Let  and  be two vectors. The value of the coefficient  in the expression , which minimizes the length of the error vector , is

The rate of increase, of a scalar field  in the direction  at a point  is

Let . Which of the following cannot be a value of ?

The value of the contour integral,

, where the contour  is

, taken in the counter clockwise direction, is

Let the sets of eigenvalues and eigenvectors of a matrix  be  and , respectively. For any invertible matrix , the sets of eigenvalues and eigenvectors of the matrix , where , respectively, are

In a semiconductor, if the Fermi energy level lies in the conduction band, then the semiconductor is known as

For an intrinsic semiconductor at temperature , which of the following statement is true?

A series RLC circuit has a quality factor  of 1000 at a center frequency of . The possible values of  and  are

For a MOS capacitor,  and  are the flat-band voltage and the threshold voltage, respectively. The variation of the depletion width for varying gate voltage  is best represented by

Consider a narrow band signal, propagating in a lossless dielectric medium , with phase velocity  and group velocity . Which of the following statement is true?

( is the velocity of light in vacuum.)

In the circuit shown below,  and  are bias voltages. Based on input and output impedances, the circuit behaves as a

A cascade of common-source amplifiers in a unity gain feedback configuration oscillates when

In the circuit shown below,  and  are the inputs. The logical function realized by the circuit shown below is

The synchronous sequential circuit shown below works at a clock frequency of . The throughput, in  bits/s, and the latency, in ns, respectively, are

The open loop transfer function of a unity negative feedback system is , where   and  are positive constants. The phase cross-over frequency, in rad/s, is

Consider a system with input  and output . The system is

Let  be a strictly band-limited signal M bandwidth B and energy E. Assuming  the energy in the signal  is

The Fourier transform  of  is

Note:

In the table shown below, match the signal type with its spectral characteristics.         

Signal Type

(i) Continuous, aperiodic

(ii) Continuous, periodic

(iii) Discrete, aperiodic

(iv) Discrete, periodic

Spectral Characteristics

(a) Continuous, aperiodic

(b) Continuous, periodic

(c) Discrete, aperiodic

(d) Discrete, periodic

The signal-to-noise ratio (SNR) of an ADC with a full-scale sinusoidal input is given to be 61.96 . The resolution of the ADC is __________ (rounded off to the nearest integer). bits.

In the circuit shown below, the current I flowing through 200 Ω resistor is ________ mA.

(rounded off to two decimal places).

For the two port network shown below, the [Y]-parameters is given as

The value of load impedance , in , for maximum power transfer will be _________.

(rounded off to the nearest integer).

For the circuit shown below, the propagation delay of each NAND gate is . The critical path delay, in ns, is ________ (rounded off to the nearest integer).

In the circuit shown below, switch S was closed for a long time. If the switch is opened at t=0, the maximum magnitude of the voltage  in volts, is ________ (rounded off to the nearest integer).         

A random variable , distributed normally as , undergoes the transformation , given in the figure. The form of the probability density function of  is (In the options given below,  are non-zero constants and  is piecewise continuous function)

The value of the line integral  along the straight line joining the points  and  is

Let  be an  real column vector with length . The trace of the matrix  is

The  of the circuit shown below is

In the circuit shown below,  and  are silicon diodes with cut-in voltage of .  and  are input and output voltages in volts. The transfer characteristic is

A closed loop system is shown in the figure where  and . The steady state error due to a ramp input  is given by

In the following block diagram,  and  are two inputs. The output  is expressed as

.  and  are given by

The state equation of a second order system is  is the initial condition.

Suppose  and  are two distinct eigenvalues of A and  and  are the corresponding eigenvectors. For constants  and , the solution, , of the state equation is

The switch  was closed and  was open for a long time. At , switch  is opened and  is closed, simultaneously. The value of , in amperes, is

Let a frequency modulated (FM) signal , where  is a message signal of bandwidth . It is passed through a non-linear system with output  . Let  denote the FM bandwidth. The minimum value of  required to recover  from  is

The h-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain  is

Consider a discrete-time periodic signal with period . Let the discrete-time Fourier series (DTFS) representation be , where

 and . The value of the sum  is

Let an input  having discrete time Fourier transform.

 be passed through an LTI system. The frequency response of the LTI system is . The output  of the system is

Let  be passed through an LTI system having impulse response . The output of the system is

Let  and  be two band-limited signals having bandwidth  each. In the figure below, the Nyquist sampling frequency, in , required to sample , is

The S-parameters of a two port network is given as

with reference to . Two lossless transmission line sections of electrical lengths  and  are added to the input and output ports for measurement purposes, respectively. The Sparameters  of the resultant two port network is

The value of the integral  over the region , given in the figure, is __________(rounded off to the nearest integer).

In an extrinsic semiconductor, the hole concentration is given to be  where  is the intrinsic carrier concentration of . The ratio of electron to hole mobility for equal hole and electron drift current is given as _________(rounded off to two decimal places).

The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is , where  and c are positive constants. The value of  is __________. (rounded off to the nearest integer).

Let  and  is shown in the figure below. For , the   is _________. (rounded off to the nearest integer).

Let  be a white Gaussian noise with power spectral density . If  is input to an LTI system with impulse response . The average power of the system output is __________ W. (Rounded off to two decimal place).

A transparent dielectric coating is applied to glass  to eliminate the reflection of red light . The minimum thickness of the dielectric coating, in , that can be used is ________. (rounded off to two decimal places).

In a semiconductor device, the Fermi-energy level is  above the valence band energy. The effective density of states in the valence band at  is . The thermal equilibrium hole concentration in silicon at  is  _________. (rounded off to two decimal places). Given KT at  is .

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of . The time for sampling switch to stay closed to charge a capacitor adequately to full scale voltage of  with 12-bit accuracy is ________ .

(rounded off to two decimal places)

In a given sequential circuit, initial states are   and . For a clock frequency of , the frequency of signal  in , is ________. (rounded off to the nearest integer).

In the circuit below, the voltage  is _______V. (rounded off to two decimal places)

The frequency of occurrence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of "yes/no" questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _______ (rounded off to two decimal places).

For a real signal, which of the following is/are valid power spectral density/densities?

The standing wave ratio on a  lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load.  can be replaced by an equivalent length  and terminating resistance  of the same line. The value of  and , respectively, are

The electric field of a plane electromagnetic wave is

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are