of the applied electric field V d = μe, μ = mobility of an electron V d μ 6. The three kinds of breakdowns possible in solid dielectrics are electrothermal, purely electrical and (A) Electromechanical Electrochemical Purely thermal (D) Spontaneous The break down mechanism in dielectric material can be classified into are - () Avalanche Breakdown (pure electrical) () Thermal Breakdown (electrothermal) () Electro-chemical Breakdown (4) Defect Breakdown ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

23 64. For a particular material, the Hall coefficient is found to be zero. The material is (A) Intrinsic semiconductor Extrinsic semiconductor Metal (D) Insulator (D) 65. A V automobile light is rated at 0 W. The total charge that flows through the filament in one minute is (A) 0 C C 50 C (D) 80 C Q it ; p vi 0 i.5 Q Coulombs in one minute 66. At very high temperature, an n-type semiconductor behaves like (A) A p-type semiconductor An intrinsic semiconductor A superconductor (D) An n-type semiconductor Effect of Temperature: When the temperature of an n-type semiconductor is raised, the number of electron-hole pairs due to thermal excitation from the valence band to the conduction band will increase. Thus at a very high temperature the concentration of thermally generated free electrons from the valence band will be much larger than the concentration of free electrons contributed by the donors. At this situation, the hole and the electron concentrations will be nearly equal and the semiconductor will behave like an intrinsic one. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

24 67. The Fermi level in a p-type semiconductor lies close to (A) Top of the valence band Bottom of the valence band Top of the conduction band (D) Bottom of the conduction band (A) E E vacuum q q ptype ntype E C E F,n E i E F,p E V 68. Covalent bond energy in germanium is about (A) 7.4 ev ev.4 ev (D) 0.4 ev 0.7 ev (Not matching with given options) E g for Ge = 0.7eV 69. The relationship between relative permeability r and magnetic susceptibility of the medium is (A) r r r (A) r (D) r 70. Ferromagnetic property may be explained on the basis of (A) Faraday s theory Domain theory Curie-Weiss theory (D) Einstein s theory Weiss proposed domain theory to explain ferromagnetism. According to this theory, a single crystal of ferromagnetic solid compresses a large number of small regions and each region is spontaneously magnetized to saturation extent called a domain. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 4

25 7. Soft iron is characterized by the saturation magnetization M S, coercivity H C and retentivity B C. It is suitable for an electromagnet because (A) M S, H C and B C are small M S, is small, H C and B C are large M S, is large, H C and B C are small (D) M S, H C and B C are large The various applications of soft iron require the following properties - Ease of magnetization to high values, high saturation polarization, high maximum permeability, and low coercivity which means that M S is large and H C, B C are small. 7. Diamagnetic susceptibility is very (A) Small and negative Small and positive Large and negative (D) Large and positive (A) Magnetic susceptibility is negative for diamagnetic material. As a result, the magnetic field is weakened in the presence of the material. 7. Magnetostriction is the effect produced when change of magnetization in magnetic material results in (A) Change of permeability Change in dimensions Change of temperature (D) Change of magnetic field strength Magnetostriction is a property of ferromagnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation in magnetization due to the applied magnetic field on material changes the magnetostrictive strain until reaching its saturation value. 74. Commonly used dielectric in electrolytic capacitors is (A) Magnesium oxide Cadmium nitride Aluminium oxide (D) Manganese oxide ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 5

26 75. How many 6 F,00V capacitors are needed to make a capacitor of 8 F, 600V? (A) 8 9 (D) 7 (D) Energy principle must be statisfied. Here CT 8 F VT 600 CTVT n CV 66 n A voltage of 000 V exists across cm insulating space between two parallel conducting plates. An electron of charge the electron is coulomb is introduced into the space. The force on 6 (A) 8. 0 N 4. 0 N N (D) N v F qe q l 4 F. 0 N A capacitor of 00 F stores 0 mj of energy. What is the amount of charge (in coulomb) stored in it (A) (D) V 0m J V 4.4 Q CV.44 0 C 78. In degenerately doped n-type semiconductor, the Fermi level lies in conduction band when (A) Concentration of electrons in the conduction band exceeds the density of states in the valence band. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 6

27 Electron energy Electron energy Objective Paper-I EC- Objective Paper-I IES-04 Concentration of electrons in the valence band exceeds the density of states in the conduction band. Concentration of electrons in the conduction band exceeds the product of the density of states in the valence band and conduction band (D) None of the above Conduction band E F Filled states (electrons) E C E V a Conduction band Empty states (holes) ValenceBond E C E V E F b Valence band Simplified Energy Band Diagram for deg enerately doped a ntype semiconductor b ptype semiconductor 79. The electrical conductivity and electron mobility for aluminium are ohm m and 0.00m / V-s respectively. What is the Hall voltage for an aluminium specimen that is 5 mm thick for a current of 5 A and a magnetic field of 0.6 tesla (imposed in a direction perpendicular to the current) for the given value of Hall coefficient.6 0 V m/ A-tesla? R H as (A) V V V (D) V ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 7

28 V H R H BI Thickness d Volts The purpose of connecting a Zener diode in a UJT circuit, used for triggering thyristors, is to (A) Expedite the generation of triggering pulses Delay the generation of triggering pulses Provide a constant voltage to UJT to prevent erratic firing (D) Provide a variable voltage to UJT as the source voltage changes 8. A moving-coil meter has a resistance of and gives full-scale deflection with 0 ma. What external resistance should be added in series so that it can measure voltages up to 00 V? (A) (D) 0.0 Given, Rm I m 0mA V I R 90 mv se m m m V 00 Volts R R m 00 90* Consider the following system function of a discrete-time LTI system: Hz z a * az where a* is the complex conjugate of a. The frequency response of such a system is (A) Aperiodic; depends on frequency ω Aperiodic; does not depends on frequency ω Periodic; depends on frequency ω (D) Periodic; does not depends on frequency ω ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 8

29 (D) Hz z a az * This is a standard transfer function of APF with magnitude response H (Link for reference: ) 8. Absolute encoders are normally used for (A) One revolution Continuous speed in clockwise direction Continuous speed in counter-clockwise direction (D) Counting least significant bits (A) Absolute encoders are position feedback devices that report absolute positional information. An absolute encoder generates a unique code for each position. 84. Consider the following statements: Piezoelectric transducer has. A very good HF response. Typical output voltage of the order of mv to 0 mv per unit of acceleration. No requirement of external power and is self-generating 4. No response for static conditions Which of the above statements are correct? (A), and only, and 4 only and 4 only (D),, and 4 (D) 85. An inductive pick-up used to measure the speed of a shaft has 0-tooth wheel. If the number of pulses produced in a second is 000, the r.p.m of the shaft is (A) (D) R.P.M of shaft ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 9

30 86. A piezoelectric crystal having a thickness of mm and a voltage sensitivity of 0.0 V-m/N is subjected to a pressure of 0 0 Pa. What is the output voltage? (A) V 0.80 V V (D) V Output voltage = P g t V 87. A resistance strain gauge with gauge factor of is cemented to a steel member subjected to a 6 strain 0. If the original resistance is 00, what is the change in resistance? (A) m 00 (D) 00 (A) G R? R R strain R GR The dynamic characteristics of capacitive transducers are similar to those of (A) Low-pass filter High-pass filter Notch filter (D) Band-stop filter 89. Cold junction in a thermocouple is (A) The reference junction maintained at a known constant temperature The junction maintained at a very low temperature The junction at which the temperature is sensed (D) None of the above (A) The thermocouple voltage is a function of the difference between the hot junction temperature T A and the cold junction temperature T B. If the cold junction temperature is kept fixed or constant, the thermocouple output is a measure of the hot junction temperature T A. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 0

31 90. The output voltage of a linear variable differential transformer is.5 V at maximum displacement. At a load of 0.5M, the deviation from linearity is maximum and it is 0.00V from a straight line through origin. What is the linearity at the given load? (A).5% 0. %. % (D) 5 % Directions: Each of the next Ten (0) items consists of two statements, one labelled as the Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the code given below. Code: (A) Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I) Both Statement (I) and Statement (II) are individually true but Statement (II) is not the correct explanation of Statement-(I) Statement (I) is true but Statement (II) is false (D) Statement (I) is false but Statement (II) is true 9. Statement (I): Hard magnetic materials are used for making permanent magnets Statement (II): Hard magnetic materials have relatively small and narrow hysteresis loop. Statement (I) - True Ferromagnetic materials are difficult to magnetize, but once magnetized, it is difficult to demagnetize. These materials are called hard magnetic materials, and are suitable for applications such as permanent magnets and magnetic recording media. Hard magnetic materials have high magnetocrystalline anisotropy. Since large magnetic field is required to demagnetize their coercivity, H c is usually high. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

32 Statement (II) - False B SOFT HARD Large hysteresis loop for hard magnetic materials H 9. Statement (I): With a small additional energy usually thermal, the valence electrons in germanium can become free electrons. Statement (II): The valence electrons in germanium are in the fourth orbit and are at high energy level. 9. Statement (I): An FET is a current-controlled device. Statement (II): Operation of an FET depends only on majority carriers. (D) FET is a voltage-controlled device and its operation depends only on majority carriers. So Statement I is wrong, Hence, ans is (D) 94. Statement (I): Thermal runaway is not possible in an FET Statement (II): As the temperature of FET increases, the mobility of carriers decreases (A) Statement (I) - True FETs prevent the thermal runaway phenomena that may occur in BJTs. Statement (II) - True ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

33 This means that, as the device temperature increases, the current through the device decreases due to two competing mechanisms.. Increasing the temperature of an FET tends to decrease the mobility of the charge carriers in the channel, effectively reducing the current through the channel.. Simultaneously however, increasing the temperature also narrows the depletion regions of the pn junctions, thereby increasing the drain current. Statements I and II both are correct and Statement-II is correct explanation of Statement-I. 95. Statement (I): In an enhancement type MOSFET (with n-type source and drain regions), only positive voltage can be applied to the gate with respect to the substrate (p-type) Statement (II): Only with a positive voltage to the gate, an inversion layer is formed and conduction can take place. (A) Source Gate Drain S G D N P N N N N Depletion P inverted channel depletion 96. Statement (I): Under steady-state condition, a pure capacitor behaves as an open circuit for direct voltage. Statement (II): (A) dv i C dt The current through a capacitor is proportional to the rate of change of voltage. dv for D.C. is always 0 dt So i 0 open circuit ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India

34 dv Sin ce dt i.e., rate of change of voltage is 0 Capacitor is behaving like open circuit. 97. Statement (I): The standard definition of stability precludes sin 0t term in impulse response. Statement (II): (A) sin t is a periodic function Statement (I): Helical antenna has the largest bandwidth, high directivity and circular polarization. Statement (II): Log-periodic antenna has a broad bandwidth. 99. Statement (I): Current-limiting resistor is used in series with the light-emitting diode (LED) to limit current and light output. Statement (II): The light output of a light-emitting diode (LED) is approximately proportional to the current passing through it. (A) Statement (I): Series resistors are a simple way to stabilize the LED current, but energy is wasted in the resistor. The resistance of the cell itself is usually the only current limiting device. Statement (II): Light emitting diode can emit any form of light. It needs a current to flow through it, as it is a current dependent device with their light output intensity being directly proportional to the forward current flowing through the LED. 00. Statement (I): An analog system has at its output stage a PMMC indicating instrument, while a digital meter output stage has an LCD/LED display device. Statement (II): ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 4

35 Since the analog system is continuous in time, display device can respond to it if the signal frequency is low, while digital system being a discrete one, it does not require change and can be latched at the value of measurement. 0. A bridge rectifier uses a 9V a.c. input voltage. The diodes are ideal. What is the d.c. output voltage? (A).76 V -.76 V 9 V (D) 8. V (D) V V V m m Vdc ; rms Vm.7 V dc V 0. A half-wave rectifier is used to supply 50V d.c. to a resistive load of 800. The diode has resistance of 5. What is the required a.c. voltage? (A) (D) 5 V dc m V M V 50 A.C voltage across diode Require A.C. voltage If an input signal ranges from 0 A -40 A with an output signal ranging from 0.5 ma-.5 ma, what is the a.c.? (A) (D) 500.5mA 0.5mA ma a.c 50 40A 0A 0A ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 5

36 04. The best device for improving the switching speeds of bipolar transistors is (A) Speed-up capacitor Transistor with higher cut-off frequency Clamping diode (D) Clamping diode with zero storage time (D) 05. The early effect in bipolar junction transistor is caused by (A) Fast turn-off Fast turn-on Large emitter to base forward bias (D) Large collector to base reverse bias (D) The Early effect is the variation in the width of the base in a bipolar junction transistor (BJT) due to a variation in the applied base-to-collector voltage, A greater reverse bias across the collector-base junction, for example, increases the collector-base depletion width, decreasing the width of the charge neutral portion of the base. 06. The basic material for fabrication of an LED is (A) Gallium arsenide Gallium arsenide phosphide Indium antimonide (D) Indium antimonide phosphide (A) In LED, direct band gap materials are used for fabrication (GaAs, GaN, InN, AIN, GaP, InP etc.) among which the basic binary parent compound is Gallium Arsenide. 07. To get higher cut-off frequency in a BJT, sheet resistance should be (A) Low High Equal to cut-off frequency (D) Zero (A) In order to reduce the transit time, the base width is required to scale to provide an increase in the unity current gain cutoff frequency, f T. Moreover, the base doping concentration must be increased to achieve a high unity power gain cutoff frequency, f MAX, to provide a low base sheet resistance as the base width is scaled. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 6

37 08. A BJT operates as a switch (A) In the active region of transfer characteristics With no signal condition Under small signal conditions (D) Under large signal conditions (D) 09. n-p-n transistors are preferred over p-n-p transistors because they have (A) High mobility of holes High mobility of electrons Low mobility of holes (D) Higher mobility of electrons than the mobility of holes in p-n-p transistors 0. What is the biasing condition of junctions in bipolar junction transistor to work as an amplifier? (A) Reverse biased base to emitter junction and reverse biased base to collector junction. Forward biased base to emitter junction and reverse biased base to collector junction. Forward biased base to emitter junction and forward biased base to collector junction. (D) Reverse biased base to emitter junction and forward biased base to collector junction.. In a JFET, operating above pinch-off voltage, the (A) Drain current increases steeply. Drain current remains practically constant. Drain current starts decreasing. (D) Depletion region reduces. (i) The drain current I D rises rapidly with drain-source voltage (V DS ) but then becomes constant. The drain-source voltage above which drain current becomes constant is known as pinch off voltage. (ii) After pinch off voltage, the channel width becomes so narrow that depletion layers almost touch each other. The drain current passes through the small passage between these layers. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 7

38 Therefore, increase in drain current is very small with V DS above pinch off voltage. Consequently, drain current remains constant.. If V CC = 8V, voltage divider resistances R = 4.7k and R = 500, what is the base bias voltage? (A) 8.70 V 4.5 V.90 V (D) 0.70 V V k k CC VB 4.5V. An SCR has an anode supply of sine voltage 00 V r.m.s., 50 Hz applied through a 00 resistor and fired at an angle of 60. Assuming no voltage drop, the r.m.s. value of the output voltage is nearly. (A) 90 V 6 V 66 V (D) 00 V m V o rms V sin 00 sin V ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 8

39 4. In a GTO, anode current begins to fall when gate current (A) Is negative peak at time t = 0. Is negative peak at time t = storage period Just begins to become negative at t = 0 (D) Just begins to become positive at t = 0 V A E dc I A V A V A I A Spike voltage I d Tail current t TS T f Tt Voltage and Current waveforms Ig Toff during turn off of a GTO Gate current t 0 I gp 5. An SCR is turned off when its turn-off time is (A) Less than the circuit time constant Greater than the circuit time constant Less than the circuit turn-off time (D) Greater than the circuit turn-off time For realiable turn-off of device, device turn-off time (t q ) should be less than circuit turn off time (t c ). ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 9

40 6. A system is characterized by the input-output relation y(t) = x(t)+x(t) for all t, where y(t) is the output and x(t) is the input. It is (A) Linear and causal Non-linear and causal Let input = x (t) & output = y (t) y t x t x t Let input = x (t) & output = y (t) y t x t x t Let input = x (t) + x (t) and output be y (t) y t x t x t x t x t y t x t x t x t x t y t y t y t Hence system is linear. For causality substitute certain values. Let t =, y x x Present output defends on future inputs Hence system is non-causal. Linear and non-causal (D) Non-linear and non-causal m 7. A discrete-time system has input x[.] and output y[.] satisfying ym x j. The j system is (A) Linear and unstable Non-linear and stable (A) Linear and stable (D) Non-linear and unstable y m x j m j m y m x j j m y m x j x j j m m j j x j x j ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 40

41 y m y m y m System is linear. Let input x[j] be a bounded input u[j]. m ym u j j m u j y m j0 ym rm = ramp sequence = unbounded output. Hence system is unstable. 8. The Fourier transform of a rectangular pulse for a period (A) A sinc function A cosine function (A) A sine function T T t to t is (D) A sine-squared function Fourier transform of a finite durated rectangular pulse of a certain period transformers to a sine function of infinite duration. 9. The current waveform i(t) in a pure resistor of 0 is shown in the figure it t The power dissipated in the resistor is (A) 5 W 70 W 540 W (D) 4.58 W RMS P i t R RMS P i t.0 irms t dt t 0 RMS 0 i 9t dt ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 4

42 RMS t.9. i 7 P 7 0 P 540W 0 0. A p-type silicon sample has an intrinsic carrier concentration of /cm and a hole concentration of /cm. Then the electron concentration is (A) /cm 0 5 /cm 0 0 /cm (D) 0 By mass-action law, In P-type n p n n p p i n n p n i i p 5 pp.50 5 n 0 p cm ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series India s No. institute for GATE Training 65+ Centers across India 4