** 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<∞, are a) 0 and 270 b) 0 and 180 c) 90 and 270 d) 90 and 180 70. The bode plot corresponding to a proportional derivative controller is the one shown in given figure 71. In frequency modulation, the instantaneous a) amplitude of the carrier signal is varied with the instantaneous amplitude of the message signal b) amplitude of the carrier signal is varied with the instantaneous frequency of the message signal c) frequency of the carrier signal is varied with the instantaneous amplitude of the message signal d) frequency of the carrier signal is varied with the instantaneous frequency of the message signal 72. If X is a zero mean Gaussian random variable, then P{X<=0} is a) 0 b) 0.25 c) 0.5 d) 1 73. 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 is a) 5W b) 10W c) 12W d) 15W 74. In a superheterodyne receiver, rejection of the image signal can be achieved by using a a) higher local oscillatorn frequency b) crystal oscillator c) narrow band IF filter d) narrow band filter at RF stage 75. The number of bbits per sample of a PCM system depends upon the a) sampler type b) quantizer type c) number of levels of the quantizer d) sampling rate 76. Which one of the following is used for the detection of AM‐DSB‐SC signal a) Ratio detector b) Foster‐Seeley discriminator c) Product demodulator d) Balanced‐slpoe detector 77. Which one of the following signal pairs can represent a BPSK signal a) A cos2πfct, A sinπfct b) A cos2πfct, ‐ A sinπfct c) ‐ A cos2πfct, A sinπfct d) A sin2πfct, A cosπfct 78. Which one of the following can be used for the detection of the noncoherent BPSK signal a) matched filter b) phase‐locked loop c) envelope detector d) product demodulator 79. 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 frequency a) |F – Fc|Tb = 0 b) |F – Fc|Tb = 1 c) |F – Fc|Tb = 2 d) |F – Fc|Tb = 4 80. 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, is a) (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 is a) –p(t‐T), 0<=t<=T b) –p(T‐t), 0<=t<=T c) p(t‐T), 0<=t<=T d) p(T‐t), 0<=t<=T 82. The multiple access communication scheme in which each user is allocated the full available channel spectrum for a specified duration of time is known as a) CDMA b) FDMA c) TDMA d) MC‐CDMA 83. GSM system uses TDMA with a) 32 users per channel b) 16 users per channel c) 8 users per channel d) 4 users per channel 84. 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 is a) EX^3 – E^3X b) EX^3 + 2E^3X – 3EX Ex^2 c) 3EX^3 – E^3X d) 2EX^3 + E^3X – 3EX EX^2 86. 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 is a) ¼ b) 1 c) 7/4 d) 2 87. 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 is a) 600 bps b) 1200 bps c) 4800 bps d) 7200 bps 88. For the vectors A = X ax + Y ay and B = Z az, del . (A X B) is a) 0 b) 1 c) XZ d) YZ 89. Which one of the following relations represents Strokes’ theorem (symbols have their usual meaning)? a) ∫s del X A.ds = 0 b) ∫L A.dl = ∫s del X A.ds c) ∫s A X dS = ‐∫v (del X A)dv d) ∫v del.Adv = ∫s A.ds 90. Which one of the following relations is not correct (symbols have their usual meaning)? a) del X E = ‐ ∂B/∂t b) del X H = J + ∂E/∂t c) del.D = ρv d) del.B = 0