Q. No. 1 – 5 Carry One Mark Each
Q. Choose the grammatically CORRECT sentence:
Statement: You can always give me a ring whenever you need.
Which one of the following is the best inference from the above statement?
In the summer of 2012, in New Delhi, the mean temperature of Monday to
Wednesday was 41ºC and of Tuesday to Thursday was 43ºC. If the temperature
on Thursday was 15% higher than that of Monday, then the temperature in ºC on
Thursday was
Let the temperature of Monday be T_{M}
Sum of temperatures of Tuesday and Wednesday = T and
Temperature of Thursday =T_{Th}
Now, T_{m} +T = 41x 3 =123
& T_{th+} T= 43x 3= 129
T_{th} T_{m=} 6, Also T_{th=} 1.15T_{m}
0.15T_{m=} 6 T_{m} =40
Temperature of thursday= 40+ 6= 46^{o} C
Complete the sentence:
Dare ____________ mistakes.
They were requested not to quarrel with others.
Which one of the following options is the closest in meaning to the word quarrel?
Q. No. 6 – 10 Carry Two Marks Each
Q.
A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16km in the third quarter. The average speed of the car in km per hour over the entire journey is
Average speed = Total distance/Total Time
Find the sum to n terms of the series 10 + 84 + 734 + …
Explanations:Using the answer options, substitute n = 2. The sum should add up to 94
Alternative Solution:
The given series is 10+84+734+………………………..+n terms
Statement: There were different streams of freedom movements in colonial India
carried out by the moderates, liberals, radicals, socialists, and so on.
Which one of the following is the best inference from the above statement?
The set of values of p for which the roots of the equation 3x^{2} + 2x + p( p − 1) = 0
are of opposite sign is
What is the chance that a leap year, selected at random, will contain 53
Sundays?
There are 52 complete weeks in a calendar year 852 × 7 =364days
Number of days in a leap year = 366
Probability of 53 Saturdays 2/7
Q. No. 11 – 35 Carry One Mark Each
Q.
A bulb in a staircase has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by any one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles
From Truth Table, it can be verified that ExOR logic is implemented
Consider a vector field The closed loop line integral
can be expressed as
Stoke’s Theorem: “ The Line Integral of a vector around a closed path L is
equal to the integral of curl of over the open surface S enclosed by the closed
path L”.
Two systems with impulse responses h_{1}(t) and h_{2}(t) are connected in cascade.
Then the overall impulse response of the cascaded system is given by
In a forward biased pn junction diode, the sequence of events that best describes
the mechanism of current flow is
In IC technology, dry oxidation (using dry oxygen) as compared to wet oxidation
(using steam or water vapor) produces
The maximum value of q until which the approximation sinθ ≈ θ holds to within 10%
error is
Out of all possible options we need to go for max theta below 45° Hence it is
18°
The divergence of the vector field
The impulse response of a system is h(t) = tu(t). For an input u(t − 1) , the output is
For LTI system, if input gets delayed by one unit, output will also get delayed by
one unit.
The Bode plot of a transfer function G (s) is shown in the figure below
The gain (20 log G(s) ) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively.
The phase is negative for all ω. The G(s) is
Any two paints on same line segment of Bode plot satisfies the equation of
straight line.
In the circuit shown below what is the output voltage ( ) out V if a silicon transistor
Q and an ideal opamp are used?
Consider a delta connection of resistors and its equivalent star connection as shown below. If all elements of the delta connection are scaled by a factor k, k> 0, the elements of the corresponding star equivalent will be scaled by a factor of
Above expression shown that if R_{a} , R_{b} & R_{c} is scaled by k, R_{a} , R_{b} & R_{c} is scaled
by k only.
For 8085 microprocessor, the following program is executed
MVI A, 05H;
MVIB, 05H;
PTR: ADD B;
DCR B;
JNZ PTR;
ADI 03H;
HLT;
At the end of program, accumulator contains
Accumulator changes as follows (05 + 05 + 04 +03 +02 +01)H
At the end of Loop accumulator contains = 14H
ADI O3H →A=(14+03)=17H
The bit rate of a digital communication system is R kbits/s. The modulation used is
32QAM. The minimum bandwidth required for ISI free transmission is
Bit rate given = R Kbits/second
Modulation = 32QAM
No. of bits/symbol = 2 5 [log 32]
Symbol rate =R/5 k symbols / sec ond
Finally we are transmitting symbols.
For a periodic signal v (t) = 30sin100t + 10cos300t + 6 sin(500t + π / 4) , the
fundamental frequency in rad/s
ω_{o} =100 rad / sec fundamental
3ω_{o }= 300 rad / sec third harmonic
5ω_{o }= 500 rad / sec fifth harmonic
In a voltagevoltage feedback as shown below, which one of the following
statements is TRUE if the gain k is increased?
In voltagevoltage feedback
A bandlimited signal with a maximum frequency of 5 kHz is to be sampled.
According to the sampling theorem, the sampling frequency which is not valid is
Given: f_{m} = 5kHz
According to sampling frequency
f_{s}2f
f_{s}10 kHz
So, only in option (a) it is less than 10KHz ie., (5KHz)
In a MOSFET operating in the saturation region, the channel length modulation
effect causes
No channel length modulation
under the presence of channel length modulation
which is reduced from ∞ to finite value
Which one of the following statements is NOT TRUE for a continuous time causal
and stable LTI system?
For an LTI system to be stable and causal all poles or roots of characteristic
equation must lie on LHS of splane i.e., left hand side of jω− axis
[Refer Laplace transform].
The minimum Eigen value of the following matrix is
So the matrix is singular
Therefore atleast one of the Eigen value is ‘0’
As the choices are non negative, the minimum Eigen value is ‘0’
A polynomial f( x) = a_{4} x^{4} + a_{3} x^{3} + a_{2} x^{2} + a_{1} x − a_{0} with all coefficients positive has
Use Routh Hurwitz Criteria to get the condition.
Assuming zero initial condition, the response y(t) of the system given below to a
unit step input u(t) is
Integration of unit step function is ramp output
^{}
Writing in time domain
The transfer function V_{2}(s) / V_{1}(s) of the circuit shown below is
A source V_{s} (t) = V cos100πt has an internal impedance of (4 + j3)? . If a purely
resistive load connected to this source has to extract the maximum power out of the
source, its value in ? should be
For maximum power Transfer
The return loss of a device is found to be 20 dB. The voltage standing wave ratio
(VSWR) and magnitude of reflection coefficient are respectively
Let , and h(t) is a filter matched to g(t). If g(t) is applied as input to h(t),
then the Fourier transform of the output is
The concept of matched filter assumes that the input signal is of the same form
g(t) as the transmitted signal(except difference in amplitude).this requires that the
shape of the transmitted signal not change on reflection.
Q. No. 36 – 65 Carry Two Marks Each
Q
Let U and V be two independent zero mean Gaussian random variables of variances1/4 and 1/9 respectively,. The probability P (3V 2U) is
Let A be an m x n matrix and B an n x m matrix. It is given that determinant
( I_{m} + AB) = determinant (I_{n} + BA) , where I_{k} is the k × k identity matrix. Using the
above property, the determinant of the matrix given below is
In the circuit shown below, if the source voltage V_{s} =10053.13^{o} V then the
Thevenin’s equivalent voltage in Volts as seen by the load resistance R_{L} is
The openloop transfer function of a dc motor is given as when
connected in feedback as shown below, the approximate value of a K that will reduce the time constant of the closed loop system by one hundred times as compared to that of the openloop system is
In the circuit shown below, the knee current of the ideal Zener diode is 10mA. To
maintain 5V across R_{L} , the minimum value of R_{L} in ? and the minimum power
rating of the Zener diode in mW, respectively, are
Minimum power rating of Zener should = 50 mA x 5V
= 250 mW
The following arrangement consists of an ideal transformer and an attenuator which attenuates by a factor of 0.8 An ac voltage V_{wx1} = 100V is applied across WX to get an open circuit voltage V_{YZ1} across YZ. Next, an ac voltage V_{YZ2} =100V is applied across YZ to get an open circuit voltage V_{WX2} across WX.
Then, V_{YZ1} / V_{WX1} , V_{WX2} / V_{YZ2} are respectively.
The potentiometer gives an attenuation factor of 0.8 over v_{2}
Since potentiometer and transformer are bilateral elements. Hence
Two magnetically uncoupled inductive coils have Q factors q_{1} and q_{2} at the chosen operating frequency. Their respective resistances are R_{1} and R_{2}. When connected in series, their effective Q factor at the same operating frequency is
When such two coils are connected in series individual inductances and
resistances are added.
The impulse response of a continuous time system is given by
h(t) = δ (t − 1) + δ (t − 3) . The value of the step response at t = 2 is
h(t) =δd (t − 1) + δ (t −)
y(t) =u(t1)+u(t3)
y(2)=u(1)+u(1) =1
The smallsignal resistance ( i.e dV_{B/}dI_{D}) in k? offered by the nchannel MOSFET M shown in the figure below, at a bias point of V_{B} = 2 V is (device data for M: device Transconductance parameter k_{N} = μ C_{ox} (W / L0 = 40μA / V^{2 }threshold voltage V_{TN} = 1V, and neglect body effect and channel length
modulation effects)
The ac schematic of an NMOS commonsource stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the nchannel MOSFET M, the Transconductance g_{m} = 1mA / V, and body effect and channel length modulation effect are to be neglected. The lower cutoff frequency
in Hz of the circuit is approximately at
A system is described by the differential equation
Let x(t) be a rectangular pulse given by
Assuming that y(0)=0 and dy/dt =0 at t = 0, the Laplace transform of y(t) is
A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by y(t) for t>0, when the forcing function is x(t) and the initial condition is y(0). If one wishes to modify the system so that the solution becomes 2y(t) for t>0, we need to
So if we want −2y (t) as a solution both x(t) and y(0) has to be doubled and
multiplied by –ve sign
x(t) → 2x(t)
y(0) → 2x(0)
Consider two identically distributed zeromean random variables U and V. Let the
cumulative distribution functions of U and 2V be F(x) and G(x) respectively.
Then, for all values of x
F (x) = P{X x}
G (x) = P {2X x}
=P{ X x/2}
For positive value of x,
F (x) − G(x) is always greater than zero
For negative value of x.
F (x) − G(x) is − ve
but . F (x) − G(x) . x 0
The DFT of vector [ a b c d] is the vector[ α β γ δ] . Consider the product
The DFT of the vector [ p q r s] is a scaled version of
The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is
In the circuit shown below the opamps are ideal. The V_{out} in Volts is
V_{1 }= 1(1+ 1) 2(1) =4V
V_{out} =2V_{1=} 8V
In the circuit shown below, Q_{1} has negligible collectortoemitter saturation
voltage and the diode drops negligible voltage across it under forward bias. If
V_{cc} is + 5V,X and Y are digital signals with 0 V as logic 0 and V_{CC} as logic 1,
then the Boolean expression for Z is
A voltage 1000sin ωt Volts is applied across YZ. Assuming ideal diodes, the
voltage measured across WX in Volts, is
Three capacitors C_{1} ,C_{2} and C_{3} whose values are 10μF, 5μF, and 2μF respectively, have breakdown voltages of 10V, 5V, and 2V respectively. For the interconnection shown below, the maximum safe voltage in Volts that can be applied across the combination, and the corresponding total charge in μC stored in the effective capacitance across the terminals are respectively.
From (3), V 10 Volts
To operate Circuit safe, V should be minimum of those =2.8V
There are four chips each of 1024 bytes connected to a 16 bit address bus as
shown in the figure below. RAMs 1,2,3 and 4 respectively are mapped to
addresses
In the circuit shown below, the silicon npn transistor Q has a very high value of
b . The required value of R_{2} in k? to produce I_{C} = 1mA is
Let U and V be two independent and identically distributed random variables such
that P(U= 1+) = P(U= 1)=1/2 The entropy H(U + V) in bits is
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the
respective received signals for both bits are as shown below.
Q.
If the detection threshold is 1, the BER will be
Bits 1 and 0 are transmitted with equal probability. At the receiver, the pdf of the
respective received signals for both bits are as shown below.
Q.
The optimum threshold to achieve minimum bit error rate (BER) is
Optimum threshold = The point of intersection of two pdf’s
Consider the following figure
The current I_{S} in Amps in the voltage source, and voltage V_{S} in Volts across the
current source respectively, are
I_{s}+8+5 =0
I_{s }=13A
Consider the following figure
Q.
The current in the 1? resistor in Amps is
I ? 10A = we can use principle of superposition to determine the current across 1 ohm resistance.
A monochromatic plane wave of wavelength λ = 600μm is propagating in the direction as shown in the figure below. denote incident, reflected, and transmitted electric field vectors associated with the wave.
The angle of incidence θ_{1} and the expression for are
The given oblique incidence is an vertical polarization ie., is parallel to the
plane of incidence, is perpendicular to the plane of incident
A monochromatic plane wave of wavelength l = 600μm is propagating in the direction as shown in the figure below. denote incident, reflected, and transmitted electric field vectors associated with the wave.
Q.
The expression for is
The reflection coefficient for parallel polarization is given by
But θ_{r = }θ_{i }since reflected ray and incident ray lies in the same medium by using
snell’s law
The state diagram of a system is shown below. A system is described by the statevariable equations
Q. The statevariable equations of the system shown in the figure above are
The state diagram of a system is shown below. A system is described by the
statevariable equations
Q.
The state transition matrix e^{At} of the system shown in the figure above is
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