The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 μs, then the number of Tstates needed for executing the instruction is
Consider a single input single output discretetime system with x[n] as input and y[n] as output, where the two are related as
Which one of the following statements is true about the system?
For an inputoutput relation if the present output depends on present and past input values then the given system is “Causal”.
For the given relation,
For n ranging from 0 to 10 present output depends on present input only.
At all other points present output depends on present and past input values.
Thus the system is “Causal”.
Stability
If x[n] is bounded for the given finite range of n i.e. 0 < n < 10 y [n] is also bounded. Similarly x [n]  x [n 1] is also bounded at all other values of n Thus the system is “stable”.
Consider the following statement about the linear dependence of the real valued functions y_{1} = 1, y_{2} = x and y_{3} = x^{2} , over the field of real numbers.
I. y_{1}, y_{2} and y_{3} are linearly independent on
II. y_{1} , y_{2} and y_{3} are linearly dependent on
III. y_{1}, y_{2} and y_{3} are linearly independent on
IV. y_{1}, y_{2} and y_{3} are linearly dependent on
Q.
Which one among the following is correct?
Consider the 5 × 5 matrix
It is given that A has only one real eigen value. Then the real eigen value of A is
The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance isvolts, Where ℓ is the distance along the length of the cable in meters. γ = (0.1 + j40)m^{1} is the complex propagation constant, and rad s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.
A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statement is true?
Silicon atoms act as P type dopants in Arsenic sites and n type dopants in Gallium sites.
The rank of the matrix
For a narrow base PNP BJT, the excess minority carrier concentration (Δn_{E} for emitter, Δp_{B} for base.Δn_{C} for collector) normalized to equilibrium minority carrier concentration (n_{E0} for emitter, p_{B0} for base, n_{C0} for collector) in the quasineutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in?
As per the change carrier profile, base – to – emitter junction is reverse bias and base to collector junction is forward bias, so it works in Inverse active.
The Miller effect in the context of a Common Emitter amplifier explains
Miller effect increase input capacitance, so that there will be decrease in gain in the high frequency cutoff frequency.
Consider the DLatch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a onefifth period delayed version of CLK1. The duty cycle at the output latch in percentage is ___________.
Which of the following can be polezero configuration of a phaselag controller (lag compensator)?
In phase lag compensator pole is near to jw axis,
In the latch circuit shown, the NAND gates have nonzero, but unequal propagation delays. The present input condition is: P = Q = ‘0’. If the input condition is changed simultaneously to P = Q = ‘1’, the outputs X and Y are
Unequal propagation delay
∴ Either x = 1, y = 0 or x = 0, y =1
Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) __________.
A periodic signal x(t) has a trigonometric Fourier series expansion
we can conclude that
If x (t) = x (t) the given periodic signal is odd symmetric. For an odd symmetric signal n a = 0 for all n.
where T_{0} is fundamental period then the given
condition satisfies halfwave symmetry.
For halfwave symmetrical signal all coefficients a_{n} and b_{n} are zero for even value of n.
The open loop transfer function
Where p is an integer, is connected in unity feedback configuration as shown in figure.
Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________.
An n^{+}  n Silicon device is fabricated with uniform and nondegenerate donor doping concentrations ofcorresponding to the n + and n regions respectively. At the operational temperature T, assume complete impurity ionization, kT/q = 25 mV, and intrinsic carrier concentration to be . What is the
magnitude of the builtin potential of this device?
For the operational amplifier circuit shown, the output saturation voltages are ±15V. The upper and lower threshold voltages for the circuit are, respectively.
In the circuit shown, the positive angular frequency ω (in radians per second) at which magnitude of the phase difference between the voltages V1 and V2 equals is
__________.
In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is inter symbol interference zero?
For ISI free pulse, If P(t) is having spectrum P(f)
R_{s} = 2 KSpa
Thin condition is met by pulse given in option B.
Consider a stable system with transfer function
Where are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to 60 dB decade as A possible pair of values for p and q is
If s^{qp} = s^{3} , when p = 0 and q = 3, then
It have 60dB/dec at
A good transconductance amplifier should have
A good trans conductance amplifier should have high input and output resistance.
Let (X_{1} , X_{2}) be independent random variables. X_{1} has mean 0 and variance 1, while X_{2} has mean 1 and variance 4. The mutual information I (X_{1}; X_{2}) between X_{1} and X_{2} in bits is
For two independent random variable
I(X;Y) = H(X) = H(X/Y)
H(X/Y) = H(X) for independent X and Y
⇒ I(X; Y) = 0
Consider the following statements for continuoustime linear time invariant (LTI) systems.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?
If a system is noncausal then a pole on right half of the splane can give BIBO stable system. But for a causal system to be BIBO all poles must lie on left half of the complex plane.
Which one of the following statements about differential pulse code modulation (DPCM) is true?
DPCM Block diagram
e[n] is quantized e[n]
e [n] is difference of message signal sample with its prediction.
Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged, the maximum capacity of the wireless link
Channelcpacityremainsame.
Starting with x = 1, the solution of the equation x^{3} + x = 1, after two iterations of NewtonRaphson’s method (up to two decimal places) is _________.
By Newton Raphson method,
In binary frequency shift keying (FSK), the given signal waveform are
Where T is the bitduration interval and t is in seconds. Both u_{0} (t) and u_{1} (t) are zero outside the interval . With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u_{0} (t) and u_{1} (t) uncorrelated is
For u_{0 }(t) and u_{1 }to be orthogonal, it is necessary that
For the DC analysis of the CommonEmitter amplifier shown, neglect the base current and assume that the emitter and collector current are equal. Given that V_{T} = 25mV, V_{BE} = 0.7V, and the BJT output resistance r_{0} is practically infinite. Under these conditions, the midband voltage gain magnitude. , is _________.
The figure shows an RLC circuit exited by the sinusoidal voltage 100 cos (3t) volts, where t is in seconds.
Which one of the following is the general solution of the first order differential equation = (x + y  1)^{2}, where x, y are real?
A linear time invariant (LTI) system with the transfer function
is connected in unity feedback configuration as shown in the figure.
For the closed loop system shown, the root locus for 0 < K < ∞ intersects the imaginary axis for K = 1.5. The closed loop system is stable for
If closed loop system to be stable all coefficients to positive
where x, y, z are real, and let C be the straight line segment from point A : (0, 2,1) to point B : (4,1, 1) . The value of I is _________.
The straight line joining A(0, 2, 1) and B(4, 1, 1) is
As shown, two Silicon (Si) abrupt pn junction diodes are fabricated with uniform donor doping concentration of N_{D1} = 10^{14 }cm^{3} and N_{D2} = 10^{16} cm^{3} in the nregions of the diodes, and uniform acceptor doping concentration of N_{A1} = 10^{14 }cm^{3} and N_{A2} = 10^{16} cm^{3} in the pregions of the diodes, respectively. Assuming that the reverse bias voltage is >> builtin potentials of the diodes, the ratio C_{2}/C_{1} of their reverse bias capacitances for the same applied reverse bias, is __________.
An optical fiber is kept along direction. The refractive indices for the electric fields along directions in the fiber are n_{x} = 1.5000 and n_{y} = 1.5001, respectively (n_{x} ≠ n_{y}) due to the imperfection in the fiber crosssection). The free space wavelength of a light wave propagating in the fiber is 1.5 μm. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeter, is ___________.
For circular polarization the phase difference between E_{x} & E_{y} is π/2
⇒ The phase difference for linear polarization should be π
So the wave must travel a minimum distance such that the extra phase difference of π/2 must occur.
Two discretetime signals x[n] and h[n] are both nonzero for n = 0, 1, 2 and are zero otherwise. It is given that x [0] = 1, x [1] = 2, x [2] = 1, h [0] = 1.
Let y[n] be the linear convolution of x[n] and h[n]. Given that y[1] = 3 and y[2] = 4, the value of the expression (10y[3] + y[4]) is _________.
y[n] = {1, 2 + a, 2a + b +1, 2b + a, b}
It is given that y [1] = 3
∴ 2+a =3 ⇒ a =1
Similarly 2a + b + 1 = 4 Þ b = 3  2 (1) = 1
b = 1
∴ y [3] = 2 (1) + 1 = 3
y [4] = b = 1
∴10y [3] + y [4] = 30 + 1 = 31
Which one of the following options correctly describes the locations of the roots of the equation s^{4} + s^{2} + 1 = 0 on the complex plane?
F (s) = s^{4} + s^{2} + 1 = 0
Let take s^{2} = t
t^{2} + t + 1 = 0
Hence two roots contain RHS and two roots contain LHS plane.
The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of and electronic charge . If a bias of 5V is applied across a 1 mm region of this semiconductor, the resulting current density in this region, in kA/cm^{2}, is _________.
For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage
V_{tn} = 1V and its transconductance parameter . Neglect channel length modulation and body bias effects. Under these conditions, the drain current I_{D} in mA is ___________.
Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response
As shown in Figure (b). The output of the lowpass filter is Y(t).
Let E be the expectation operator and consider the following statements.
I. E (X(t)) = E(Y(t))
II. E(X^{2}(t)) = E(Y^{2}(t))
III. E(Y^{2}(t)) = 2
Select the correct option:
Since DC components in same in S_{x} (f) and Sy (f)
⇒ E[x(t)] = E[y(t)]
As shown a uniformly doped Silicon (Si) bar of length L = 0.1 mm with a donor concentration N_{D} = 10^{16} cm^{3} is illuminated at x = 0 such that electron and hole pairs are generated at the
rate of where Hole lifetime is 10^{4} s, electronic charge hole diffusion coefficient D_{p} = 100 cm^{2}/s and low level injection condition prevails. Assuming a linearly decaying steady state excess hole concentration that goes to 0 at x = L, the magnitude of the diffusion current density at x = L/2, in A/cm^{2}, is _________.
The Nyquist plot of the transfer function
does not encircle the point (1 + j0) for K = 10 but does encircle the point (1+ j0) for K = 100. Then the closed loop system (having unity gain feedback) is
So If k = 10 touching point= 0.5
If k = 100 touching point = 5
N = P Z, Here P = 0
N = Z
If closed loop system to be stable, then Z = 0, ⇒ N = 0,
So, k = 10 is stable system
In the figure shown, the npn transistor acts as a switch
For the input V_{in} (t) as shown in the figure, the transistor switches between the cutoff and saturation regions of operation, when T is large. Assume collectortoemitter voltage saturation V_{CE(sat)} = 0.2V and basetoemitter voltage V_{BE} = 0.7V. The minimum value of the commonbase current gain (α) of the transistor for the switching should be _________.
A three dimensional region R of finite volume is described by , Where x, y, z are real. The volume of R (up to two decimal places) is ___________.
is the radius of variable circle at some Z.
⇒ PQ^{2} = x^{2} + y^{2} = z^{3} (Given)
∴ Volume of region revolved around
The expression for an electric field in free space is , where x, y, z represent the spatial coordinates, t represents time, and ω,k are constants. This electric field
The dot product between above two is = 1  1 + 0 = 0
⇒ It is a plane wave
We observed that
are normal to each other.
So electric field can be resolved into two normal component along
The magnitude are
So elliptical polarization.
A finite state machine (FSM) is implemented using the D flipflops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are Q_{A}Q_{B} = 00, 01,10 and 11.
Assume that X_{1N} is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state Q_{A}Q_{B} = 00 and clocked, after a few clock cycles, it starts cycling through
In given diagram
When X_{in} = 0 2State
When X_{in }= 1 3 State
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a_{k}} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
I. The complex Fourier series coefficients of x(3t) are {a_{k}} where k is integer valued
II. The complex Fourier series coefficients of x(3t) are {3a_{k}} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6π rad/s
For the three statements above, which one of the following is correct?
Fourier series coefficient ak is unaffected by scaling operating. Thus (I) is true and (II) is false.
T = 1sec for x(t) and if it compressed by ‘3’ then the resultant period T = 1/3
Thus (III) is correct.
A 4bit shift register circuit configured for rightshift operation, i.e, D_{in} → A, A → B, B → C, C → D, is shown. If the present state of the shift register is ABCD = 1101, the number of clock cycles required to reach the state ABCD = 1111 is _________.
10 clock pulse required.
Let for real x. From among the following, choose the Taylor series approximation of f(x) around x = 0, which included all powers of x less than or equal to 3.
We have Taylor series of f(x) around x = 0 is f (x)
(upto powers of ‘x’ less than or equal to ‘3’)
Given
The following FIVE instructions were executed on an 8085 microprocessor.
MVI A, 33H
MVI B, 78H
ADD B
CMA
ANI 32H
The Accumulator value immediately after the execution of the fifth instruction is
In the circuit shown, the voltage V_{1N} (t) is described by:
Where t is in seconds. The time (in seconds) at which the current I in the circuit will reach the value 2 Amperes is ___________.
Under dc condition inductor acts as short all
A half wavelength dipole is kept in the xy plane and oriented along 45° from the xaxis. Determine the direction of null in the radiation pattern for . Here the angle is measured from the zaxis, and the angle is measured from the xaxis in the xy plane.
The null occurs along axis of the antenna which is
The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (opamp), and has an openloop voltage gain, A_{o} = 10^{5} V/V and an openloop cutoff frequency f_{c} = 8Hz. The voltage gain of the amplifier at 15 kHz, in V/V is __________.
Given Amplifier is using –ve feed back
Let h[n] be the impulse response of a discretetime linear time invariant (LTI) filter. The impulse response is given by
Let H (ω) be the discretetime Fourier system transform (DTFT) of h[n], where ω is the normalized angular frequency in radians. Given that H (ω_{0}) = 0 and 0 < ω_{0} < π, the value of ω_{0} (in radians) is equal to __________.
It is given that,
Which one of the following gives the simplified sum of products expression for the Boolean function F = m_{0} + m_{2} + m_{3} + m_{5} , where m_{0} , m_{2} , m_{3} and m_{5} are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
F = M_{o} + M_{2} + M_{3} + M_{5} → minterm
A continuous time signal x (t) = 4 cos (200pt) + 8 cos (400pt), where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response
Let y(t) be the output of this filter. The maximum value of
She has a sharp tongue and it can occasionally turn _______.
Some table are shelves. Some shelves are chairs. All chairs are benches. Which of the following conclusion can be deduced from the preceding sentences?
(i) At least one bench is a table
(ii) At least one shelf is a bench
(iii) At least one chair is a table
(iv) All benches are chairs
40% of deaths on city roads may be attributed to drunken driving. The number of degree needed to represent this as a slice of a pie chart is
Given 40% of deaths on city roads are drunken driving
In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.
Which of the following statement is correct?
Let H is house hold consumption and P is the other consumption.
Given
I ________ made arrangements had I _________informed earlier.
“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”.
Here, the word ‘antagonistic’ is closest in meaning to
There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?
No. of sub groups such that every sub group has at least one Indian
Alternate method
Sub groups containing only Indians
Subgroups containing one Indian and rest chinese
Sub groups containing two Indian and remaining Chinese
Sub groups containing three Indian and remaining Chinese
∴ Total no. of sub groups = 7+21+21+7 = 56.
A contour line joints 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 25 m intervals in this plot. The path from P to Q is best described by
Down upDown
Trucks (10m long) and cars (5 m long) go on a single lane bridge. There must be a gap of atleast 20 m after each truck and a gap of atleast 15m after each car. Trucks and cars travel at a speed of 36 km/h. If cars and trucks go alternatively, what is the maximum number of vehicles that can use the bridge in one hour?
Given speeds both car & Truck = 36 km/hour
They travel in 1 hr = 36 km = 36000 m.
∴ Maximum no.of vehicles than can use the bridge in1hour
Alternate method
Length of truck + gap required = 10+20 = 30m
Length of car + gap required = 5+15 = 20m
Alternative pairs of Truck and car needs 30+ 20 = 50 m.
Let 'n' be the number of repetition of (Truck + car) in 1 hour (3600 sec).
S, T, U, V, W, X, Y and Z are seated around a circular table. T’s neighbours are Y and V. Z is seated third to the left of T and second to the right of S.U‟s neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?
Following circular seating arrangement can be drawn.
Only one such arrangement can be drawn.
The person on third to the left of V is X.
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