Q. 1  Q. 5 carry one mark each.
Q.
If (1.001)^{1259} = 3.52 and (1.001)^{2062} = 7.85, then (1.001)^{3321}
Choose the most appropriate alternate 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.
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Choose the most appropriate word from the options given below to complete the
following sentence :
Give the seriousness of the situation that he had to face, his........was impressive.
Which one of the following options is the closest in meaning to the word given
below ?
Latitude
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.
Q. 6  Q. 10 carry two marks each
Q.
One of the legacies of the Roman legions was discipline. In the legious, 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 ?
Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money values of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is
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 minimum number of weighings required to identify the heavier bag is
The data given in the following table summarizes the monthly budget of an average
household.
The approximate percentages of the monthly budget NOT spent on savings is
A and B are friends. They decide to meet between 1 PM and 2 PM on a given day.
There is a conditions that whoever arrives first will not wait for the other for more
than 15 minutes. The probability that they will meet on that days is
Q. 11  Q. 35 carry one mark each
Q.
The current ib through the base of a silicon npn transistor is 1 + 0.1 cos (10000 π t)mA
At 300 K, the r_{π} in the small signal model of the transistor is
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
In a baseband communications link, frequencies upto 3500 Hz are used for signaling.
Using a raised cosine pulse with 75% excess bandwidth and for no intersymbol
interference, the maximum possible signaling rate in symbols per second is
A plane wave propagating in air with is incident on a perfectly conducting slab positioned at x 0. The E field of the reflected wave is
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
Consider the given circuit
In this circuit, the race around
The output Y of a 2bit comparator is logic 1 whenever the 2bit input A is greater than the 2bit input B. The number of combinations for which the output is logic 1, is
The i v characteristics of the diode in the circuit given below are
The current in the circuit is
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
The average power delivered to an impedance (4 − j3)Ω by a current 5 cos (100 π t + 100)A is
The unilateral Laplace transform of f (t) is^{ } The unilateral Laplace transform of tf (t) is
With initial condition x(1) = 0.5, the solution of the differential equation
The diodes and capacitors in the circuit shown are ideal. The voltage v(t) across the diode D_{1} is
In the circuit shown
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 ε and decreases that of the second by ε. After encoding, the entropy of the source
A coaxialcable with an inner diameter of 1mm and outer diameter of 2.4 mm is
filled with a dielectric of relative permittivity 10.89. Given μ0 = 4πx 10^{7} H/m,
the characteristic impedance of the cable is
The radiation pattern of an antenna in spherical coordinates is given by
F(θ) = cos^{4}θ ; 0 θ π/2
The directivity of the antenna is
If then the region of convergence (ROC) of its z
transform in the z plane will be
In the sum of products function the prime implicants are
A system with transfer function
is excited by sin(ωt). The steadystate output of the system is zero at
The impedance looking into nodes 1 and 2 in the given circuit is
In the circuit shown below, the current through the inductor is
Given
If C is a counter clockwise path in the z plane such that z + 1 = 1, the value of
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
If then the value of x^{x} is
Q. 36 to Q. 65 carry two marks each.
Q.
The source of a silicon (n_{i }= 10^{10} per cm^{3} ) nchannel MOS transistor has an area of 1 sq μm and a depth of 1 μm. If the dopant density in the source is 10^{19}/cm^{3}, the number of holes in the source region with the above volume is approximately
A BPSK scheme operating over an AWGN channel with noise power spectral density
of N0/2, uses equiprobable signals
over the symbol interval (0,T). If the local oscillator in a coherent receiver is ahead in phase by 45c with respect to the received signal, the probability of error in the resulting system is
A transmission line with a characteristic impedance of 100 Ω is used to match a
50 Ω section to a 200 Ω section. If the matching is to be done both at 429MHz and
1GHz, the length of the transmission line can be approximately
The input x(t) and output y(t) of a system are related as . The system is
The feedback system shown below oscillates at 2 rad/s when
The Fourier transform of a signal h(t) is H(jω) = (2 cosω) (sin2ω)/ω. The value of
h(0) is
The state variable description of an LTI system is given by
where y is the output and u is the input. The system is controllable for
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
Consider the differential equation
The numerical value of is
The direction of vector A is radially outward from the origin, with where r^{2} = x^{2}+ y^{2}+ z^{2} and k is a constant. The value of n for which 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
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
The signal m(t) as shown is applied to both a phase modulator (with kp as the
phase constant) and a frequency modulator (with kf 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
The magnetic field among the propagation direction inside a rectangular waveguide
with the crosssection shown in the figure is
H_{z}= 3 cos (2.094 x 10^{2 } x)cos (2.618 x10^{2}y)cos (6.283 x10^{10}t βz)
The phase velocity v_{p} of the wave inside the waveguide satisfies
The circuit shown is a
Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)^{n}u[n] and g[n]
is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals
The state transition diagram for the logic circuit shown is
The voltage gain Av of the circuit shown below is
The maximum value of f (x) = x^{3}− 9x^{2}+ 24x + 5 in the interval [1,6] is
With 10 V dc connected at port A in the linear nonreciprocal twoport network
shown below, the following were observed :
(i) 1Ω connected at port B draws a current of 3A
(ii) 2.5 Ω connected at port B draws a current of 2A
Q.
With 10 V dc connected at port A, the current drawn by 7 Ω connected at port B
is
With 10 V dc connected at port A in the linear nonreciprocal twoport network
shown below, the following were observed :
Q.
For the same network, with 6 V dc connected at port A, 1Ω connected at port B
draws 7/3 A. If 8 V dc is connected to port A, the open circuit voltage at port B is
In the three dimensional view of a silicon nchannel MOS transistor shown below, δ = 20 nm. The transistor is of width 1 μm. The depletion width formed at every pn junction is 10 nm. The relative permittivity of Si and SiO_{2}, respectively, are 11.7 and 3.9, and ε_{0 = }8.9 x 10^{12 }F/m
Q.
The gate source overlap capacitance is approximately
In the three dimensional view of a silicon nchannel MOS transistor shown below, δ = 20 nm. The transistor is of width 1 μm. The depletion width formed at every pn junction is 10 nm. The relative permittivity of Si and SiO_{2}, respectively, are 11.7 and 3.9, and ε_{0 = }8.9 x 10^{12 }F/m
Q.
The sourcebody junction capacitance is approximately
Statement for Linked Answer Question 61 and 62
An infinitely long uniform solid wire of radius a carries a uniform dc current of
density J
Q.
The magnetic field at a distance r from the center of the wire is proportional to
An infinitely long uniform solid wire of radius a carries a uniform dc current of
density J
Q.
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
A binary symmetric channel (BSC) has a transition probability of 1/8. If the
binary symbol X is such that P(X = 0) = 9/10, then the probability of error for
an optimum receiver will be
Correct answer will be uploaded soon
Statement for Linked Answer Question 64 and 65
The transfer function of a compensator is given as
Q.
Gc (s) is a lead compensator if
The transfer function of a compensator is given as
Q.
The phase of the above lead compensator is maximum at
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25 docs263 tests

Electronics and Communication Engineering  (EC) 2024 GATE Paper with solution Doc  41 pages 
Electronics and Communication Engineering  (EC) 2023 GATE Paper with Solution Doc  52 pages 
Electronics and Communication Engineering  (EC) 2022 GATE Paper with solution Doc  50 pages 
Electronics and Communication Engineering  (EC) 2021 GATE Paper with solution Doc  46 pages 
Electronics and Communication Engineering  (EC) 2020 GATE Paper with solution Doc  34 pages 