GATE 2012 Electronics & Communication

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given $${\mu _0} = \,4\,\pi \, \times \,{10^...

If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is

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

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

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....

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 i...

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

Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the value of $${A^3}$$ is

The average power delivered to an impedance $(4-j 3) \Omega$ by a current $5 \cos (100 \pi t+100) A$ is

The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$ The phase of the above lead compensator is maximum at

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 amou...

A transmission line with a characteristic impedance of 100 $$\Omega $$ is used to match a 50 $$\Omega $$ section to a 200 $$\Omega $$ section. If the matching is to be done both at...

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 rece...

The electric field of a uniform plane electromagnetic wave in free spce, along the positive x direction, is given by $$\vec E = 10\left( {{{\widehat a}_y} + j{{\widehat a}_z}} \rig...

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

In a base band communications link, frequencies up to 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, th...

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

A BPSK scheme operating over an AWGN channel with noise power spectral density of N 0 2, uses equi-probable signals $$${s_1}\left( t \right) = \sqrt {{{2E} \over T}\,\sin \left( {{...

The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$ $${G_C}(s)$$ is a lead compensator if

The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is

If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform...

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 ins...

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...

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...

Consider the differential equation $${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$ with $$y\left( t...

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the min...

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 impre...

The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} = {x^2} + {y^2} + {z^2}$$ and $$K$$ is constant. The value of...

Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in the interval $$\left[ { - 1,1} \right].$$ The probability that max $$\left[ {X,Y} \right]$$ is less th...

A system with transfer function g(s) = $${{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \right)\left( {s + 3} \right)\left( {s + 4} \right)}},$$ is excit...

With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solution of the differential equation, $$\,\,\,t{{dx} \over {dt}} + x = t\,\,\,$$ is

Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-plane such that $$\left| {z + 1} \right| = 1,$$ the value of $...

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

The Fourier transform of a signal h(t) is $$H(j\omega )$$ =(2 cos $$\omega $$) (sin 2$$\omega $$) / $$\omega $$. The value of h(0) is

The source of a silicon (n i = 10 10 per cm 3 ) n - channel MOS transistor has an aewa of 1 sq $$\mu m$$ and a depth of 1 $$\mu m$$ . If the dopant density in the source is 10 19 /...

Let $$y\left[ n \right]$$ denote the convolution of $$h\left[ n \right]$$ and $$g\left[ n \right]$$, where $$h\left[ n \right]$$ $$ = \,{\left( {1/2} \right)^2}\,\,u\left[ n \right...

The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau $$. The system is

A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \right){\mkern 1mu} {\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y}...

An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$ The magnetic field at a distance r from the center of the wire is...

The radiation pattern of an antenna in spherical co-ordinates is given by $$$F\,(\theta )\, = {\cos ^4}\,\theta \,\,\,;\,\,0\,\, \le \,\,\theta \,\, \le \,\,\pi /2$$$ The directivi...