Starting with x = 1, the solution of the equation , after two iterations of Newton-Raphson’s method (up to two decimal places) is ____________

A periodic signal x (t) has a trigonometric Fourier series expansion

, we can conclude that

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let  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  where k is integer valued

II. The complex Fourier series coefficients of x(3t) are  where k is integer valued

III. The fundamental angular frequency of x(3t) is

For the three statements above, which one of the following is correct?

Which of the following can be the pole-zero configuration of a phase-lag controller (lag compensator)?

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  intersects the imaginary axis for The closed loop system is stable for

Let be independent random variables, has mean 0 and variance 1, while  has mean 1 and variance 4. The mutual information I between and in bits is ______________.

Consider a single input single output discrete-time 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?

Which one of the following options correctly describes the locations of the roots of the equation on the complex plane?

Which one of the following is the general solution of the first order differential equation

where x, y are real?

For a narrow base PNP BJT, the excess minority carrier concentrations (for emitter, for base, for collector) normalized to equilibrium minority carrier concentrations (for emitter,for base, for collector) in the quasi-neutral emitter, base and collector regions are shown below. Which one of the following biasing modes is the transistor operating in?

Consider the following statements for continuous-time 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 no causal and BIBO stable system with a pole in the right half of the complex plane.  

Which one among the following is correct?

Two discrete-time signals x[n] and h[n] are both non-zero only for n = 0, 1, 2, and are zero otherwise. It is given that  

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 _____________ .

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) _______

Consider the following statements about the linear dependence of the real valued functions  and , over the field of real numbers.         

1.  and  are linearly independent on
2.  and  are linearly dependent on
3.  and  are linearly independent on
4.  and  are linearly dependent on

Which one among the following is correct?

Consider the 5 × 5 matrix

It is given that A has only one real eigenvalue. Then the real eigenvalue of A is

The rank of the matrix

The open loop transfer function

Where p is an integer, is connected in unity feedback configuration as shown in the 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 ________________.

For the circuit shown, assume that the NMOS transistor is in saturation. Its threshold voltage  and its trans-conductance parameter . Neglect channel length modulation and body bias effects. Under these conditions, the drain current  in mA is ________ .

A continuous time signal  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 ___________ .

Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by  .

Let  be the discrete-time Fourier transform (DTFT) of h[n], where is the normalized angular frequency in radians. Given that the value of (in radians) is equal to ___________ .

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

A half wavelength dipole is kept in the x-y plane and oriented along 45° from the x-axis. Determine the direction of null in the radiation pattern for . Here the angle is measured from the z-axis, and the angle is measured from the x-axis in the x-y plane

An  Silicon device is fabricated with uniform and non-degenerate donor doping concentrations of  and  corresponding to the 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 built-in potential of this device?

As shown, two Silicon (Si) abrupt p-n unction diodes are fabricated with uniform donor doping concentrations of  and in the n-regions of the diodes, and uniform acceptor doping concentrations of  in the p-regions of the diodes, respectively. Assuming that the reverse bias voltage is built-in potentials of the diodes, the ratio  of their reverse bias capacitances for the same applied reverse bias, is _________ .  

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 T-states needed for executing the instruction is

The following FIVE instructions were executed on an 8085 microprocessor.        

MVI A, 33H

MVI B, 78H

ADD B

CMA

ANI 32 H

The Accumulator value immediately after the execution of the fifth instruction is

A bar of Gallium Arsenide (GaAs) is doped with Silicon such that the Silicon atoms occupy Gallium and Arsenic in the GaAs crystal. Which one of the following statements is true?

As shown, a uniformly doped Silicon (Si) bar of length L = 0.1 µm with a donor concentration is illuminated at x = 0 such that electron and hole pairs are generated at the rate of . Hole lifetime is , electronic charge hole diffusion coefficient 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, is ____________.

Which one of the following gives the simplified sum of products expression for the Boolean function are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?

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 5 V is applied across a 1 µm region of this semiconductor, the resulting current density in this region, in , is ____________.

In the circuit shown, the voltage 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 ___________.

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  

The Nyquist plot of the transfer function

does not encircle the point  for K = 10 but does encircle  the point for K = 100. Then the closed loop system (having unity gain feedback) is  

In the latch circuit shown, the NAND gates have non-zero, 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

Consider the D-Latch 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 one-fifth period delayed version of CLK1. The duty cycle at the output of the latch in percentage is __

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is Volts, where l is the distance along the length of the cable in metres, is the complex propagation constant, and rad/s is the angular frequency. The absolute vale of the attenuation in the cable in dB/metre is ___________.

The expression for an electric field in free space is , where x, y, z represent the spatial coordinates, t represents time, and , k are constants. This electric field

A 4-bit shift register circuit configured for right-shift operation, i.e. 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 ___________ .

In the circuit shown, the positive angular frequency (in radians per second) at which the magnitude of the phase difference between the voltages and equals  radians, is

Angle of must befor which real & imaginary part must be equal or

Let where x, y, z are real, and let C be the straight line segment form point A: (0, 2, 1) to point B: (4, 1, –1). The value of I is __________.

An optical fiber is kept along the direction. The refractive indices for the electric fields along and directions in the fiber are respectively

(due to the imperfection in the fiber cross-section). 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 centimeters, is ______________.

A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are

Assume that  is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state  and clocked, after a few clock cycles, it starts cycling through

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 ______________.

The figure shows an RLC circuit excited by the sinusoidal voltage 100 cos (3t) Volts, where t is in seconds. The ratio  is _________________.

Let  for real x. From among the following, choose the Taylor series approximation of f(x) around x = 0, which includes all powers of x less than or equal to 3.

Let X(t) be a wide sense stationary random process with the power spectral density  as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal lowpass filter with the 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.  

III.

Select the correct option:

The Miller effect in the context of a Common Emitter amplifier explains

For the operational amplifier circuit shown, the output saturation voltages are . The upper and lower threshold voltages for the circuit are, respectively,

For the DC analysis of the Common-Emitter amplifier shown, neglect the base current and assume that the emitter and collector currents are equal. Given that and the BJT output resistance is practically infinite. Under these conditions, the midband voltage gain magnitude, , is ____________.

A good transconductance amplifier should have

In the figure shown, the npn transistor acts as a switch.

For the input as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage at saturation and base-to-emitter voltage The minimum value of the common-base current gain of the transistor for the switching should be ____________.

The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain,  and an open-loop cut-off frequency, . The voltage gain of the amplifier at 15 kHz, in V/V, is _______________ .

In 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 the inter symbol interference zero?

Which one of the following statements about differential pulse code modulation (DPCM) is true?

In binary frequency shift keying (FSK), the given signal waveforms are

where T is the bit-duration interval and t is in seconds. Both  and  are zero outside the interval .With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have  and  uncorrelated is