#### Q 2.

###
The power spectral density of a real process *X(t)* for positive frequencies is shown below. The values of E[*X*^{2}(t)] and |E[*X(t)*]| , respectively, are

*X(t)*for positive frequencies is shown below. The values of E[

*X*] and |E[

^{2}(t)*X(t)*]| , respectively, are

(A) 6000/ | (B) 6400/ |

(C) 6400/ | (D) 6000/ |

#### Q 4.

###
A plane wave propagating in air with E? =(8a?x+6a?y+5a?z)ej(wt+3x?4y) V/m is incident on a perfectly conducting slab positioned at x?0 .The E? field of the reflected wave is

(A) |

(B) |

(C) |

(D) |

#### Q 5.

###
The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by E? =10(a?y+ja?z)e?j25x .The frequency and polarization of the wave, respectively, are

(A) 1.2 GHz and left circular | (B) 4 Hz and left circular |

(C) 1.2 GHz and right circular | (D) 4 Hz and right circular |

#### Q 6.

###
Consider the given circuit.

In this circuit, the race around

(A) does not occur | (B) occurs when CLK = 0 |

(C) occurs when CLK = 1 and A = B = 1 | (D) occurs when CLK = 1 and A = B = 0 |

#### Q 8.

###
The *i-v *characteristics of the diode in the circuit given below are

i={v?0.7500A,0 A,v?0.7vv<0.7v

The current in the circuit is

*i-v*characteristics of the diode in the circuit given below are

(A) 10 mA | (B) 9.3 mA | (C) 6.67 mA | (D) 6.2 mA |

#### Q 9.

###
In the following figure, C_{1} and C_{2} are ideal capacitors. C_{1} has been charged to 12 V before the ideal switch S is closed at *t* = 0. The current *i(t)* for all *t* is

_{1}and C

_{2}are ideal capacitors. C

_{1}has been charged to 12 V before the ideal switch S is closed at

*t*= 0. The current

*i(t)*for all

*t*is

(A) zero | (B) a step function |

(C) an exponentially decaying function | (D) an impulse function |

#### Q 10.

###
The average power delivered to an impedance (4-*j*3)? by a current 5cos(100?t+100)A is

*j*3)

(A) 44.2 W | (B) 50 W | (C) 62.5 W | (D) 125 W |

#### Q 11.

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

*f (t)*is

*is*

*t*f (t) (A) | (B) |

(C) | (D) |

#### Q 12.

###
With initial condition x(1)=0.5 , the solution of the differential equation,

tdxdt+x=t is

(A) | (B) | (C) | (D) |

#### Q 13.

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

*v(t)*across the diode D1 is

(A) | (B) | (C) | (D) |

#### Q 15.

###
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

*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

(A) increases | (B) remains the same |

(C) increases only if N = 2 | (D) decreases |

#### Q 17.

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

F(?)=cos4?;0????/2

The directivity of the antenna is

(A) 10 dB | (B) 12.6 dB | (C) 11.5 dB | (D) 18 dB |

#### Q 18.

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

(A) | (B) | (C) | (D) |

#### Q 19.

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

*f(X,Y,Z)=*

(A) | (B) |

(C) | (D) |

#### Q 20.

###
A system with transfer function

G(s)=(s2+9)(s+2)(s+1)(s+3)(s+4)

is excited by sin(?t) . The steady-state output of the system is zero at

(A) | (B) |

(C) | (D) |

#### Q 21.

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

(A) 50 | (B) 100 | (C) 5 k | (D) 10.1 k |

#### Q 22.

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

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

#### Q 23.

###
Given

f(z)=1z+1?2z+3. If C is a counterclockwise path in the z-plane such that ?z+1?=1 , the value of 12?j?Cf(z)dz

(A) ?2 | (B) ?1 | (C) 1 | (D) 2 |

#### Q 24.

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

(A) 3/4 | (B) 9/16 | (C) 1/4 | (D) 2/3 |

#### Q 27.

###
A BPSK scheme operating over an AWGN channel with noise power spectral density of *N*_{0}/2, uses equiprobable signals s1(t)=2ET????sin(?ct) and s2(t)=?2ET????sin(?ct) over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45° with respect to the received signal, the probability of error in the resulting system is

*N*/2, uses equiprobable signals

_{0} (A) | (B) | (C) | (D) |

#### Q 29.

###
The input *x(t)* and output *y(t)* of a system are related as y(t)=???tx(?)cos(3?)d?. The system is

*x(t)*and output

*y(t)*of a system are related as

(A) time-invariant and stable | (B) stable and not time-invariant |

(C) time-invariant and not stable | (D) not time-invariant and not stable |

#### Q 30.

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

(A) | (B) |

(C) | (D) |

#### Q 31.

###
The Fourier transform of a signal *h(t)* is H(j?)=(2cos?)(sin2?)/?. The value of *h(0)* is

*h(t)*is

*h(0)*is

(A) 1/4 | (B) 1/2 | (C) 1 | (D) 2 |

#### Q 32.

###
The state variable description of an LTI system is given by

???x1.x2.x3.???= ???00a3a1000a20??? ???x1x2x3???+???001???u

y=(100)???x1x2x3???

where y is the output and u is the input. The system is controllable for

(A) | (B) |

(C) | (D) |

#### Q 33.

###
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

(A) 0.8 | (B) 1.4 | (C) 2 | (D) 2.8 |

#### Q 36.

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

(A) 1/3 | (B) 1/2 | (C) 2/3 | (D) 3/4 |

#### Q 37.

###
In the CMOS circuit shown, electron and hole mobilities are equal, and M1 and M2 are equally sized. The device M1 is in the linear region if

(A) V_{in} < 1.875 V |

(B) 1.875 V < V_{in} < 3.125 V |

(C) V_{in} > 3.125 V |

(D) 0 < V_{in} < 5 V |

#### Q 39.

###
The signal *m(t)* as shown is applied both to a phase modulator (with *k*_{p} as the phase constant) and a frequency modulator (with *k*_{f} as the frequency constant) having the same carrier frequency.

The ratio *k*_{p}/*k*_{f }(in rad/Hz) for the same maximum phase deviation is

*m(t)*as shown is applied both to a phase modulator (with

*k*as the phase constant) and a frequency modulator (with

_{p}*k*as the frequency constant) having the same carrier frequency.

_{f}*k*/

_{p}*k*(in rad/Hz) for the same maximum phase deviation is

_{f } (A) 8 | (B) 4 | (C) 2 | (D) |

#### Q 40.

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

Hz=3cos(2.094×102x)cos(2.618×102y)cos(6.283×1010t??z)

The phase velocity *v*_{p} of the wave inside the waveguide satisfies

*v*of the wave inside the waveguide satisfies

_{p} (A) v>_{p}c | (B) v = _{p}c | (C) 0<v<_{p}c | (D) v=0_{p} |

#### Q 41.

###
The circuit shown is a

(A) low pass filter with |

(B) high pass filter with |

(C) low pass filter with |

(D) high pass filter with |

#### Q 44.

###
The voltage gain AV of the circuit shown below is

(A) | (B) | (C) | (D) |

#### Q 46.

###
The maximum value of *f*(*x*) = *x*^{3} - 9*x*^{2} + 24*x* + 5 in the interval [1, 6] is

*f*(

*x*) =

*x*

^{3}- 9

*x*

^{2}+ 24

*x*+ 5 in the interval [1, 6] is

(A) 21 | (B) 25 | (C) 41 | (D) 46 |

#### Q 47.

###
Given that

A=[?52?30] and I=[1001] , the value of *A*^{3} is

*A*^{3}is

(A) 15 | (B) 19 |

(C) 17 | (D) 17 |

#### Q 48.

###
With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:

(i) 1? connected at port B draws a current of 3 A

(ii) 2.5? connected at port B draws a current of 2 A

With 10 V dc connected at port A, the current drawn by 7? connected at port B is

(ii) 2.5?

(A) 3/7 A | (B) 5/7 A | (C) 1 A | (D) 9/7 A |

#### Q 50.

###
In the three dimensional view of a silicon n-channel MOS transistor shown below, ? = 20 nm. The transistor is of width 1 ? m. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of Si and SiO_{2}, respectively, are 11.7 and 3.9, and ?0 = 8.9 × 10^{-12} F/m.

The gate-source overlap capacitance is approximately

_{2}, respectively, are 11.7 and 3.9, and

^{-12}F/m.

(A) 0.7 fF | (B) 0.7 pF | (C) 0.35 fF | (D) 0.24 pF |

#### Q 51.

###
In the three dimensional view of a silicon n-channel MOS transistor shown below, ? = 20 nm. The transistor is of width 1 ? m. The depletion width formed at every p-n junction is 10 nm. The relative permittivities of Si and SiO_{2}, respectively, are 11.7 and 3.9, and ?0 = 8.9 × 10^{-12} F/m.

The source-body junction capacitance is approximately

_{2}, respectively, are 11.7 and 3.9, and

^{-12}F/m.

(A) 2 fF | (B) 7 fF | (C) 2 pF | (D) 7 pF |

#### Q 52.

###
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

(A) | (B) |

(C) | (D) |

#### Q 53.

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

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

The magnetic field inside the hole is

*b*(

*b*<

*a*) is now drilled along the length of the wire at a distance

*d*from the center of the wire as shown below.

(A) uniform and depends only on d | (B) uniform and depends only on b |

(C) uniform and depends on both b and d | (D) non uniform |

#### Q 54.

###
The transfer function of a compensator is given as

Gc(s)=s+as+b .

Gc(s) is a lead compensator if

(A) a =1, b = 2 | (B) a = 3, b = 2 |

(C) a = ?3, b = ?1 | (D) a = 3, b = 1 |

#### Q 55.

###
The transfer function of a compensator is given as

Gc(s)=s+as+b .

The phase of the above lead compensator is maximum at

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

#### Q 56.

###
If (1.001)^{1259} = 3.52 and (1.001)^{2062} = 7.85, then (1.001)^{3321} =

^{1259}= 3.52 and (1.001)

^{2062}= 7.85, then (1.001)

^{3321}=

(A) 2.23 | (B) 4.33 | (C) 11.37 | (D) 27.64 |

#### Q 57.

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

**If the tired soldier wanted to lie down, he ___****___** the mattress out on the balcony.

**If the tired soldier wanted to lie down, he ___**

**___**the mattress out on the balcony.(A) should take |

(B) shall take |

(C) should have taken |

(D) will have taken |

#### Q 58.

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

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

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

(A) beggary | (B) nomenclature | (C) jealousy | (D) nonchalance |

#### Q 59.

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

**Latitude**

**Latitude**

(A) Eligibility | (B) Freedom | (C) Coercion | (D) Meticulousness |

#### Q 60.

###
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.**

**INCORRECT**?

**I requested that he should be given the driving test today instead of tomorrow.**

(A) requested that |

(B) should be given |

(C) the driving test |

(D) instead of tomorrow |

#### Q 61.

###
**One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. 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?

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

(A) Thorough regimentation was the main reason for the efficiency of the Roman legions even in adverse circumstances. |

(B) The legions were treated inhumanly as if the men were animals. |

(C) Discipline was the armies? inheritance from their seniors. |

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

#### Q 64.

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

Category | Amount (Rs.) |

Food | 4000 |

Clothing | 1200 |

Rent | 2000 |

Savings | 1500 |

Other expenses | 1800 |

The approximate percentage of the monthly budget **NOT **spent on savings is

(A) 10% | (B) 14% | (C) 81% | (D) 86% |