#### Q 2.

###
?×?×P, , where *P* is a vector, is equal to

*P*is a vector, is equal to

(A) |

(B) |

(C) |

(D) |

#### Q 4.

###
A probability density function is of the form

p(x)=Ke??|x|,x?(??,?)

The value of *K* is

*K*is

(A) 0.5 | (B) 1 |

(C) 0.5 | (D) |

#### Q 5.

###
A solution for the differential equation

x.(t)+2x(t)=?(t)

with initial condition x (0 ?) = 0 is:

(A) | (B) |

(C) | (D) |

#### Q 6.

###
A low-pass filter having a frequency response H(j?)=A(?)ej?(?) does not produce any phase distortion if

(A) | (B) |

(C) | (D) |

#### Q 8.

###
The concentration of minority carriers in an extrinsic semiconductor under equilibrium is:

(A) directly proportional to the doping concentration |

(B) inversely proportional to the doping concentration |

(C) directly proportional to the intrinsic concentration |

(D) inversely proportional to the intrinsic concentration |

#### Q 9.

###
Under low level injection assumption, the injected minority carrier current for an extrinsic semiconductor is essentially the

(A) diffusion current | (B) drift current | (C) recombination current | (D) induced current |

#### Q 10.

###
The phenomenon known as ?Early Effect? in a bipolar transistor refers to a reduction of the effective base-width caused by

(A) electron-hole recombination at the base |

(B) the reverse biasing of the base-collector junction |

(C) the forward biasing of emitter-base junction |

(D) the early removal of stored base charge during saturation-to-cutoff switching. |

#### Q 11.

###
The input impedance (Zi ) and the output impedance ( Zo ) of an ideal transconductance (voltage controlled current source) amplifier are

(A) |

(B) |

(C) |

(D) |

#### Q 12.

###
An n-channel depletion MOSFET has following two points on its ID?VGS curve:

(i) VGS=0 at ID=12MA and

(ii) VGS=?6 at ID=0

Which of the following Q-points will give the highest trans-conductance gain for small signals

(A) |

(A) |

(C) |

(D) |

#### Q 13.

###
The number of product terms in the minimized sum-of-product expression obtained through the following K-map is (where ?d? denotes don?t care states)

1 | 0 | 0 | 1 |

0 | d | 0 | 0 |

0 | 0 | d | 1 |

1 | 0 | 0 | 1 |

(A) 2 | (B) 3 | (C) 4 | (D) 5 |

#### Q 14.

###
Let x(t) ?x(j?) be Fourier Transform pair. The Fourier Transform of the signal *x (5t ? 3) in terms of X ( jw* ) is given as

*x (5t ? 3) in terms of X ( jw*) is given as

(A) |

(B) |

(C) |

(D) |

#### Q 15.

###
The Dirac delta function ?(t) is defined as

(A) |

(B) |

(C) |

(D) |

#### Q 16.

###
If the region of convergence of x1[n]+x2[n] is 13<|z|<23, then the region of convergence of xn[n]?x2[n] includes

(A) |

(B) |

(C) |

(D) |

#### Q 18.

###
In the system shown below, *x (t ) = (sint )u (t )*. In steady-sate, the response *y (t *)will be:

*x (t ) = (sint )u (t )*. In steady-sate, the response

*y (t*)will be:

(A) |

(B) |

(C) |

(D) |

#### Q 19.

###
The electric field of an electromagnetic wave propagating in the positive zdirection is given by

E=a?xsin(?t??z)+a?y sin(?t??z)+a?y sin(?t??z+?2) .

The wave is

(A) linearly polarized in the z-direction |

(B) elliptically polarized |

(C) left-hand circularly polarized |

(D) right-hand circularly polarized |

#### Q 20.

###
A transmission line is feeding 1 Watt of power to a horn antenna having a gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is:

(A) 10 Watts | (B) 1 Watt | (C) 0.1 Watt | (D) 0.01 Watt |

#### Q 21.

###
The eigenvalues and the corresponding eigenvectors of a 2 × 2 matrix are given by

Eigenvalue | Eigenvector | |

| | |

| |

The matrix is:

(A) |

(B) |

(C) |

(D) |

#### Q 22.

###
For the function of a complex variable *W = ln Z* (where, *W = u + jn* and *Z = x + jy*), the u = constant lines get mapped in *Z*-plane as

*W = ln Z*(where,

*W = u + jn*and

*Z = x + jy*), the u = constant lines get mapped in

*Z*-plane as

(A) set of radial straight lines |

(B) set of concentric circles |

(C) set of confocal hyperbolas |

(D) set of confocal ellipses |

#### Q 25.

###
Three companies, X, Y and Z supply computers to a university. The percentage of computers supplied by them and the probability of those being defective are tabulated below.

Company | % of computers supplied | Probability of being defective |

X | 60% | 0.01 |

Y | 30% | 0.02 |

Z | 10% | 0,03 |

Given that a computer is defective, the probability that it was supplied by Y is:

(A) 0.1 | (B) 0.2 |

(C) 0.3 | (D) 0.4 |

#### Q 26.

###
For the matrix [4224] the eigenvalue corresponding to the eigenvector [101101] is:

(A) 2 | (B) 4 |

(C) 6 | (D) 8 |

#### Q 27.

###
For the differential equation d2ydx2+k2y=0

(i) y = 0 for *x* = 0 and

(ii) y = 0 for *x* = a

The form of non-zero solutions of *y* (where mvaries over all integers) are

*x*= 0 and

*x*= a

*y*(where mvaries over all integers) are

(A) |

(B) |

(C) |

(D) |

#### Q 28.

###
Consider the function *f (t )* having Laplace transform

F s = ? 0 s 2 + ? 0 2 R e s > 0

The final value of *f (t *)would be:

*f (t )*having Laplace transform

*f (t*)would be:

(A) 0 | (B) 1 | (C) | (D) |

#### Q 29.

###
As x increased from ?? to ? , the function

f(x)=ex1+ex

(A) monotonically increases | (B) monotonically decreases |

(C) increases to a maximum value and then decreases | (D) decreases to a minimum value and then increases |

#### Q 30.

###
A two port network is represented by ABCD parameters given by

[V1I1]=[ACBD][V2?I2]

If port-2 is terminated by , L R the input impedance seen at port-1 is given by

(A) |

(B) |

(C) |

(D) |

#### Q 31.

###
In the two port network shown in the figure below, z_{12} and z_{21} are, respectively

_{12}and z

_{21}are, respectively

(A) | (B) |

(C) | (D) |

#### Q 32.

###
The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by

(A) RL network only | (B) RC network only |

(C) LC network only | (D) RC as well as RL networks |

#### Q 33.

###
A 2 mH inductor with some initial current can be represented as shown below, where s is the Laplace Transform variable. The value of initial current is

(A) 0.5 A | (B) 2.0 A | (C) 1.0 A | (D) 0.0 A |

#### Q 34.

###
In the figure shown below, assume that all the capacitors are initially uncharged. If vi(t)=10u(t) Volts,vo(t) is given by

(A) | (B) |

(C) | (D) 8 Volts |

#### Q 35.

###
Consider two transfer functions

G1(s)=1s2+as+b and G2(s)=ss2+as+b

The 3-dB bandwidths of their frequency responses are, respectively

(A) |

(B) |

(C) |

(D) |

#### Q 36.

###
A negative resistance* R*_{neg} is connected to a passive network N having driving point impedance *Z*_{1} (s) as shown below. For *Z*_{2} (s) s to be positive real,

*R*is connected to a passive network N having driving point impedance

_{neg}*Z*as shown below. For

_{1}(s)*Z*s to be positive real,

_{2}(s) (A) |

(B) |

(C) |

(D) |

#### Q 38.

###
The majority carriers in an n-type semiconductor have an average drift velocity *v* in a direction perpendicular to a uniform magnetic field *B*. the electric field *E* induced due to Hall effect acts in the direction

*v*in a direction perpendicular to a uniform magnetic field

*B*. the electric field

*E*induced due to Hall effect acts in the direction

(A) v × B | (B) B × v |

(C) along v | (D) opposite to v |

#### Q 39.

###
Find the correct match between Group 1 and Group 2:

Group 1 | Group 2 |

(E) Varactor diode | (1) Voltage reference |

(F) PIN diode | (2) High frequency switch |

(G) Zener diode | (3) Tuned circuits |

(H) Schottky diode | (4) Current controlled attenuator |

(A) E - 4 F - 2 G - 1 H - 3 |

(B) E - 2 F - 4 G - 1 H - 3 |

(C) E - 3 F - 4 G - 1 H - 2 |

(D) E - 1 F - 3 G - 2 H - 4 |

#### Q 40.

###
A heavily doped n ? type semiconductor has the following data:

Hole-electron mobility ratio | :0.4 |

Doping concentration | : 4.2 ×10^{8} atoms/m^{3} |

Intrinsic concentration | : 1.5 ×10^{4} atoms/m^{3} |

The ratio of conductance of the *n ?* type semiconductor to that of the intrinsic semiconductor of same material and at the same temperature is given by

(A) 0.00005 | (B) 2000 |

(C) 10000 | (D) 20000 |

#### Q 41.

###
For the circuit shown in the following figure, the capacitor C is initially uncharged. At *t* = 0, the switch *S* is closed. The voltage *V*_{C} across the capacitor at *t* = 1millisecond is:

*t*= 0, the switch

*S*is closed. The voltage

*V*across the capacitor at

_{C}*t*= 1millisecond is:

(A) 0 Volt | (B) 6.3 Volt |

(C) 9.45 Volts | (D) 10 Volts |

#### Q 43.

###
A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-5 number is represented by its corresponding 3-bit binary code. For example, the base-5 number 24 will be represented by its BCP code 010100. In this numbering system, the BCP code 100010011001 corresponds to the following number in base-5 system

(A) 423 | (B) 1324 |

(C) 2201 | (D) 4231 |

#### Q 44.

###
An I/O peripheral device shown in figure (b) below is to be interfaced to an 8085 microprocessor. To select the I/O device in the I/O address range D4 H ? D7 H, its chip-select (CS ) should be connected to the output of the decoder shown in figure (a) below:

(A) output 7 | (B) output 5 |

(C) output 2 | (D) output 0 |

#### Q 45.

###
For the circuit shown in figures below, two 4 - bit parallel - in serial - out shift registers loaded with the data shown are used to feed the data to a full adder. Initially, all the flip - flops are in clear state. After applying two clock pulse, the output of the full-adder should be

(A) S = 0, C_{ }_{0}= 0 | (B) S = 0, C_{0} = 1 |

(C) S = 1, C_{0} = 0 | (D) S = 1, C_{0} = 1 |

#### Q 47.

###
Two *D* - flip - flops, as shown below, are to be connected as a synchronous counter that goes through the following sequence

00?01?11?10?00?...

The inputs *D*_{0} and *D*_{1} respectively should be connected as,

*D*- flip - flops, as shown below, are to be connected as a synchronous counter that goes through the following sequence

The inputs

*D*and

_{0}*D*

_{1}respectively should be connected as,

(A) | (B) |

(C) | (D) |

#### Q 48.

###
Following is the segment of a 8085 assembly language program

LXI SP, EFFF H |

CALL 3000 H |

: |

: |

: |

3000 H LXI H, 3CF4 |

PUSH PSW |

SPHL |

POP PSW |

RET |

On completion of RET execution, the contents of SP is

(A) 3CF0 H | (B) 3CF8 H |

(C) EFFD H | (D) EFFF H |

#### Q 49.

###
The point *P* in the following figure is stuck at 1. The output *f* will be

*P*in the following figure is stuck at 1. The output

*f*will be

(A) | (B) |

(C) | (D) |

#### Q 51.

###
The minimum sampling frequency (in samples/sec) required to reconstruct the following signal from its samples without distortion

x(t)=5(sin2?100t?t)3+7(sin2?100t?t)2 would be

(A) | (B) |

(C) | (D) |

#### Q 52.

###
A uniformly distributed random variable *X* with probability density function

fx(x)=110(u(x+5)?u(x?5))

Where *u *(.) is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable *Y* would be

*X*with probability density function

*u*(.) is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable

*Y*would be

(A) |

(B) |

(C) |

(D) |

#### Q 53.

###
A system with input x[n] and output y[n] is given as y[n]=(sin56?n)x(n) The system is:

(A) linear, stable and invertible |

(B) non-linear, stable and non-invertible |

(C) linear, stable and non-invertible |

(D) linear, unstable and invertible |

#### Q 54.

###
The unit-step response of a system starting from rest is given by

C(t)=1?e?2t for t?0

The transfer function of the system is:

(A) |

(B) |

(C) |

(D) |

#### Q 55.

###
The Nyquist plot of *G ( j*? )H ( j? ) for a closed loop control system, passes through (?1, j0) point in the GH plane. The gain margin of the system in dB is equal to

*G ( j*? )H ( j? )for a closed loop control system, passes through (?1, j0) point in the GH plane. The gain margin of the system in dB is equal to

(A) infinite |

(B) greater than zero |

(C) less than zero |

(D) zero |

#### Q 56.

###
The positive values of ?K? and ?a? so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

(A) 1, 0.75 |

(B) 2, 0.75 |

(C) 1, 1 |

(D) 2, 2 |

#### Q 59.

###
A linear system is described by the following state equation

X.(t)=AX(t)+BU(t),A=[0?110]

The state-transition matrix of the system is:

(A) |

(B) |

(C) |

(D) |

#### Q 61.

###
A zero-mean white Gaussian noise is passed through an ideal lowpass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period* t*_{s}=0.03 msec. The samples so obtained would be

*t*=0.03 msec. The samples so obtained would be

_{s}(A) correlated | (B) statistically independent | (C) uncorrelated | (D) orthogonal |

#### Q 62.

###
A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as

(A) 6000 bits/sec |

(B) 4500 bits/sec |

(C) 3000 bits/sec |

(D) 1500 bits/sec |

#### Q 64.

###
In the following figure the minimum value of the constant ?C?, which is to be added to y1(t) t such that y1(t) and y2(t) are different, is

(A) | (B) |

(C) | (D) |

#### Q 65.

###
A message signal with bandwidth 10 kHz is Lower-Side Band SSB modulated with carrier frequency Fc1=106 HZ The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency Fc2=109 = Hz. The bandwidth of the output would be

(A) |

(B) |

(C) |

(D) |

#### Q 66.

###
A medium of relative permittivity ?r2=2 forms an interface with free-space. A point source of electromagnetic energy is located in the medium at a depth of 1 meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section over the interface. The area of the beam crosssection at the interface is given by

(B) |

(B) |

(C) |

(D) |

#### Q 67.

###
A medium is divided into regions I and II about* x *= 0 plane, as shown in the figure below. An electromagnetic wave with electric field E1=4a?x+3a?y+5a?z is incident normally on the interface form region-I. The electric field E2 in region-II at the interface is:

*x*= 0 plane, as shown in the figure below. An electromagnetic wave with electric field

(A) |

(B) |

(C) |

(D) |