Questions on Communication Systems

1. An AM signal has the form x(t) = [ 10 + 3 cos 3000πt +4 cos 6000πt].cos 2πf_ct, where f_c =10⁶ Hz. The modulation index is ------------------

2. A super heterodyne receiver uses an IF frequency of 455 KHz. The receiver is tuned to a transmitter having a carrier frequency of 2400 KHz. High side band tuning is to be used. The image rejection ratio will be (Q=50)

a) 32.715

b) 35.25

c) 25.715

d) 23.715

3. An angle modulated signal is given by s(t) = Cos 2π ( 2 x 10⁶ t + 30 sin 300 t + 40 cos 300t). The maximum frequency and phase deviation of s(t) are

a) F_m = 11.18 KHz, ∆φ =100

b) F_m = 70.24 KHz, ∆φ =50

c) F_m = 11.18 KHz, ∆φ =100 π

d) F_m = 1.1 KHz, ∆φ =100 π

4. A speech signal band limited to 5 kHz and peak voltage varying between +7V and -3V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits. The number of quantization levels required to reduce the quantization noise by a factor of √2 would be

a) 1024

b) 512

c) 256

d) 362

5. An analog signal has spectral components from 2 KHz to 7 KHz. What is the minimum band pass sampling rate?

a) 14 KHz 

b) 5 KHz

c) 9 KHz

d) 10 KHz

6. A communication channel having AWGN has a bandwidth of 6 KHz and SNR of 7. The highest transmission rate that such a channel can support is

a) 18 Kbps

b) 42 Kbps

c) 16 KPbs

d) 20 Kbps

7. The sum of two signals E₁= 3 sin 4 π x 10³t and E₂= 5 sin 2 π x 256 t are sampled at 1024 Hz. 

The sampled signal is passed through a LPF with fc = 2048 Hz. The output of this filter will contain components at 

a) only 1024 Hz

b) 256 Hz and 1744 Hz

c) 256 Hz and 1024 Hz

d) only 256 Hz

8. An angle modulated signal is expressed by F(t) = 2 cos (2 x 10⁸ π t + 75sin 4 x 10³ π t).

 Find the total power and bandwidth of the signal.

a) Pt = 4 Watts; BW = 304 KHz

b) Pt = 152 watts; BW = 4 KHz

c) Pt = 2 watts; BW = 304 KHz

d) Pt = 15 watts; BW = 4 KHz

9. When a radio receiver is tuned to 750 KHz its local oscillator provides the mixer with the input at 1250 KHz. At the output, another signal is also received along with the desired signal. The frequency of the other station is

a) 1750 KHz

b) 1500 KHz

c) 1250 KHz

d) 500 KHZ

10. 25 telephone channels, each band limited to 4 KHz, are to be time division multiplexed(TDM) by using  PCM. Calculate the transmission rate of the PCM system for 64 quantization levels and sampling frequency is 1.25 times the Nyquist rate.

a) Rb= 1200 Kbps

b) Rb =750 Kbps

c) Rb =1750 Kbps

d) Rb = 1500 Kbps

11. Which of the following demodulator can be used for demodulating the signal

X(t) = 3( 1 + 2.5 cos 500 πt). Cos 50 10³πt is 

a) Envelope detector

b) Synchronous demodulator

c) Square law demodulator

d) All the above

12. 14 signals each band limited to 4 KHz are to be transmitted over a single channel by FDM.

If AM-SSB modulation guard band of 0.75KHz is used, then the bandwidth of the multiplexed signal will be

a) 63.75 KHz

b) 121.75 KHz

c) 37.75 KHz

d) 70 KHz

13. A delta modulator is designed to operate on speech signals limited to 3.4 KHz. The sampling rate is 10 times the Nyquist rate. The step size is 100mV. The modulator is tested with 1KHz sinusoidal signal. The maximum amplitude of the test signal required to avoid slope overload distortion is 

a) 1 mV

b) 2.08 mv

c) 2.08 V

 d) 1.08 V

14. A source generates four equiprobable symbols. If the source coding is adopted, the average length of the code for 100% efficiency is --------- bits per symbol.

15. An AM wave is given by s(t) = 10( 1 + 0.4 cos 2 π x 10³t + 0.3 cos 2 π x 10⁴ t). Cos 2π x10⁶t. 

The following frequency will not be present in the spectrum is/are

a) 1 MHz

b) 2 MHz

c) 1010 KHz, 1001 KHz

d) 990 KHz, 999KHz

16. A source generates 3 symbols with probabilities 1/2, 1/4 and 1/4 at a rate of 2500 symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate

a) 3750 bits/sec

b) 1666 bits/sec

c) 4500 bits/sec

d) 3500 bits/sec

17. A single tone frequency modulated wave is processed through a non-linear system y(t) = x²(t). (β  and ∆f are modulation index and frequency deviation of original FM wave). The bandwidth required to transmit the output of the non-linear device is

a) 4 ∆f + 4 fm

b) 4 ∆f + 2 fm

c) 2 ∆f + 2 fm

d) 2 ∆f + 4 fm

18. An SSB transmission contains  8kW. This transmission is to be replaced by a standard amplitude modulated signal with same power content. If the modulation index is 0.75, then the upper side band power is -----------------

19. In a multitone modulation, the maximum peak to peak voltage of an AM wave is 14mV and the minimum peak to peak voltage is 6 mV and second modulating wave has modulation index µ = 0.5. The overall modulation index is --------------

20. The frequency deviation of an FM signal is increased from 30 kHz to 60 kHz. For the same sinusoidal modulating signal of 12kHz, the improvement in the demodulated signal to noise power ratio will be ______________

21. To overcome slope over distortion and granular noise problem, which type of integrator is used in Delta modulation?

a) Linear Slope

b) Fixed Slope

c) Companding

d) Variable slope

22. A carrier wave with frequency 8 MHz and peak amplitude value of 10V is DSB-SC amplitude modulated by a 5 kHz sine wave of amplitude 6 V. The amplitude of the side band component is _______

23. The tuned-circuit of the oscillator in an A.M. transmitter uses a 25µH coil and 2.5 nF capacitor. Now if the oscillator output is modulated by audio frequencies upto 5kHz, then the frequency range of side bands would be

a) 631.62 kHz to 641.62 kHz

b) 630 kHz to 645 kHz

c) 630.62 kHz to 646.62 kHz

d) 646 kHz to 656 kHz

24. A 3 V, 1 kHz signal modulates the carrier to cause frequency deviation of 6.5 kHz. On increasing the modulating voltage to 12 V, the frequency deviation is ___________

25. A TDM link has 15 signal channel, each sample is represented by 8 binary bits and it contains an additional bit for synchronisation. If the total bit rate for the TDM link is 1250kbps, then the value of sampling duration (Ts) is ___________

a) 108µs

b) 54µs

c) 125µs

d) 250µs  

  26. For an AM signal, the bandwidth is 8 kHz and the lowest frequency component present is 800kHz. The carrier frequency used for this AM signal (in kHz) is --------------

Questions on Probability

1. Five cards are drawn at random one after another from a deck of 52 cards with replacement. The probability that, a spade card occurs at most once is
a) 81/128       b) 27/32     c) 37/64    d) 81/256

2. A bag contains 4 tickets marked AAB, ABA, BAA, BBB. One ticket is drawn at random from the bag. Let Ei(i=1,2,3) denote the event that ith letter on the ticket is B; then which of the following is false?
a) E1 and E3 are independent
b) E2 and E3 are independent
c) E1 and E2 are independent
d) None of these

3.Probability that a factor of 30 ²⁹ is a multiple of 30 ²⁴ is

     a)    1/125     b) 6/125               c) 9/125                d)12/125

4. A biased coin is tossed 16 times. If the probability of getting 8 heads is same as that of getting 9 heads, then the probability of getting a head in a single toss is
a) 9/17       b) 8/17         c) 7/17          d) 10/17

5. In 512 sets of rolls of a fair six-sided die, the expected number of sets(rounded off to the nearest integer) in which 12 prime numbers and 3 non-prime numbers occur is
a) 5            b) 4               c) 7      d) 9

6. From a bag containing 8 white and 6 red balls, Ramu selected  balls at random at a time first and then Somu selected 3 balls at random at a time without replacing Ramu's balls. Probability that the balls selected by Ramu are all white and that of Somu are all red

a)  5/429            b) 5/143       c) 5/286       d) 7/286

7. Among the aspirants of PSU jobs in BHEL, NTPC and HPCL,  of a reputed university, the probabilities of a student getting selected in both BHEL and NTPC, in both NTPC and HPCL, in both HPCL and BHEL and in all the three among BHEL, NTPC and HPCL are 0.4, 0.3, 0.5 and 0.2 respectively. The probability that a student, among these aspirants, getting selected in exactly two of the three PSUs is  ---------------------------

8. Two friends decided to meet between 7:00 p.m. and 8:00 p.m. on a certain day at a certain venue. They agreed that whoever arrived first among them at the venue would wait for at most 20 minutes for the other person. Find the probability that they will not meet on that day
a) 4/9       b) 5/9      c) 5/19   d) 13/18


9. Let S = { 0, 1,2,3,............2015}. If a number is selected at random from the set S, the probability that it is a prime factor of 2015 is
a) 3/2015           b) 1/1008         c) 1/226         d) 1/672

10. The probability that Rohan will pass atleast one of the two subjects Maths and Science is 0.6 and the probability that Rohan will pass both Maths and Science is 0.2. Then the sum of the probabilities of Rohan not passing Maths and not passing Science is

a) 0.4           b) 0.8           c) 1.2                d) 1.4      

11. Two biased dice are thrown together. On one of them, 6 appears twice as often as any other number while on the other, an odd number appears thrice as frequently as an even number. What is the probability that the sum of the scores on them is 11 0r 12?

a) 1/12             b) 9/28             c) 3/28              d) 5/12


12. For two rolls of a fair die, the probability of getting a prime number in the first roll and a composite number in the second roll is ---------------------


13. Find the probability of a randomly selected leap year having 53 Mondays and 53 Wednesdays.
a) 1/7       b) 2/7      c) 3/7     d) 0

14. Urn 1 contains 14 marbles out of which 4 are blue. Urn 2 contains 16 marbles out of which 6 are blue. If one marble is drawn at random from each Urn simultaneously, the probability of getting exactly one marble is --------------

15. A man speaks truth 2 out of 3 times. He threw a biased coin, that has 60% chance of getting heads and reports that it turned up heads. What is the percentage of chance that it actually turned up on heads?
a) 25%         b) 60%     c) 66%        d) 75%

16. At a certain factory, three machines M1, M2 and M3 manufacture 50%, 30% and 20% respectively, of the total spare parts. Out of this total, 4% of the output of M1, 2% of that of M2 and 5% of that of M3 end up being defective. If a randomly drawn spare part from the total output is defective, find the probability that the part was manufactured by either  M1 or M3.
a) 4/5       b) 5/6      c) 11/12         d)1/6

17. An event  is called statistically independent if
a) The probability of occurrence of one event is not affected by the occurrence of the other event.
b) The probability of occurrence of one event is affected by the occurrence of the other event.
c) The probability of occurrence of one event is affected by the occurrence of same event.
d) Non of these

Ans: Option a)

18. A fair coin is tossed 4 times, the probability that at least once head turns up is
a) 1/16
b) 15/16
c) 7/8
d) 1/8

19. The probability that Anil speaks truth is 4/5 while that of Bindu is 3/4, the probability that they are likely to contradict each other in stating the same fact is
a) 3/20
b) 4/5
c) 7/20
d) 1/5

20. Probability that at least one of the events A and B occur is 2/3 and probability that both the events A and B occur is 1/6. Then the value of P(A^c ) + P(B^c ) is

a) 7/6        b) 6/7       c) 6/5       d)5/6

21. Find the probability that a two-digit number selected randomly from all the two-digit numbers between 1 and 100 is divisible by neither 3 nor 5.

a) 8/15         b) 3/5          c)  2/5            d) 7/15

22. Find the probability that a two-digit number selected randomly from all the two-digit numbers between 1 and 100 is divisible by neither 3 nor 5.

a) 8/15         b)3/5            c)2/5            d)7/15

23. For a biased coin, when tossed 12 times, probability of getting exactly 7 heads is same as probability of getting exactly 6 heads. Then the probability of getting heads, when that coin is tossed once is --------------------

a) 5/13                 b) 8/13               c) 6/13                d) 7/13

24. A bag contains 5 red balls 8 green balls. Two balls are drawn from the bag one after another without replacing the first ball. What is the probability that both balls are different color?

a) 10//39             b) 5/39                c) 5/13            d) 20/39

25. What is the probability that a quadratic equation ax²+bx+c has equal roots if a,b and c are distinct and are taken from {1,2,3,4,6,8,9}

a) 1/35       b) 2/35       c) 1/105         d) 2/105   

26. An unbiased coin is tossed six times. The outcome of each toss is either head or tail. The probability of getting at least two heads is --------------