INDIAN SPACE RESEARCH ORGANISATION. Recruitment Entrance Test for Scientist/Engineer SC 2017

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1 1. The signal m (t) as shown is applied both to a phase modulator (with kp as the phase constant) and a frequency modulator with ( kf as the frequency constant) having the same carrier frequency. The ratio deviation is kp / kf (in rad/hz) for the same maximum phase 8 π 4 π π π. message m (t) bandlimited to the frequency fm has a power of Pm. The power of the output signal in the figure is ( P mcosθ )/ ( Pm sin ) / P m / 4 P mcos θ / 4 θ 3. The input x(t) and output y(t) of a system are related as t y ( t) = x ( t) cos(4t) dt The system is time-invariant and stable stable and not time-invariant time-invariant and not stable not time-invariant and not stable Electronics 3

2 4. Consider a system shown in the figure. Let X (f ) and Y (f ) denote the Fourier transforms of x (t) and y (t) respectively. The ideal HPF has the cut-off frequency 10 KHz. The positive frequencies where Y (f ) has spectral peaks are 1 KHz and 4 KHz KHz and 4 KHz 1 KHz and 14 KHz KHz and 14 KHz 1 5. Let x ( t) = rect t where rect ( t) = 1 for Transform of x( t) + x( t) will be given by 1 1 t and zero otherwise, then Fourier sinc ω ω sinc ω ω sinc cos ω ω sinc sin Electronics 4

3 6. signal x( t) = sinc ( α t), where α is a real constant, is the input to a Linear Time Invariant system whose impulse response is h( t) = sinc ( β t), where β is a real constant. If min( α, β ) denotes the minimum of α and β and similarly, max( α, β ) denotes the maximum of α and β, and K is a constant, which one of the following sin(π x) statements is true about the (here, sinc ( x) = ) output of the system? π x It will be of the form K sinc ( γ t) where γ = min( α, β ) It will be of the form K sinc ( γ t) where γ = max( α, β ) It will be of the form K sinc ( α t) It cannot be a sinc type of signal 7. message signal given by m t) = (1/ ) cos( ω t) (1/ )sin( ω ) is amplitude modulated with a carrier of frequency ( 1 t ω to generate s( t) = [1 + m( t)]cos( ω t). What is the power c efficiency achieved by this modulation scheme? 8.33% 11.11% 0% 5% c 8. If E b, the energy per bit of a binary digital signal, is one-sided power spectral density of the white noise, SNR of the matched filter is 5 10 Ws (Watt-Second) and the N 0 = 10 6 W/Hz, then the output 6 db 10 db 0 db 13 db 9. t a given probability of error, binary coherent FSK is inferior to binary coherent PSK by. 6 db 3 db db 0 db 10. If z 0 is a zero of a (real-valued) linear-phase FIR filter then following is/are also zero/zeros of a (real-valued) linear-phase FIR filter, 0 z 1/ z0 0 1/ z 0, z and 1/ z 0 1/ z 0 and 1/ z 0 Electronics 5

4 11. What will be the minimum numbers of tap require to realize a FIR filter having fpass = 10 khz and fstop =15 khz, 0.1 db pass band ripple and 60 db attenuation in stop band. Sampling frequency is 00 khz The system with the transfer function for the input signal Y( s) s = X( s) s + p has an output π x ( t) = pcos t. Then, the system parameter p is 3 1 / 3 3 / π y( t) = cos t The approximate Bode magnitude plot of a minimum phase system is shown in the figure below. The transfer function of the system is db P 1P 0 3Z ω 10 8 ( s + 0.1) ( s + 10) ( s + 100) 10 7 ( s + 0.1) ( s + 10) 3 ( s + 100) 10 8 ( s + 0.1) ( s + 10) 3 ( s + 100) 10 7 ( s + 0.1) ( s + 10) ( s + 100) Electronics 6

5 14. For the circuit of the figure the inductor current i L just before t = 0 is 5H The network shown in below figure consist of two coupled coils and a capacitor. t t t = 0, the switch is closed connecting a voltage generator, v in = V sin. What MC dv will be the value of a ( 0+ )? dt V L M C V L V M 0 L C Electronics 7

6 16. In the network shown below, switch is moved from position a to b at t = 0. The current i L (t) for t > 0 is given as ( 4 6t) e (3 6t) e (3 9t) e (3 8t) e 4t 4t 5t 5t 17. The voltage gain values of C is v out v in of a circuit shown below is zero. If ω = rad/s, the 3.33 mf mf 3.33 uf uf Electronics 8

7 18. In the network shown below, switch is opened at t = 0 after long time. The current i L (t) for t > 0 is given as e t (cost + 4sin t) e t (3sin t 4cost) e t ( 4sin t + cost) e t (sint 4cost) 19. The Q factor of a RLC circuit is 5 at its resonance frequency of 1 khz. Find the bandwidth of the circuit 100 Hz 00 Hz 400 Hz 50 Hz 0. For the circuit shown in figure, find the frequency at which this circuit will be at resonance j/ω Ω I 1 jω Ω I Zin I 1 Ω 1 rad/sec rad/sec 0.5 rad/sec 0.5 rad/sec 1. What is the power loss in the 10 Ω resistor in the Network shown in figure? Electronics 9

8 10 Ω 8 Ω 3 Ω 5 Ω + 15 V Ω W W 1.3 W 13. W. The voltmeter in the circuit shown in the figure is ideal. The transformer has two identical windings with perfect coupling. The reading on the voltmeter will be V 0 V, 50 Hz 440 V 0 V 110 V Zero Electronics 10

9 3. The Theveαnin s equivalent circuit of the network shown in figure is across a-b is + a I Ω 6 Ω V =10 V 1 Ω Ω 3 Ω 4 Ω 4. The average power consumed by the following circuit is + I b R = 3.33 Ω V XL =.5 Ω Vrms = V 100 W 110 W 10 W 160 W 5. The given figure shows the pole zero pattern of a filter in the S-plane. The Filter in question is a j ω S-plane ω o σ ω o Band elimination filter Band pass filter Low Pass Filter High Pass Filter Electronics 11

10 6. Output voltage V0 of the circuit shown in figure below. (The input voltages are V1 =.5 V & V = 1 V).5 V 1 V V1 V 1 k 3.3 k +. k V0 1.5 k 4.0 V 4.0 V 4.5 V 4.5 V 7. Without any additional circuitry an 8:1 MUX can be used to obtain Some but not all Boolean functions of 3 variables ll function of 3 variables but none of 4 variables ll functions of 3 variables and some but not all of 4 variables ll functions of 4 variables 8. The circuit shown in the figure converts BCD to binary code Binary to Excess-3 code Excess-3 to Gray code Gray to Binary code Electronics 1

11 9. The following CMOS transistor based circuit with, B, C as input and X, Y as output represents which circuit? Positive edge trigger J-K Flip-Flop Negative edge trigger J-K Flip-Flop Positive edge trigger S-R Flip-Flop None of the above 30. Minimum number of complementary CMOS transistors pair will be required to implement function, F = BC + ( + B + C) are The CMOS circuit shown below implements the function ( + B) C + D ( B + C) + D ( + B) C + D ( B + C) D Electronics 13

12 3. If input to T flip flop is 00 Hz signal, then what will be the output signal frequency if four T flip flops are connected in cascade 00 Hz 50 Hz 800 Hz None of the above 33. Simplify the below function represented in sum of minterms F (, B, C, D, E) = (0, 1,, 3,8, 9, 16, 17, 0, 1, 4, 5, 8, 9, 30, 31) D + ( C + D) + B C + ( + B + C ) DE + ( C + E) D + B CD + E C DB + ( C + B) + C D E + ( B + C + D ) C + ( D + E) + E + ( C + D + E ) 34. ll transistor in the N output current mirror in figure given below are matched with a finite gain β and early voltage V =. The expression for load current is V + I1 I IN Iref R1 QS QR Q1 Q QN V I ref (1 + N ) 1 + β( β + 1) I ref N 1 + β ( β + 1) β I ref (1 + N ) 1 + β( β + 1) β I ref N 1 + β ( β + 1) Electronics 14

13 35. Class C amplifier operates Entire cycle of i/p signal Half of the cycle of i/p signal Slightly more than half of the cycle of i/p signal Less than half of the cycle of i/p signal 36. particular amplifier circuit used for frequency doubling is. Push-push Push-pull Pull-push Pull-pull 37. The configuration of given figure is a + Vo Precision Integrator Hartley Oscillator Butterworth high pass filter Wein bridge oscillator 38. For current flowing through semi-conductor, which of the following statement is true Only conduction current Only Diffusion Current Conduction Current + Diffusion Current None of the above 39. Which of the following statement is true for Programmable Logic array(pl)? Electronics 15

14 Fixed ND array and Fused programmable OR array Fused programmable ND array and Fixed OR array Fused programmable ND array and Fused programmable OR array None of the above 40. When transistors are used in digital circuits they usually operate in the: ctive region Breakdown region Saturation and cut-off regions Linear region 41. Two initially identical samples & B of pure germanium are doped with donors to concentrations of and respectively. If the hole concentration in is then the hole concentration in B at the same temperature will be m m m m 3 4. The built in potential (diffusion potential) in a p-n junction Is equal to the difference in the fermi level of the sides, expressed in volts Increase with the increase in the doping levels of the two sides Increase with the increase in temperature ll of the above 43. Transistors Q 1 and Q are identical and β >> 1 in the circuit shown in the figure below. The output voltage is (Vt = 0.06 V): Electronics 16

15 R1 R v1 v 0 kω 0 kω 333 kω 333 kω v 0 v log 10 v 1 R R 1 v log 10 v 1 R R 1 v.3 log 10 v 1 R R 1 v 4.6 log 10 v 1 R R Consider following 8085 microprocessor program MVI, DT1 OR JM DISPLY OUT PORT1 CM DISPLY : DI 01H OT PORT1 HLT If DT1 = 7H, the output at PORT1 is 7H 58H 00H 59H 45. From the figure, obtain state equation Electronics 17

16 [ X ] = [ X ] + u [ X ] = X + u 4 1 [ ] [ X ] = [ X ] + u [ X ] = X + u 4 0 [ ] In an DC, the minimum Effective Number of Bits (ENOB) requires to represent each quantization level to achieve Signal to Noise and Distortion Ratio (SIND) of 70 db is 8 bits 10 bits 11 bits 1 bits 47. Two isotropic antennas are separated by a distance of two wavelengths. If both the antennas are fed with currents of equal phase and magnitude, the number of lobes in the radiation pattern in the horizontal plane are The half-power beam width (HPBW) of an antenna in the two orthogonal planes are 10 and 40 respectively. The directivity of the antenna is approximately equals to 10 db 6.5 db 1 db 8.5 db 49. Two resistors R 1 and R (in ohms) at temperatures T 1 K and T K respectively, are connected in series. Their equivalent noise temperature is T 1 + T R 1T1 + RT R T + R T )/( R ) R T + R T )/( R + ) ( 1 1 1R ( R Electronics 18

17 50. The Gray code for ( 5) 16 is equivalent to In Direct Broadcast System (DBS), MPEG- is used for video compression MPEG- is used for video enhancing MPEG- is used for audio compression None of these 5. If analog sampling frequency of a band limited signal is doubled then corresponding digital sampling frequency will be π π π / None of the above 53. In communication system, if for a given rate of information transmission requires channel bandwidth, B 1 and signal-to-noise ratio SNR 1. If the channel bandwidth is doubled for same rate of information then new signal-to-noise ratio will be SNR 1 SNR 1 SNR 1 SNR 1 / 54. Output SNR of a 10 bit PCM was found to be 30 db, desired SNR is 4 db. To achieve desired SNR by increasing the number of quantization levels, then new levels will be Electronics 19

18 55. Let Y (k) be the 5-point DFT of the sequence y ( n) = { }. What is the 5-point DFT of the sequence Y (k)? [ j j j.5 3.4j] [ ] [ ] [ ] 56. Let be the series ( 1) = log( n + n n 1 ) and B be the series n = 3n 4 3k + ( n+ 1) 3 for real numbers. Then which of the following is true. Both the series and B are divergent Both the series and B are convergent Series is convergent and series B is divergent Series is conditionally convergent and series B is divergent 57. test has 5 multiple-choice questions. Each question has 4 answer options (, B, C, D). What is the probability that a student will choose B for at least three questions if he/she leaves no questions blank? 1/104 1/64 53/51 9/18 Electronics 0

19 58. The DTFT of a sequence x [n] is given by X ( e ). Since X ( e ) is period function of ω, it can be expressed classical Fourier series as, jω jω X( e jω jnω0ω ) = Cne n = where ω 0 is a fundamental frequency. Which of the following statement is correct? ω 0 = π, C n = x[n] ω 0 = π, C n = x[ n] ω 0 = 1, C n = x[ n] ω 0 = 1, C n = x[ n] 59. Evaluate 1 ln( x + 1). dx x π π ln ln 8 π ln ln 60. Fourier transform of a real and odd function is Real and odd Real and even Imaginary and odd Imaginary and even 61. Let F (w) be the Fourier Transform of a function f (t). The F (0) is f( t) dt f( t) dt t f( t) dt t f( t) dt Electronics 1

20 6. Laplace transform of e at f(t) is at F( s) F ( s) e F( s a) F ( s + a) + a s 63. monochromatic plane wave of wavelength 500 µm is propagating in the direction as shown in the figure below. E i, E r and E t denotes incident, reflected and transmitted electric field vectors associated with the wave. Ei Er Kr Hi Ki θi θ r Hr εr = 4.0 εr = 8.0 X 30 Et Ht Kt Y The expression for E t and E r are 4 π 10 ( x+ y) E j 0 5 ( aˆ x aˆ y) e 4 π 10 ( x y) E j 0 5 V/m and 0.10 ( aˆ x + aˆ y) e V/m 4 π 10 ( x + y) E j 0 5 ( aˆ x aˆ y) e V/m and 0.10 E0 ( aˆ x + aˆ y ) e π 10 ( x y) j 5 4 V/m 4 π 10 ( x y) E j 0 5 ( aˆ x + aˆ y) e 4 π 10 ( x+ y) E j 0 5 ( aˆ x aˆ y) e 4 π 10 ( x + y) E j 0 5 V/m and ( aˆ x aˆ y) e 4 π 10 ( x y) E j 0 5 V/m and ( aˆ x + aˆ y) e V/m V/m Electronics

21 64. Indicate which one of the following modes do NOT exist in a rectangular resonant cavity TE110 TE011 TM110 TM long solenoid of radius R, having N turns per unit length carries a time dependent current I( t) = I0 sin( ωt). The magnitude of induced electric field at a distance R / radially from the axis of the solenoid is R R µ 0NI0ω cos( ωt) µ 0NI0ω cos( ωt) 4 R R µ 0NI0ω sin( ωt) µ 0NI0ω sin( ωt) Penetration depth of magnetic field inside a superconductor is lways zero London depth of penetration Skin depth of penetration Inside Full bulk of material 67. parallel plate air-filled capacitor has plate area of 10 4 m and plate separation of 10 3 m. It is connected to a V, 1.8 GHz source. The magnitude of the displacement current is ( ε0 = 1/36π 10 9 F/m) 00 m 0 m 0 m 68. Two rectangular waveguide have dimensions of 1 cm 0.5 cm and 1 cm 0.5 cm respectively. Their respective cut-off frequencies will be 15 GHz and 30 GHz 30 GHz and 60 GHz 15 GHz and 15 GHz 30 GHz and 30 GHz 69. Which of the following has the highest skin depth? Electronics 3

22 l g u Cu 70. The electric field vector of a wave is given as j ( ω t + 3x 4y) 8 ax + 6 ay E = E + 0e 15 5a z V/m Its frequency is 10 GHz. The phase velocity in Y-direction will be m/s m/s m/s m/s 71. The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following equation E( z, t) = 3cos(π 10 9 t + βz) aˆ π 9 x + cos π 10 t + β z + aˆ y The type of wave polarization is Right hand elliptical Right hand circular Left hand elliptical Left hand circular 7. ring of radius R carries a linear charge density λ. It is rotating with angular speed ω. The magnetic field at its center is 3µ 0 λω µ 0 λω µ 0 λω µ0 λω π Electronics 4

23 73. transmission line with a characteristic impedance of 100 Ω is used to match a 50 Ω section to a 00 Ω section. If the matching is to be done both at 500 MHz and 1. GHz, the length of the transmission line can be approximately, 1.75 m 1.0 m 1.35 m 1.5 m 74. System has some poles lying on imaginary axis is Unconditionally stable Conditionally stable Unstable Marginally stable 75. The open-loop DC gain of a unity negative feedback system with closed loop transfer function ( S + 4)/( S + 7S + 13) is 4/13 4 4/ The unit impulse response of a system is h( t) = e, t 0. For this system, the steadystate value of the output for unit step input is equal to t 77. system has fourteen poles and two zeros. Its high frequency asymptote in its magnitude plot having a slope of 40 db/decade 40 db/decade 80 db/decade 30 db/decade 78. Consider a unity feedback system having an open loop transfer function Electronics 5

24 G ( jω) = k jω( j0.ω + 1)( j0.05ω + 1) Find open loop gain (k) with gain margin of 0 db The open loop transfer function of a unity feedback system is G S) = S ( S ( K + S + )( S + 3) The range of K for which the system is stable is 1 1 > K > 0 13 > K > 0 < K < < K < 80. For the CE (Common emitter) circuit shown, what will be the value of IE and VCE? VCC = 10V RC = kω IC + VBB = 4 V RB = 0kΩ VCE + IB VBE = 0.7V IE 3 m, 3 V 4 mv, 4 V 3.0 m, 4. V 3.0 m, 4 V Electronics 6

25 Space for rough work Electronics 7

26 Space for rough work Electronics 8

Q. 1 Q. 25 carry one mark each.

Q. 1 Q. 25 carry one mark each. Q. Q. 5 carry one mark each. Q. Consider a system of linear equations: x y 3z =, x 3y 4z =, and x 4y 6 z = k. The value of k for which the system has infinitely many solutions is. Q. A function 3 = is