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Question 1 of 65
1. Question
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
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Question 2 of 65
2. Question
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?
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Question 3 of 65
3. Question
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 −1 ≤ x ≤ 0
II. y_{1}, y_{2} and y_{3} are linearly dependent on 0 ≤ x ≤ 1
III. y_{1}, y_{2} and y_{3} are linearly independent on 0 ≤ x ≤ 1
IV. y_{1}, y_{2} and y_{3} are linearly dependent on −1 ≤ x ≤ 0
Which one among the following is correct?
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Question 4 of 65
4. Question
Consider the 5 × 5 matrix
It is given that A has only one real eigen value. Then the real eigen value of A is
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Question 5 of 65
5. Question
The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is V(ℓ) = e−^{−γℓ +jωt} volts, 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 ω = 2π × 10^{9} rad/s is the angular frequency. The absolute value of the attenuation in the cable in dB/meter is __________.
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NAT Type Question

Question 6 of 65
6. Question
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?
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Question 7 of 65
7. Question
The rank of the matrix is
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Question 8 of 65
8. Question
For a narrow base PNP BJT, the excess minority carrier concentration (∆n_{E} for emitter, ∆p_{B} for base. ∆n_{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?
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Question 9 of 65
9. Question
The Miller effect in the context of a Common Emitter amplifier explains
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Question 10 of 65
10. Question
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 ___________.
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NAT Type Question

Question 11 of 65
11. Question
Which of the following can be polezero configuration of a phaselag controller (lag compensator)?
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Question 12 of 65
12. Question
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
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Question 13 of 65
13. Question
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) __________.
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NAT Type Question

Question 14 of 65
14. Question
A periodic signal x(t) has a trigonometric Fourier series expansion
If x(t) = −x – (t) = −x(t – π/ω_{0}), we can conclude that
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Question 15 of 65
15. Question
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 _________.
CorrectIncorrectHint
NAT Type Question

Question 16 of 65
16. Question
An n^{+} − n Silicon device is fabricated with uniform and nondegenerate donor doping concentrations of N_{D1} = 1 × 10^{18} cm^{−3} and N_{D2} = 1 × 10^{15} cm^{−3} corresponding 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 n_{i} = 1 × 10^{10} cm^{−3}. What is the magnitude of the builtin potential of this device?
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Question 17 of 65
17. Question
For the operational amplifier circuit shown, the output saturation voltages are ±15V. The upper and lower threshold voltages for the circuit are, respectively.
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Question 18 of 65
18. Question
In the circuit shown, the positive angular frequency ω (in radians per second) at which magnitude of the phase difference between the voltages V_{1} and V_{2} equals is________.
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NAT Type Question

Question 19 of 65
19. Question
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?
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Question 20 of 65
20. Question
Consider a stable system with transfer function
Where b_{1},….,b_{p} and a_{1},….a_{q} are real valued constants. The slope of the Bode log magnitude curve of G(s) converges to −60 dB decade as ω→∞. A possible pair of values for p and q is
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Question 21 of 65
21. Question
A good transconductance amplifier should have
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Question 22 of 65
22. Question
Let (X_{1} ,X_{2}) be independent random variables. X_{1} has been 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 _______.
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NAT Type Question

Question 23 of 65
23. Question
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?
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Question 24 of 65
24. Question
Which one of the following statements about differential pulse code modulation (DPCM) is true?
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Question 25 of 65
25. Question
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
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Question 26 of 65
26. Question
Starting with x = 1, the solution of the equation x^{3} + x = 1, after two iterations of NewtonRapson’s method (up to two decimal places) is ________.
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NAT Type Question

Question 27 of 65
27. Question
In binary frequency shift keying (FSK), the given signal waveform are
u_{0}(t) = 5 cos(20000πt); 0≤t ≤ T, and
u_{1}(t) = 5 cos(22000πt); 0≤t≤T
Where T is the bitduration interval and t is in seconds. Both u_{0}(t) and u_{1}(t) are zero outside the interval 0 ≤ t ≤ T. 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
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Question 28 of 65
28. Question
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} = 25 mV, V_{BE} = 0.7V, and the BJT output resistance r_{0} is practically infinite. Under these conditions, the midband voltage gain magnitude. A_{c} = V_{o}/V_{i}V/V, is ____________.
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NAT Type Question

Question 29 of 65
29. Question
The figure shows an RLC circuit exited by the sinusoidal voltage 100cos (3t) volts, where t is in seconds. The ratio is _________.
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NAT Type Question

Question 30 of 65
30. Question
Which one of the following is the general solution of the first order differential equation where x, y are real?
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Question 31 of 65
31. Question
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
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Question 32 of 65
32. Question
Let where x, y, z are real, and let C be th straight line segment from point A : (0, 2, 1) to point B : (4, 1, −1). The value of I is _______.
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NAT Type Question

Question 33 of 65
33. Question
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_{Al} = 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 __________.
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NAT Type Question

Question 34 of 65
34. Question
An optical fiber is kept along the 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 1.5μm. 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 ___________.
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NAT Type Question

Question 35 of 65
35. Question
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 _______.
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NAT Type Question

Question 36 of 65
36. Question
Which one of the following options correctly describes the locations of the roots of the equations s^{4} + s^{2} + 1 = 0 on the complex plane?
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Question 37 of 65
37. Question
The dependence of drift velocity of electrons on electric field in a semiconductor is shown below. The semiconductor has a uniform electron concentration of n = 1 × 10^{16} cm^{−3} and electronic charge q = 1.6 × 10^{−19} C. If a bias of 5V is applied across a 1 μm region of this semiconductor, the resulting current density in this region, in kA/cm^{2}, is ________.
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NAT Type Question

Question 38 of 65
38. Question
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 _________.
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NAT Type Question

Question 39 of 65
39. Question
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:
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Question 40 of 65
40. Question
As shown a uniformly doped Silicon (Si) bar of length L = 0.1 μm 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 G_{L0} = 10^{17} cm^{−3} s^{−1}. Hole lifetime is 10^{−4} s, electronic charge q = 1.6 × 10^{−19} C, hole diffusion coefficient D_{p} = 100 cm^{2}/s and low level injection condition prevails. Assuming 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 _______.
CorrectIncorrectHint
NAT Type Question

Question 41 of 65
41. Question
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
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Question 42 of 65
42. Question
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)} = 0.2 V and basetoemitter voltage V_{BE} = 0.7V. The minimum value of the commonbase current gain (α) of the transistor for the switching should be _______.
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NAT Type Question

Question 43 of 65
43. Question
A three dimensional region R of finite volume is described by x^{2} + y^{2} ≤ z^{3}; 0 ≤ z ≤ 1, Where x, y, z are real. The volume of R(up to two decimal places) is _________.
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NAT Type Question

Question 44 of 65
44. Question
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
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Question 45 of 65
45. Question
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_{IN} = 1is 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
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Question 46 of 65
46. Question
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?
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Question 47 of 65
47. Question
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 _______.
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NAT Type Question

Question 48 of 65
48. Question
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.
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Question 49 of 65
49. Question
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
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Question 50 of 65
50. Question
In the circuit shown, the voltage V_{IN}(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 ___________.
CorrectIncorrectHint
NAT Type Question

Question 51 of 65
51. Question
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 0 ≤ ϕ ≤ π. Here the angle θ(0 ≤ θ < π) is measured from the zaxis, and the angle ϕ(0 ≤ ϕ ≤ 2π) is measured from the xaxis in the xy plane.
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Question 52 of 65
52. Question
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 _______.
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NAT Type Question

Question 53 of 65
53. Question
Let h[n] be the impulse response of a discretetime linear time invariant (LTI) filter. The impulse response is given by
and h[n] = 0 for n < 0 and n > 2. 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 ________.
CorrectIncorrectHint
NAT Type Question

Question 54 of 65
54. Question
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?
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Question 55 of 65
55. Question
A continuous time signal x(t) = 4 cos (200 πt) + 8 cos (400 πt), 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 y(t) is _______.
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Question 56 of 65
56. Question
She has a sharp tongue and it can occasionally turn _______.
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Question 57 of 65
57. Question
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
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Question 58 of 65
58. Question
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
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Question 59 of 65
59. Question
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?
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Question 60 of 65
60. Question
I ________ made arrangements had I _________informed earlier.
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Question 61 of 65
61. Question
“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
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Question 62 of 65
62. Question
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?
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Question 63 of 65
63. Question
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
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Question 64 of 65
64. Question
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?
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Question 65 of 65
65. Question
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?
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