GATE ECE 2012
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GATE ECE

The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D1 is
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The current ib through the base of a silicon npn transistor is $$1\;+\;0.1\;\cos\left(10000\;\mathrm\pi\;\mathrm t\right View Question The voltage gain Av of the circuit shown below is View Question The circuit shown is a View Question The signal m(t) as shown is applied both to a phase modulator (with kp as the phase constant) and a frequency modulator View Question A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder i View Question In a base band communications link, frequencies up to 3500 Hz are used for signaling. Using a raised cosine pulse with 7 View Question Two independent random variable X and Y are uniformly distributed in the interval [ - 1, 1]. The probability that max [X View Question The power spectral density of a real process X(t) for positive frequencies is shown below. The value of$$E\,\left[ {{X^
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A BPSK scheme operating over an AWGN channel with noise power spectral density of N02, uses equi-probable signals $$View Question A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X View Question The feedback system shown below oscillates at 2 rad/s when View Question A system with transfer function g(s) =$${{\left( {{s^2} + 9} \right)\left( {s + 2} \right)} \over {\left( {s + 1} \rig
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The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$ The phase of the above lead
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The transfer function of a compensator is given as $${G_C}(s) = {{s + a} \over {s + b}}.$$ $${G_C}(s)$$ is a lead compe
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The state variable description of an LTI system is given by where y is the output and u is input. The system is contro
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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
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Consider the given circuit. In this circuit, the race around
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The state transition diagram for the logic circuit shown is
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An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$. A hol
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An infinitely long uniform solid wire of radius a carries a uniform dc current of density $$\widehat{\mathrm j}$$ The ma
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A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative perm
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The electric field of a uniform plane electromagnetic wave in free spce, along the positive x direction, is given by $View Question A plane wave propagating in air with $$\vec E = \left( {8{{\widehat a}_x} + 6{{\widehat a}_y} + 5{{\widehat a}_z}} \righ View Question A transmission line with a characteristic impedance of 100$$\Omega $$is used to match a 50$$\Omega $$section to a 20 View Question The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the fi View Question The radiation pattern of an antenna in spherical co-ordinates is given by$$$F\,(\theta )\, = {\cos ^4}\,\theta \,\,\,;\
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In the circuit shown
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In the three dimensional view of a silicon n-channel MOS transistor shown below, $$\delta = 20$$ nm. The transistor is
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The source of a silicon (ni = 1010 per cm3) n - channel MOS transistor has an aewa of 1 sq $$\mu m$$ and a depth of 1 $$View Question In the three dimensional view of a silicon n-channel MOS transistor shown below,$$\delta = 20$$nm. The transistor is View Question In the CMOS circuit shown, electron and hole mobilities are equal, and M1 and M2 are equally sized. The device M1 is in View Question Given that$$A = \left[ {\matrix{ { - 5} &amp; { - 3} \cr 2 &amp; 0 \cr } } \right]$$and$${\rm I} = \left[
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The direction of vector $$A$$ is radially outward from the origin, with $$\left| A \right| = K\,{r^n}$$ where $${r^2} View Question Two independent random variables$$X$$and$$Y$$are uniformly distributed in the interval$$\left[ { - 1,1} \right].$$View Question A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd View Question With initial condition$$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$the solution of the differential equation,$$\,\
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If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then
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The unilateral Laplace transform of $$f(t)$$ is $$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$View Question Consider the differential equation$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y
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If $$x = \sqrt { - 1} ,\,\,$$ then the value of $${X^x}$$ is
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Given $$f\left( z \right) = {1 \over {z + 1}} - {2 \over {z + 3}}.$$ If $$C$$ is a counterclockwise path in the $$z$$-pl
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In the circuit shown below, current through the inductor is
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The independence looking into nodes 1 and 2 in the given circuit is
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If VA - VB = 6 V then VC - VD is
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Assuming both the voltage sources are in phase the value of R for which maximum power is transferred from circuit A to c
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With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:
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With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed:
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In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed
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The average power delivered to an impedance $(4-j 3) \Omega$ by a current $5 \cos (100 \pi t+100) A$ is
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If $$x\left[ n \right]$$= $${(1/3)^{\left| n \right|}} - {(1/2)^n}u\left[ n \right]$$, then the region of convergence (R
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The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\ta View Question The Fourier transform of a signal h(t) is$$H(j\omega )$$=(2 cos$$\omega $$) (sin 2$$\omega $$) /$$\omega $$. The val View Question Let$$y\left[ n \right]$$denote the convolution of$$h\left[ n \right]$$and$$g\left[ n \right]$$, where$$h\left[ n \
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General Aptitude

If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =
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Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the
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The data given in the following table summarizes the monthly budget of an average household. The approximate percentage
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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
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There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing b
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One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was bruta
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Choose the most appropriate alternative from the options given below to complete the following sentence: If the tired so
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Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness
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Which one of the following options is the closest in meaning to the word given below? Latitude
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One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I
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