** Company: ** Electronics Corporation of India Limited

61. The characteristic equation of an LTI system is given as s^3 + Ks^2 + 5s + 10. When the system is marginally stable, the value of K and the sustained oscillation frequency w, respectively, are

a) 2 and 5

b) 0.5 and √5

c) 0.5 and 5

d) 2 and √5

62. The time required for the response of a linear time‐variant system to reach half the final value for the first time is

a) delay time

b) peak time

c) rise time

d) decay time

63. The signal flow graph of the given network is

64. Let c(t) be the unit step response of a system with transfer function K(s+a)/(s+K). If c(0+)=2 and c(∞)=10, then the values of a and K, respectively, are

a) 2 and 10

b) ‐2 and 10

c) 10 and 2

d) 2 and ‐10

65. The loop transfer function of an LTI system is G(s)H(s)= K(s+1)(s+5) / s(s+2)(s+3). For K>0, the point on the real axis that DOES NOT belong to the root locus of the system is

a) ‐0.5

b) ‐2.5

c) ‐3.5

d) ‐5.5

66. The state space equation of the circuit shown in given figure for x1=v0, x2=I is

67. The open loop gain of a unity feedback system is G(s)=wn^2 / s(s+2wn). The unit step response c(t)

of the system is

69. The angles of the asymptotes of the root loci of the equation s^3 + 5s^2 + (K+2)s + K = 0, for

0<=K<∞, area) 0 and 270b) 0 and 180c) 90 and 270d) 90 and 18070. The bode plot corresponding to a proportional derivative controller is the one shown in given figure71. In frequency modulation, the instantaneousa) amplitude of the carrier signal is varied with the instantaneous amplitude of the message signalb) amplitude of the carrier signal is varied with the instantaneous frequency of the message signalc) frequency of the carrier signal is varied with the instantaneous amplitude of the message signald) frequency of the carrier signal is varied with the instantaneous frequency of the message signal72. If X is a zero mean Gaussian random variable, then P{X<=0} isa) 0b) 0.25c) 0.5d) 173. If a single‐tone amplitude modulated signal at a modulation depth of 100% transmits a total power of 15W, the power in the carrier component isa) 5Wb) 10Wc) 12Wd) 15W74. In a superheterodyne receiver, rejection of the image signal can be achieved by using aa) higher local oscillatorn frequencyb) crystal oscillatorc) narrow band IF filterd) narrow band filter at RF stage75. The number of bbits per sample of a PCM system depends upon thea) sampler typeb) quantizer typec) number of levels of the quantizerd) sampling rate76. Which one of the following is used for the detection of AM‐DSB‐SC signala) Ratio detectorb) Foster‐Seeley discriminatorc) Product demodulatord) Balanced‐slpoe detector77. Which one of the following signal pairs can represent a BPSK signala) A cos2πfct, A sinπfctb) A cos2πfct, ‐ A sinπfctc) ‐ A cos2πfct, A sinπfctd) A sin2πfct, A cosπfct78. Which one of the following can be used for the detection of the noncoherent BPSK signala) matched filterb) phase‐locked loopc) envelope detectord) product demodulator79. Bits of duration Tb are to be transmitted using a BPSK modulation with a carrier of frequency Fc Hz. The power spectral density of the transmitted signal has the first null at the normalized frequencya) |F – Fc|Tb = 0b) |F – Fc|Tb = 1c) |F – Fc|Tb = 2d) |F – Fc|Tb = 480. The probability of bit error of a BPSK modulation scheme, with transmitted signal energy per bit Eb, in an additive white Gaussian noise channel having one‐sided power spectral density N0, isa) (1/2) erfc(Eb/2N0)b) (1/2) erfc√(Eb/2N0)c) (1/2) erfc(Eb/N0)d) (1/2) erfc√ (Eb/N0)81. For a given transmitted pulse p(t), 0<=t<=T, the impulse response of a filter matched to the received signal isa) –p(t‐T), 0<=t<=Tb) –p(T‐t), 0<=t<=Tc) p(t‐T), 0<=t<=Td) p(T‐t), 0<=t<=T82. The multiple access communication scheme in which each user is allocated the full available channel spectrum for a specified duration of time is known asa) CDMAb) FDMAc) TDMAd) MC‐CDMA83. GSM system uses TDMA witha) 32 users per channelb) 16 users per channelc) 8 users per channeld) 4 users per channel84. If Rx(τ) is the auto‐correlation function of a zero‐mean wide‐sense stationary random process X, then which one of the following is NOT true?a) Rx(τ) = Rx(‐τ)b) Rx(τ) = ‐Rx(‐τ)c) σx^2 = Rx(0)d) |Rx(τ)| <=Rx(0)85. If E denotes the expectation operator, then E[X‐EX]^3 of a random variable X isa) EX^3 – E^3Xb) EX^3 + 2E^3X – 3EX Ex^2c) 3EX^3 – E^3Xd) 2EX^3 + E^3X – 3EX EX^286. A discrete memoryless source produces symbols m1,m2,m3 and m4 with probabilities 1/2, 1/4 , 1/8 and 1/8, respectively. The entropy of the source isa) ¼b) 1c) 7/4d) 287. A channel has a signal‐to‐noise ratio of 63 and bandwidth of 1200 Hz. The maximum data rate that can be sent through the channel with arbitrary low probability of error isa) 600 bpsb) 1200 bpsc) 4800 bpsd) 7200 bps88. For the vectors A = X ax + Y ay and B = Z az, del . (A X B) isa) 0b) 1c) XZd) YZ89. Which one of the following relations represents Strokes’ theorem (symbols have their usual meaning)?a) ∫s del X A.ds = 0b) ∫L A.dl = ∫s del X A.dsc) ∫s A X dS = ‐∫v (del X A)dvd) ∫v del.Adv = ∫s A.ds90. Which one of the following relations is not correct (symbols have their usual meaning)?a) del X E = ‐ ∂B/∂tb) del X H = J + ∂E/∂tc) del.D = ρvd) del.B = 0