Electronics And Communication - ECE 2015 GATE Paper (Practice Test)
66 Questions MCQ Test Mock Tests Electronics & Communication Engineering GATE | Electronics And Communication - ECE 2015 GATE Paper (Practice Test)
A rectangular waveguide, in dominant TE mode, has dimensions 10 cm x 15 cm. The cut off frequency is
Choose the most appropriate word from the options given below to complete the following
sentence.
The principal presented the chief guest with a ________, as token of appreciation.
sentence.
The principal presented the chief guest with a ________, as token of appreciation.
Choose the appropriate word/phrase, out of the four options given below, to complete the
following sentence:
Frogs__________.
following sentence:
Frogs__________.
Choose the word most similar in meaning to the given word: ( educe)
If logx (5/7) = –1/3, then the value of x is
Q. 6 -10 Carry Two mark each
Q.
A cube of side 3 units is formed using a set of smaller cubes of side 1 unit; Find the proportion of
the number of faces of the smaller cubes visible to those which are NOT visible.
The following question presents a sentence, part of which is underlined. Beneath the sentence you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence.
Tuberculosis, together with its effects, "ranks one of the leading causes of death" in India.
Humpty Dumpty sits on a every day while having lunch. The wall sometimes breaks. A person
sitting on the wall falls if the wall breaks.
Which one of the statements below is logically valid and can be inferred from the above
sentences?
Find the missing Value:
Read the following paragraph and choose the correct statement.
Climate change has reduced human security and threatened human well being. An ignored reality
of human progress is that human security largely depends upon environmental security. But on the
contrary, human progress seems contradictory to environment security. To keep up both at the
required level is a challenge to be addressed by one and all. One of the ways to curb the climate
change may be suitable scientific innovations, while the other may be the Gandhian perspective on
small scale progress with focus on sustainability.
Q. No. 11 – 35 Carry One Mark Each
Q.
A region of negative differential resistance is observed in the current voltage characteristics
of a silicon PN junction if
A silicon sample is uniformly doped with donor type impurities with a concentration of
1016 / cm3 . The electron and hole mobilities in the sample are
1200cm3 / V-s and 400cm2 / V-s respectively. Assume complete ionization of impurities.
The charge of an electron is 1.6x 10-19 C. The resistivity of the sample (in ?- cm) is _____________.
A unity negative feedback system has the open-loop transfer function
The value of the gain K (>0) at which the root locus crosses the imaginary axis is
_________________.
By using Routh Table, s1 row should be zero. For poles to be on imaginary axis
Suppose A and B are two independent events with probabilities 
be their complements. Which one of the following statements is FALSE?
We know that A and B are independent
then 
The waveform of a periodic signal x(t) is shown in the figure
A signal g(t) is defined by
. The average power of g(t) is
__________________.
The average power of x(t) and g(t) is same because the signal g(t) is scaled and shifted
version of x(t).
In the network shown in the figure, all resistors are identical with R = 300?. The resistance
Rab (in ?) of the network is___________.
Consider a system of linear equations:
x − 2 y + 3z = −1,
x − 3y + 4z = 1, and
−2x + 4 y − 6z = k.
The value of k for which the system has infinitely many solutions is ______.
x-2y+3z = -1
x-3y+4z = 1
-2x+4y-6z = k
The system will have infinitely many solutions if p(A/B) = p(A) = r < number of variables
k-2 = 0
k = 2
The polar plot of the <transfer function 
for 0 
ω < ∞ will be in the
Let z = x + iy be a complex variable. Consider that contour integration is performed along
the unit circle in anticlockwise direction. Which one of the following statements is NOT
TRUE?
Consider the signal 
where mˆ t denotes the Hilbert
transform of m(t) and the bandwidth of m(t) is very small compared to fc . The signal s(t) is a
Given s(t) is the equation for single side band modulation (lower side band).
Thus it is a Band pass signal.
For the circuit with ideal diodes shown in the figure, the shape of the output (vout) for the
given sine wave input (vin) will be
The circuit can be re drawn as
During positive pulse, both diodes are forward biased. So output pulse of +ve polarity is
produced. As polarity at ‘d’ and ‘c’ is given opposite to input terminals, hence +ve pulse is
inverted. During negative pulse, both diodes are reverse biased. So, V0 = 0V
The result of the convolution x(-t) *δ(-t-t0) is
The value of p such that the vector 
is an eigenvector of the matrix 
is
In the given circuit, the values of V1 and V2 respectively are
In an 8085 microprocessor, the shift registers which store the result of an addition and the
overflow bit are, respectively
In an 8085 microprocessor, after performing the addition, result is stored in accumulator and if any carry (overflow bit) is generated it updates flags.
Negative feedback in a closed-loop control system DOES NOT
Negative feedback in a closed loop
(i) Increases bandwidth
(ii) Reduces gain
(iii) Improve distance rejection
A 16 Kb (=16,384 bit) memory array is designed as a square with an aspect ratio of one
(number of rows is equal to the number of columns). The minimum number of address lines
needed for the row decoder is ___________________.
Generally the structure of a memory chip = Number of Row × Number of column
= M×N
→ The number of address line required for row decoder is n where M = 2n or
n = log2M
→ As per information given in question : M = N
So M×N = M×M = M2 = 16k = 24×210
M2 = 214
M = 128
→ n = log2128 = 7
A function f(x) = 1- x2+x3is defined in the closed interval [-1, 1]. The value of x, in the
open interval (-1, 1) for which the mean value theorem is satisfied, is
By Lagrange’s mean value theorem
The electric field component of a plane wave traveling in a lossless dielectric medium is
given by 
The wavelength (in m) for the wave is
In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The energy (in μJ) taken from the 3V source to charge the 0.1μF capacitor from 0V to 3V is
So the capacitor in initially uncharged i.e. VC(0) = 0
→ The capacitor will be charged to supply voltage 3V when the switch is in position B
for ∞ time.
→ So we need to find capacitor voltage
In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6V. The output
voltage V0 (in volts) is ________________.
Zener is not Breakdown
Hence
V0 =10x (1/2) =5V
Consider a four bit D to A converter. The analog value corresponding to digital signals of values 0000 and 0001 are 0V and 0.0625V respectively. The analog value (in Volts) corresponding to the digital signal 1111 is ___________.
Analog output = [Resolution] × [Decimal equivalent of Binary]
= (0.0615) (15) = 0.9225V
In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across
the capacitor is ___________________.
A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and
step-size Δ of the delta modulator are 20,000 samples per second and 0.1V, respectively. To
prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one
of the following plots (in linear scale) qualitatively represents the dependence of 
on r,
where is the magnitude of the azimuthal component of magnetic field outside the
conductor and r is the radial distance from the conductor?
Q. No. 36 – 65 carry Two Marks Each
Q.
The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ‘1’ was transmitted is ______________________.
The transmitted signal in a GSM system is of 200 kHz bandwidth and 8 users share a
common bandwidth using TDMA. If at a given time 12 users are talking in a cell, the total
bandwidth of the signal received by the base station of the cell will be at least (in kHz)
__________________.
Since GSM requires 200 KHz and only 8 users can use it using TDMA, 9th user needs
another 200 KHz.
9th, 10th, 11th, 12th user can use another 200 KHz bandwidth on time share basis.
Thus for 12 user we need 400 KHz bandwidth.
For the discrete-time system shown in the figure, the poles of the system transfer function are
located at
The circuit shown in the figure has an ideal opamp. The oscillation frequency and the
condition to sustain the oscillations, respectively, are
Frequency of Wein bridge oscillator is ω0 =1/RC but in the question time constant is
doubled so, frequency becomes half.
A source emits bit 0 with probability1/3 and bit 1 with probability 2/3. The emitted bits are
communicated to the receiver. The receiver decides for either 0 or 1 based on the received
value R. It is given that the conditional density functions of R are as
For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are
1 × 1017 cm-3 and 1 × 1015 cm-3, respectively. The lifetimes of electrons in P region and holes in N
region are both 100 μs. The electron and hole diffusion coefficients are 49 cm2/s and 36 cm2/s,
respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 × 1010 cm-3, and
q = 1.6 × 10-19 C. When a forward voltage of 208 mV is applied across the diode, the hole current
density (in nA/cm2) injected from P region to N region is _____________.
For the NMOSFET in the circuit shown, the threshold voltage is Vth , where Vth > 0 . The
source voltage Vss is varied from 0 to VDD . Neglecting the channel length modulation, the
drain current ID as a function Vss is represented by.
In the system shown in figure (a), m(t) is a low-pass signal with bandwidth W Hz. The
frequency response of the band-pass filter H(f) is shown in figure (b). If it is desired that the
output signal z(t) = 10x(t), the maximum value of W (in Hz) should be strictly less than
m2 (t) →
2W<700
2400 - 2W >1700
w< 350
In the circuit shown, I1 =80mA and I2 = 4mA. Transistors T1 and T2 are identical. Assume
that the thermal voltage VT is 26mV at 27o C. At 50o C , the value of the voltageV12 = V1 - V2 (in mV) is ________________.
The electric field intensity of a plane wave traveling in free space is give by the following
expression 
In this field, consider a square area 10cm x 10 cm on a plane x + y = 1. The total timeaveraged
power (in mW) passing through the square area is __________________.
The maximum area (in square units) of a rectangle whose vertices lie on the ellipse
x2 + 4y2 =1 is ____________________.
Let 2x, 2y be the length, breadth respectively of the rectangle inscribed in the ellipse
x2 + 4y2 =1, then
Area of the rectangle (2x) (2y) i.e., 4xy
In the given circuit, the maximum power (in Watts) that can be transferred to the load RL is
___________________.
A lead compensator network includes a parallel combination of R and C in the feed-forward
path. If the transfer function of the compensator is GC(S) = s+2/s+4. the value of RC is
______________.
A MOSFET in saturation has a drain current of 1mA for VDS = 0.5V. If the channel length
modulation coefficient is 0.05 V-1 , the output resistance (in k?) of the MOSFET is
The built-in potential of an abrupt p-n junction is 0.75V. If its junction capacitance ( Cj) at
a reverse bias ( VR) of 1.25V is 5pF, the value of Cj in pF when VR = 7.25V is ________________.
In the circuit shown, assume that the opamp is ideal. The bridge output voltage V0 (in mV)
for δ= 0.05 is _______________________.
The damping ratio of a series RLC circuit can be expressed as
In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value
of vc(t) (in Volts) at t= 1 sec is ___________________.
Consider a uniform plane wave with amplitude (E0) of 10V/ m and 1.1GHz frequency
travelling in air, and incident normally on a dielectric medium with complex relative
permittivity (εr ) and permeability (μr) as shown in the figure.
The magnitude of the transmitted electric field component (in V/m) after it has travelled a
distance of 10 cm inside the dielectric region is __________________.
A vector 
. Which one of the following statements
is TRUE?
All the logic gates shown in the figure have a propagation delay of 20 ns. Let A=C=0 and
B=1 until time t=0. At t= 0, all the inputs flip (i.e., A = C = 1 and B = 0) and remain in that
state. For t > 0, output Z = 1 for a duration (in ns) of
As per information given on question the waveforms of A, B, C are as follows
→The logic to solve this question is first obtain X, Y waveform and using this obtain Z.
→ To obtain X, initially assume delay of NOT gate is 0 and draw its waveform and finally
shift it by 20nsec to obtain actual X. Similar procedure to be followed for obtaining Y
and Z i.e., first draw waveform with 0 delay and at the end shift by the amount of delay
given in question.
Clearly we can say that output is high during 20 nsec to 60 nsec i.e. a duration of 40 nsec
A plant transfer function is given as 
When the plant operates in a
unity feedback configuration, the condition for the stability of the closed loop system is
A plant transfer function is given as When the plant operates in a
unity feedback configuration, the condition for the stability of the closed loop system is
A 3-input majority gate is defined by the logic function M(a,b,c) = ab + bc + ca . Which one
of the following gates is represented by the function 
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide
made of a perfect electric conductor is given by the following expression
The cross-sectional dimensions of the waveguide are given as a = 0.08m and b= 0.033m. The
mode of propagation inside the waveguide is
The open-loop transfer function of a plant in a unity feedback configuration is given a
. The value of the gain K(>0) for which -1+ j2 lies on the root locus is _______________.
Two sequences [a, b, c] and [A, B, C] are related as,
then the relationship between the sequences [p, q, r] and [a, b, c] is
The solution of the differential equation
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The
zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h[0] = 1,
we can conclude
Which one of the following graphs describes the function f(x) =e-x(x2 + x + 1) ?
f(1) = e-x (x2+x+1)
f(0) = 1
f(0.5) = 1.067
For positive values of x, function never goes negative.
The Boolean expression 
converted into the
canonical product of sum (POS) form is
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