GATE ECE 2014 Set 1

## GATE ECE

A BJT is baised in forward active mode Assume VBE = 0.7 V, kT/q = 25 mV and reverse saturation current Is = 10-13A. The

View Question For the amplifier shown in the figure, the BJT parameters are VBE = 0.7 V, $$\beta $$ = 200, and thermal voltage VT = 2

View Question A good current buffer has

View Question In the low - pass filter shown in the figure, for a cut - off frequency of 5 KHz, the value of R2 (in k$$\Omega $$ ) is

View Question In the ac equivalent circuit shown in the figure, if i$${_F}$$ is very large, the type of feedback is

View Question In the voltage regulator circuit shown in the figure, the op - amp is ideal. The BJT has VBE = 0.7 V and $$\beta $$ = 10

View Question In the circuit shown, the op-amp has finite input impedance, infinite voltage gain and zero input offset voltage. The ou

View Question In a code - division multiple access (CDMA) system with N = 8 chips, the maximum number of users who can be assign

View Question Consider a random process $$X\left( t \right) = \sqrt 2 \sin \left( {2\pi t + \varphi } \right),$$ where the ra

View Question Let $$Q\left( {\sqrt y } \right)$$ be the BER of a BPSK system over an AWGN channel with two - sided noise power spectra

View Question The capacity of a Binary Symmetric Channel (BSC) with cross - over probability 0.5 is ______ .

View Question A fair coin is tossed repeatedly until a 'Head' appears for the first time. Let L be the number of tosses to get this fi

View Question The forward path transfer function of a unity negative feedback system is given by
$$$G\left(s\right)\;=\;\frac k{\left

View Question For the following feedback system $$G\left(s\right)=\frac1{\left(s+1\right)\left(s+2\right)}$$.The 2% settling time of t

View Question Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which
one of the following con

View Question The phase margin in degrees of G(s)=$${{10} \over {\left( {s + 0.1} \right)\left( {s + 1} \right)\left( {s + 10} \right)

View Question Consider the state space model of a system, as given below
The system is

View Question The Boolean expression
(X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to

View Question Consider the Boolean function,
F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline

View Question The output F in the digital logic circuit shown in the figure is

View Question Five JK flip - flops are cascaded to form circuit shown in figure. Clock pulses at a frequency of 1 MHz are applied as s

View Question The digital logic shown in the figure satisfies the given state diagram when Q1 is connected to
input A of the XOR gate.

View Question A two - port network has scattering parameters given by $$[S]$$ $$ = \left[ {\matrix{
{{s_{11}}} & {{s_{12}}} \

View Question For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglect

View Question In spherical coordinates, let $${{{\widehat a}_{_0}},\,{{\widehat a}_{_\phi }}}$$ denote unit vectors along the $$\theta

View Question When the optical power incident on a photodiode is 10μW and the responsivity is 0.8 A/W,
the photocurrent generated (in

View Question If fixed positive charges are present in the gate oxide of an n-channel enhancement type
MOSFET, it will lead to

View Question In the ac equivalent circuit shown in the figure, if in is the input current and RF is very large, the type of feedback

View Question In the following circuit employing pass transistor logic, all NMOS transistors are identical
with a threshold voltage of

View Question A depletion type N -channel MOSFET is biased in its linear region for use as a voltage controlled resistor. Assume thres

View Question For matrices of same dimension $$M,N$$ and scalar $$c,$$ which one of these properties DOES NOT ALWAYS hold ?

View Question Consider the matrix $${J_6} = \left[ {\matrix{
0 & 0 & 0 & 0 & 0 & 1 \cr
0 & 0 & 0 &

View Question $$A$$ real $$\left( {4\,\, \times \,\,4} \right)$$ matrix $$A$$ satisfies the equation $${A^2} = {\rm I},$$ where $${\rm

View Question The Taylor series expansion of $$3$$ $$sin$$ $$x$$ $$+2cos$$ $$x$$ is

View Question The volume under the surface $$z\left( {x,y} \right) = x + y$$ and above the triangle in the $$xy$$ plane defined by $

View Question Let $$\,{X_1},\,\,{X_2}\,\,$$ and $$\,{X_3}\,$$ be independent and identically distributed random variables with the uni

View Question Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mea

View Question In a housing society, half of the families have a single child per family, while the remaining half have two children pe

View Question $$C$$ is a closed path in the $$z-$$plane given by
$$\left| z \right| = 3.$$ The value of the integral
$$\oint\limits_

View Question A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is

View Question Consider the configuration shown in the figure which is a portion of a larger electrical
network
For R = 1 Ω and curr

View Question A Y-network has resistances of 10Ω each in two of its arms, while the third arm has a
resistance of 11Ω in the equivalen

View Question For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output i

View Question A 230 V rms source supplies power to two loads connected in parallel. The first load draws
10 kW at 0.8 leading power fa

View Question In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is _

View Question A periodic variable x is shown in the figure as a function of time. The root - mean - square (rms) value of x is _______

View Question A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\

View Question A system is described by the following differential equation, where u(t) is the input to the system and y(t) is output o

View Question Consider a discrete time periodic signal x$$\left[ n \right]$$= $$\sin \left( {{{\pi n} \over 5}} \right)$$. Let ak be

View Question Let x $$\left[ n\right]$$= $${\left( { - {1 \over 9}} \right)^n}\,u(n) - {\left( { - {1 \over 3}} \right)^n}u( - n - 1).

View Question For a function g(t), it is given that $$\int_{ - \infty }^\infty {g(t){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}

View Question Consider two real valued signals, $$x\left( t \right)$$ band - limited to $$\,\left[ { - 500Hz,\,\,500Hz} \right]$$ and

View Question A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer is

View Question ## General Aptitude

For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill
up Form P and all residen

View Question Find the odd one from the following group:
W,E,K,O I,Q,W,A F,N,T,X N,V,B,D

View Question A train that is 280 meters long, traveling at a uniform speed, crosses a platform in 60 seconds
and passes a man standin

View Question The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the
following bar chart. If the t

View Question You are given three coins: one has heads on both faces, the second has tails on both faces,
and the third has a head on

View Question