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Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max [X, Y] is less than ½ is

3/4

9/16

1/4

2/3

If x = , then the value of x ’ is

X

1

Given, f (z ) = . If C is a counterclock wise path in the z-plane such that |z + 1| = 1, the value of f (z) dz is

- 2

- 1

2

In the circuit shown below, the current through the inductor is

The impedance looking into nodes 1 and 2 in the given circuit is

A system with transfer function

is excited by sin . The steady-state output of the system is zero at

In the sum of products function f (X, Y,Z) = (2,3,4,5), the prime implicants are

If x [n] = u[n], then the region of convergence (ROC) of its Ztransform in the Z-plane will be

The radiation pattern of an antenna in spherical co-ordinates is given by

10dB

12.6dB

11.5dB

18 dB

A coaxial cable with an inner diameter of 1mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittvity 10.89. Given F/m, the characteristic impedance of the cable is

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 and decreases that of the second by . After encoding, the entropy of the source

increases

remains the same

increases only if N = 2

decreases

The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is

Y = (A + B) c

Y = AB + C

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

The unilateral Laplace transform of f(t) is . The unilateral Laplace transform of (t)f(t) is

The average power delivered to an impedance (4 – j3) by a current 5cos (100t + 100) A is

44.2W

50W

62.5W

125W

In the following figure, are ideal capacitors. has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is

zero

a step function

an exponentially decaying function

an impulse function

The i-v characteristics of the diode in the circuit given below areThe current in the circuit is

10mA

9.3mA

6.67mA

6.2mA

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

4

6

8

10

Consider the given circuit

In this circuits, the race around

does not occur

occurs when CLK = 0

occur when CLK = 1 and A = B = 1

occurs when CLK = 1 and A = B = 0

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

1.2 GHz and left circular

4 Hz and left circular

1.2 GHz and right circular

4 Hz and right circular

A plane wave propagating in air with V/m is incident on a perfectly conducting slab positioned at . The field of the reflected wave is

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 seconds is

1750

2625

4000

5250

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

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

Given that A = and I = the value of is

15A + 12I

19 A + 30I

17 A + 15I

17 A + 21I

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

21

25

41

46

-5V

2V

3V

6V

The voltage gain of the circuit shown below is

The state transition diagram for the logic circuit shown is

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

0

1/2

3/2

The circuit shown is a

Low pass filter with rad/s

High pass filter with rad/s

low pass filter with rad/s

high pass filter with rad/s

The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the figure is

The signal m(t) as shown is applied both to a phase modulator (with kp as the phase constant) and a frequency modulator (with as the frequency constant) having the same carrier frequency

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

7/80

63/80

9/10

1/10

In the CMOS circuit shown, electron and hole mobilities are equal, and M1 and M2 are equally

1.87V < < 3.125 V

0 < , 5V

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

1/3

The direction of vector A is radially outward from the origin, with where and k is a constant. The value of n for which . A = 0 is

Consider the differential equation

The numerical value of is

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

The state variable description of an LTI system is given by

The fourier transform of a signal h(t) is H . The value of h(0) is

The feedback system shown below oscillates at 2 rad/s when

K = 2 and a = 0.75

K = 3 and a = 0.75

K = 4 and a = 0.5

K = 2 and a = 0.5

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

time-invariant and stable

stable and not time-invariant

time-invariant and not stable

not time-invariant and not stable

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

82.5 cm

1.05 m

1.58 cm

1.75 m

A BPSK scheme operating over an AWGN channel with noise power spectral density of / 2, uses equiprobable signals and over the symbol interval (0, T) . If the local oscillator in a coherent receiver a head in phase by with respect to the received signal, the probability of error in the resulting system is

The source of a silicon n-channel MOS transistor has an area of 1 sq and a depth of 1 . If the dopant density in the soured is , the number of holes in the source region with the above volume is approximately

Common Data for Questions: 48 & 49

In the three dimensional view of a silicon n-channel MOS transistor shown below, = 20 nm The transistor is of width 1 . The depletion width formed at every p-n junction is 10nm. The relative permitivities of Si and , respectively, are 11.7 and 3.9, and F /m

2fF

7fF

2pF

7pF

The gate-source overlap capacitance is approximately

0.7fF

0.7pF

0.35fF

0.24pF

Common Data Questions: 50 & 51

With 10V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: (i) connected at port B draws a current of 3 A (ii) connected at port B draws a current of 2 A

7V

8V

9V

With 10V dc connected at port A, the current drawn by connected at port B is

3/7A

5/7A

1 A

9/7A

Statement for linked Answer Questions: 52 and 53

The transfer function of a compensator is given as

a = 1, b = 2

a = 3, b = 2

a = -3, b = -1

a = 3, b = 1

The phase of the above lead compensator is maximum at

Statement for Linked Answer Questions: 54 and 55

An infinitely long uniform solid wire of radius a carries a uniform dc current of density.

The magnetic field at a distance r from the center of the wire is proportional to

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

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

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

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

A hole radius b(b < a) is now drilled along the length of the wire at a distance d from the centre of the wire as shown below.

uniform and depends only on d

uniform and depends only on b

uniform and depends on both b and d

non uniform

Which one of the following options is the closest in meaning to the word given below?

Latitude

Eligibility

Freedom

Coercion

Meticulousness

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

requested that

should be given

the driving test

instead of tomorrow

If

2.23

4.23

11.37

27.64

Choose the most appropriate alternative from the options given below to complete the following sentence:

If the tried soldier wanted to lie down, he _______ the mattress out on the balcony

should take

shall take

should have taken

will have taken

Choose the most appropriate word from the options given below to comlete the following sentence:

Given the seriousness of the situation that he had to face, his _________ was impressive.

beggary

nomenclature

jealousy

nonchalance

The data given in the following table summarizes the monthly budget of an average household.

10%

14%

81%

86%

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

1/16

7/16

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brustal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them.

Which one of the following statements best sums up the meaning of the above passage?

Through regimentation was the main reason for the efficiency of the Roman legions even in adverse circumstances.

The legions were treated inheritance from their seniors.

Discipline was the armies’ inheritance from their seniors.

The harsh discipline to which the legions were subjected to led to the odds and conditions being against them.

Raju has 14 currency notes in his pocket consisting of only Rs.20 notes and Rs. 10 notes. The total money value of the notes is Rs.230. The number of Rs. 10 notes that Raju has is

5

9

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighting balance is of unimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is

3

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