A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

1.1/3

2.1/2

3.2/3

4.3/4

One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow.

1. requested that

2.should be given

3.the driving test

4.instead of tomorrow

The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by . The frequency and polarization of the wave, respectively, are

1. 1.2 GHz and left circular

2.4 Hz and left circular

3.1.2 GHz and right circular

4.4 Hz and right circular

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is

1.4

2.6

3.8

4.10

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is

1.1/4

2.1/16

3.7/16

4.9/16

A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0) = 9/10, then the probability of error for an optimum receiver will be

1.7/80

2.63/80

3. 9/10

4.1/10

A BPSK scheme operating over an AWGN channel with noise power spectral density of N0 / 2 , uses equiprobable signals s1(t) = âˆš2E/T sin(wc t) and s2(t) = -âˆš2E/T sin(wc t) over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45o with respect to the received signal, the probability of error in the resulting system is

1. Q(âˆš2E/N0)

2.Q(âˆšE/N0)

3. Q(âˆšE/2N0)

4.Q(âˆšE/4N0)

A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount ÃŽÂµ and decreases that of the second by ÃŽÂµ . After encoding, the entropy of the source

1.increases

2.remains the same

3. increases only if N = 2

4.decreases

A system with transfer function G(s) = [(s2 + 9)(s + 2)] / [(s + 1)(s + 3)(s + 4)] is excited by sin(w t) . The steady-state output of the system is zero at

1.w = 1 rad/s

2.w = 2 rad/s

3. w = 3 rad/s

4.w = 4 rad/s

A transmission line with a characteristic impedance of 100 Ã¢â€žÂ¦ is used to match a 50 Ã¢â€žÂ¦ section to a 200 Ã¢â€žÂ¦ section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately

1.82.5 cm

2.1.05 m

3.1.58 m

4.1.75 m

An infinitely long uniform solid wire of radius a carries a uniform dc current of density j. The magnetic field at a distance r from the center of the wire is proportional to

1.r for r < a and 1/r2 for r > a

2.0 for r < a and 1/r for r > a

3.r for r < a and 1/r for r > a

4.0 for r < a and 1/r2 for r > a

If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =

1.2.23

2.4.33

3.11.37

4.27.64

If x = âˆš-1 , then the value of xx is

1.e-Ãâ‚¬/2

2.eÃâ‚¬/2

3.x

4.1

If x[n] = (1/3)|n| - (1/ 2)n u[n], then the region of convergence (ROC) of its Z-transform in the Z-plane will be

1.1/3 < |z| < 3

2.1/3 < |z| < 1/2

3.1/2 < |z| < 3

4.1/3 < |z|

In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is

1.1720

2.2625

3.4000

4.5250

Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

1.0

2.1/2

3.1

4.3/2

The average power delivered to an impedance (4 - j3) Ã¢â€žÂ¦ by a current 5cos(100Ãâ‚¬ t + 100) A is

1.44.2 W

2.50 W

3.62.5 W

4.125 W

The current ib through the base of a silicon npn transistor is 1 + 0.1 cos(10000 Ãâ‚¬ t) mA. At 300 K, the rÃâ‚¬ in the small signal model of the transistor is

1.250 Ã¢â€žÂ¦

2.27.5 Ã¢â€žÂ¦

3.25 Ã¢â€žÂ¦

4.22.5 Ã¢â€žÂ¦

The Fourier transform of a signal h(t) is H(jw) = (2cosw)(sin2w) /w . The value of h(0) is

1.1/4

2.1/2

3.1

4.2

The input x(t) and output y(t) of a system are related as y(t) = . The system is

1.time-invariant and stable

2.stable and not time-invariant

3.time-invariant and not stable

4.not time-invariant and not stable

The maximum value of f(x) = x3 - 9x2 +24x + 5 in the interval [1, 6] is

1.21

2.25

3.41

4.46

The power spectral density of a real process X(t) for positive frequencies is shown below. The values of E[X2(t)] and E[X(t)] , respectively, are

1.6000/Ãâ‚¬, 0

2.6400/Ãâ‚¬, 0

3.6400/Ãâ‚¬, 20/(Ãâ‚¬ âˆš2)

4. 6000/Ãâ‚¬, 20/(Ãâ‚¬ âˆš2)

The radiation pattern of an antenna in spherical co-ordinates is given by F(ÃŽÂ¸) = cos4 ÃŽÂ¸; 0 Ã¢â€°Â¤ ÃŽÂ¸ Ã¢â€°Â¤ Ãâ‚¬ /2 The directivity of the antenna is

1.10 dB

2.12.6 dB

3.11.5 dB

4.18 dB

The source of a silicon (ni = 1010 per cm3) n-channel MOS transistor has an area of 1 sq ÃŽÂ¼m and a depth of 1 ÃŽÂ¼m. If the dopant density in the source is 1019/cm3, the number of holes in the source region with the above volume is approximately

1.107

2.100

3.10

4.0

The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). Gc (s) is a lead compensator if

1. a =1, b = 2

2.a = 3, b = 2

3.a = "â€œ3, b = "â€œ1

4.a = 3, b = 1

The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). The phase of the above lead compensator is maximum at

1.âˆš2 rad/s

2.âˆš3 rad/s

3.âˆš6 rad/s

4.1/âˆš3 rad/s

The unilateral Laplace transform of f(t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is

1.- s/(s2 + s + 1)2

2.- (2s + 1)/(s2 + s + 1)2

3. s/(s2 + s + 1)2

4.(2s + 1)/(s2 + s + 1)2

Two independent random variables X and Y are uniformly distributed in the interval [â€œ1, 1]. The probability that max[X, Y] is less than 1 2 is

1.3/4

2.9/16

3.1/4

4.2/3

With initial condition x(1) = 0.5 , the solution of the differential equation, t dx/dt + x = t is

1.x = t - 1/2

2. x = t2 - 1/2

3.x = t2/2

4.x = t/2

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