Consider the circuit shown in the figure.
The Boolean expression F implemented by the circuit is
An LTI system with unit sample response is a
Obtain
Thus Ideal behaviour of h[n] is Band pass filter.
In the circuit shown, V is a sinusoidal voltage source. The current I is in phase with voltage V.
If I &V are in phase then the circuit is in resonance
At resonance
In a DRAM,
Consider an nchannel MOSFET having width W, length L, electron mobility in the channel μ_{n} and oxide capacitance per unit area C_{ox}. If gatetosource voltage V_{GS} = 0.7V, draintosource voltage V_{DS} = 0.1V, (μ_{n} C_{ox}) = 100μA / V^{2} , threshold voltage V_{TH} = 0.3 V and (W/L) = 50, then the transconductance g_{m} (in mA/V) is ___________.
Here, V_{DS} < V_{GS}  V_{PH}, so nchannel MOSFET is working in linear region.
So, transconductance g_{m} is in linear region and is given by
Two conducting spheres S1 and S2 of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.
For some charge placed on this structure, the potential and surface electric field on S1 are V_{a} and E_{a}, and that on S2 are V_{b} and E_{b}, respectively, which of the following is CORRECT?
⇒ bc_{3} two spheres are joined with a conducting wire, the voltage on two spheres is same.
For the circuit shown in the figure, P and Q are the inputs and Y is the output.
The logic implemented by the circuit is
An nchannel enhancement mode MOSFET is biased at V_{GS} > V_{TH} and V_{DS} > (V_{GS}  V_{TH}) , where V_{GS} is the gatetosource voltage, V_{DS} is the draintosource voltage and V_{TH} is the threshold voltage. Considering channel length modulation effect to be significant, the MOSFET behaves as a
If channel length modulation is considered and significant it means λ ≠ 0
If V_{AS} > V_{TH} and V_{DS }> (V_{DS}  V_{TH}) then it indicates that MOSFET is working in saturation region and it can be used as an amplifier. So it can act as current source with finite output impedance.
A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10Ω, 5Ω, 2Ω are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ____________.
The maximum resistance
The minimum resistance
An npn bipolar junction transistor (BJT) is operating in the active region. If the reverse bias across the base – collector junction is increased, then
If the reverse bias voltage across the base collector junction is increased, then their effective base width will decrease and collector current will increase, therefore their commonemitter current gain increases.
Consider the state space realization
, with the initial condition
where u(t) denotes the unit step function. The value of
Apply L.T to above equation
The rank of the matrix
A two – wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is ______________
Percentage of power reflected is
The input x(t) and the output y(t) of a continuoustime system are related as
Given Inputoutput relationship describes integration over a fundamental period T. The integration over one period is linear and timeinvariant.
Which of the following statements is incorrect?
The phaselead controller adds zero and a pole, with the zero to the right of the pole, to the forwardpath transfer function. The general effect is to add more damping to the closedloop system. The rise time and settling time are reduced in general.
→ Reduces the steady state error
→ Reduces the speed of response
→ Increases the gain of original network without affecting stability
→ Permits the increases of gain if phase margin is acceptable
→ System becomes lesser stable
→ Reduces the effect of noise
→ Decrease the bandwidth
The residues of a function
Z = 4 is a pole of order ‘1’ (or) simple pole
z = – 1 is a pole of order ‘3’.
A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signaltoquantization noise ratio (SQNR) at the output of the quantizer is 40dB. The minimum number of bits per sample needed to achieve the desired SQNR is _______
For sinusoidal signal
(SNR)_{Q} in dB = 6.0 n + 1.75
Given required (SNR)_{Q} = 40 dB
The general solution of the differential equation in terms of arbitrary
constants K_{1} and K_{2} is
D^{2} + 2D  5 = 0
Where k_{1}, k_{2} are arbitrary constants.
Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover probability P?
For memory less binary Symmetric channel
Channel capacity
The output V_{0} of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the diode, is ____________.
Consider the random process X (t) = U+ Vt, where U is a zeromean Gaussian random variable and V is a random variable uniformly distributed between 0 and 2. Assume that U and V are statistically independent. The mean value of the random process at t = 2 is ____________
Given x (t) = U+ Vt
For the system shown in the figure, Y(s) / X(s) = __________.
The smaller angle (in degrees) between the planes x + y + z =1 and 2x – y + 2z = 0 is
x + y + 2 = 1
2x – y + 2z = 0
We have angle between two planes
Consider the circuit shown in the figure. Assume baseto emitter voltage V_{BE} = 0.8 V and common base current gain (α) of the transistor is unity.
The value of the collector to – emitter voltage V_{CE} (in volt) is _______.
In the figure, D1 is a real silicon pn junction diode with a drop of 0.7V under forward bias condition and D2 is a zener diode with breakdown voltage of 6.8 V. The input V_{in}(t) is a periodic square wave of period T, whose one period is shown in the figure.
Assuming 10t << T. where t is the time constant of the circuit, the maximum and minimum values of the output waveform are respectively,
When V_{i} = 14V, the equivalent circuit is
If the vector function is irrotational, then the values of the constants k_{1}, k_{2} and k_{3} respectively, are
The unmodulated carrier power in an AM transmitter is 5kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is 50%. If it is reduced to 40%, then the maximum unmodulated carrier power (in kW) that can be used without overloading the transmitter is ___________
Total power when μ = 50% is
When μ = 40%
Total power remains 5.625
P_{c} = 5.22
Consider an LTI system with magnitude response
And phase response Arg {H (f)} = 2f.
If the input to the system is
Then the average power of the output signal y (t) is _________.
Consider an LTI system with magnitude response
And phase response Arg {H (f)} = 2f.
If the input to the system is
Then the average power of the output signal y (t) is _________.
28. Obtain X (f ) for the given x(t)
A MOS capacitor is fabricated on ptype Si (silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV. E_{C}F_{F} = 0.9 eV, where E_{C} and E_{F} are the conduction band minimum and the Fermi energy levels of Si, respectively. Oxide F / cm. oxide thickness t_{ox} = 0.1 μm and electronic charge q = 1.6 ×10^{19} C. If the measured flat band voltage of the capacitor is 1V, then the magnitude of the fixed charge at the oxidesemiconductor interface, in nC/cm^{2}, is __________.
An electron (q_{1}) is moving in free space with velocity 10^{5} m/s towards a stationary electron (q_{2}) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is ___________ ×10^{8}m.
[Given, mass of electron m = 9.11×10^{31}kg, charge of electron e = 1.6×10^{19}C , and permittivity
Work done due to field and external agent must be zero
The values of the integrals
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is 40% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is _________.
Let ‘X’ is a random variable which takes number of attempts
Given probability of any attempts to be successful,
∴ Average number of attempts that passengers need to make to get seat reserved is ‘2.5’
Figure I shows a 4bits ripple carry adder realized using full adders and Figure II shows the circuit of a fulladder (FA). The propagation delay of the XOR, AND and OR gates in Figure II are 20 ns, 15 ns and 10 ns respectively. Assume all the inputs to the 4bit adder are initially reset to 0.
At t = 0, the inputs to the 4bit adder are changed to
The output of the ripple carry adder will be stable at t (in ns) = ___________
The permittivity of water at optical frequencies is 1.75 ε_{0} . It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5m, as shown in the figure. The critical angle is θ_{c}.
The value of d (in meter) is _____________
A unity feedback control system is characterized by the openloop transfer function
The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below.
If 0 < K < 1, then the number of poles of the closedloop transfer function that lie in the right – half of the splane is
N = 0, Because 0 < L < 1
There are no encircles around (Y, 0)
And
C.E = S^{3} + 3S^{2} +10KS + 20K +10
If stable 30 K > 20K+10
K > 1
Here, in the question asking 0 < K < 1 So, System is unstable
The signal x (t) = sin (14000πt) , where t is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows :
What is the number of sinusoids in the output and their frequencies in kHz?
Given input signal x (t) = sin (1400πt)
Input signal spectrum
Sampled signal spectrum is the spectrum of X(f) which repeats with integer multiples of 9 kHz.
Sampled signal spectrum:
The sampled signal spectrum is passed through a LPF of cutoff frequency 12 KHz. Thus the filtered out sinusoids are of 2 KHz 7 KHz and 11 KHz frequency.
A unity feedback control system is characterized by the openloop transfer function
The value of k for which the system oscillates at 2 rad/s is ________.
Take auxiliary equation
Consider the circuit shown in the figure.
The Thevenin equivalent resistance (in Ω) across P – Q is _________.
The transfer function of a causal LTI system is H(s) = 1/s. If the input to the system is x(t) = [sin(t) / π]u(t), where u(t) is a unit step function, the system output y(t) as t → ∞ is ______.
By using frequency integration property,
An integral I over a counter clock wise circle C is given by
If C is defined as z = 3, then the value of I is
Consider a binary memory less channel characterized by the transition probability diagram shown in the figure.
It is a useless channel as
MAP criteria cannot decide anything on receiving ‘0’ we cannot decide what is transmitted.
An abrupt pn junction (located at x = 0) is uniformly doped on both p and n sides. The width of the depletion region is W and the electric field variation in the xdirection is E(x). Which of the following figures represents the electric field profile near the pn junction?
If left side is pregion and right side is nregion then electric field triangle will be down warded and if the left side is nregion and right side is pregion, then electric field triangle will be upward.
A second – order LTI system is described by the following state equations,
Where x_{1} (t) and x_{2} (t) are the two state variables and r(t) denotes the input. The output c(t) = x_{1}(t). The system is.
Consider the parallel combination of two LTI systems shown in the figure.
The impulse responses of the systems are
If the input x(t) is a unit step signal, then the energy of y(t) is ____________.
Since h_{1} (t) and h_{2} (t) are connected in parallel the resultant system can be given as follows.
Assuming that transistors M_{1} and M_{2} are identical and have a threshold voltage of 1V, the state of transistors M_{1} and M_{2} are respectively
then transistor is working in saturation region.
So, For M_{2} transistor
Assume that M_{1} is working in saturation, so that
Now, for M_{1}, transistor to work in saturation but it is not satisfied by M_{1} transistor and V_{G1} > V_{TH}, so, transistor M_{1} is ON but working in linear region.
A programmable logic array (PLA) is shown in the figure.
The Boolean function F implemented is
A modulating signal given By x(t) = 5 sin (4π10^{3 }t  10π cos2π10^{3} t) V is fed to a phase modulator with phase deviation constant k_{p} = 0.5rad/V. If the carrier frequency is 20 kHz, the instantaneous frequency (in kHz) at t = 0.5 ms is __________
The minimum value of the function in the int erval occurs at x =
________.
The switch in the circuit, shown in the figure, was open for a long time and is closed at t = 0.
The current i(t) (in ampere) at t = 0.5 seconds is ________
In the voltage reference circuit shown in the figure, the opamp is ideal and the transistors Q_{1} Q_{2}….., Q_{32} are identical in all respects and have infinitely large values of common – emitter current the relation I_{C} = I_{S} exp ((V_{BE}/V_{T}), where Is is the saturation current. Assume that the voltage V_{P} shown in the figure is 0.7 V and the thermal voltage V_{T} = 26mV.
The output voltage V_{out}(in volts) is __________.
KCL at node ‘a’
The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input ‘In’ and an output ‘Out’. The initial state of the FSM is S_{0}.
From the state diagram, let us obtain the transition of states and out when IN channel.
Initial state is So, the input sea is 10101101001101
→ The ticketed mark now corresponding to output = 1.
So output will be 1 ‘4’ times.
Standard air – filled rectangular waveguides of dimensions a = 2.29 cm and b = 1.02 cm are designed for radar applications. It is desired that these waveguides operate only in the dominatnt TE_{10} mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is.
For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (J_{L}) is 2.5 mA/cm^{2} and the opencircuit voltage (V_{oc}) is 0.451 V. consider thermal voltage (V_{T}) to be 25mV. If the intensity of the incident light is increased by 20 times, assuming that the temperature remains unchanged. V_{oc} (in volts) will be ______.
Now if the intensity of the light is increased by 20 times it means their photocurrent will also increased by 20 times.
In the circuit shown, transistors Q_{1} and Q_{2} are biased at a collector current of 2.6mA. Assuming that transistor current gains are sufficiently large to assume collector current equal to emitter current and thermal voltage of 26 mV, the magnitude of voltage gain V_{0}/V_{s} in the midband frequency range is _____________ (up to second decimal place).
a.c equivalent circuit for the given figure
Two nchannel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double that of T1. Both the transistors are biased in the saturation region of operation, but the gate overdrive voltage (V_{GS}V_{TH}) of T2 is double that of T1, where V_{GS} and V_{TH} are the gate – to – source voltage and threshold voltage of the transistors, respectively. If the drain current and transconductance of T1 are I_{D1} and g_{m1} respectively, the corresponding values of these two parameters for T2 are
Drain current in saturation is
The ninth and the tenth of this month are Monday and Tuesday ___________.
500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186). Mathematics (295). Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?
It is _________ to read this year’s textbook __________ the last year’s.
Fatima starts from point P, goes North for 3 km, and then East for 4km to reach point Q. She then turns to face point P and goes 15km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P?
The required distance
A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinking beer. What must be checked to ensure that the rule is being followed?
For rules to be followed, we need to check P's drink and S's age.
Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Z and W are married and are parents of R. Which one of the following must necessarily be FALSE?
The number of 3digit numbers such that the digit 1 is never to the immediate right of 2 is
Total no. of 3 digit no’s = 9 10 10 = 900
The no. of 3digit numbers in which ‘1’ is to the immediate right of 2 = 19
∴ The no. of 3digit no’s such that the digit 1 is never to immediate right of 2 is 900  19= 881
Alternate method
Total no. of 3 digit numbers are
So, no. of 3 digit numbers such that the digit 1 is never to the immediate right of 2 are = 90019 = 881
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot.
Which of the following is the steepest path leaving from P?
Closer lines represents steepest path
Alternate method
The steepest path will be the path which is deepest from sea level. So, P to R is the steepest path.
1200 men and 500 women can build a bridge in 2 weeks. 900men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?
Given 1200 Men + 500 Women can build a bridge in 2 weeks. And 900 Men + 250 Women will take 3 weeks to build the same bridge
∴ To complete in a week; there are 2400 Men + 1000W required in the first equation and 2700 Men + 750 Women required in the second equation.
∴ 2400 M + 1000W = 2700M + 750W
∴ The no. of men required to build the bridge in one week
Alternate method
Let a man can build the bridge in x weeks and a woman can build the bridge in y weeks.
By equations i and ii ; we get
x = 3600; y = 3000
⇒ A man build the bridge 3600 weeks
⇒ Required men = 3600 to build in a week.
“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective section, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters.”
Which of the following statements best reflects the author’s opinion?
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