If , where  and  indicate the bases of the corresponding numbers, then        

Consider a real-valued base-band signal , band limited to . The Nyquist rate for the signal  is

The exponential Fourier series representation of a continuous-time periodic signal  is defined as

where  is the fundamental angular frequency of  and the coefficients of the series are  The following information is given about  and

I.  is real and even, having a fundamental period of 6.

II. The average value of  is 2.

III.

The average power of the signal  (rounded off to one decimal place) is ________.

A unity feedback system that uses proportional. integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters  and . The maximum value of  that can be chosen so as to keep the overall system stable or, in the worst case, marginally stable (rounded off to three decimal places) is ________.

The block diagram of a feedback control system is shown in the figure.

The transfer function  of the system is        

A digital transmission system uses a  systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword pairs in this code , where  is the codeword corresponding to the  message  are known to be , (1110 ;  and , then which of the following is a valid codeword in this code?

An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0V to 7.68V. If the digital input code is 10010110 (the leftmost bit is MSB, then the analog output voltage of the DAC (rounded off to one decimal place) is _______ V.

Consider the integral

where  is a counter-clockwise oriented circle defined as . The value of the integral is

Two continuous random variables  and  are related as

Let  and  denote the variance of  and , respectively. The variances are related as

Consider the differential equation given below:

The integrating factor of the differential equation is

A standard air-filled rectangular waveguide with dimension , operates at . For the dominant mode of wave propagation, the phase velocity of the signal is . The value (rounded off to two decimal places) of , where  denotes the velocity of light, is _______.

A box contains the following three coins,

I. A fair coin with head on one face and tail on the other face.

II. A coin with heads on both the faces.

III. A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is

In a high school having equal number of boy students and girl students,  of the students study Science and the remaining  students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is ________ bits.

Consider the two-port network shown in the figure.         

The admittances parameters, in Siemens, are

The electrical system shown in the figure converts input source current  to output voltage .

Current  in the inductor and voltage  across the capacitor are taken as the state variables, both assumed to be initially equal to zero, i.e.,  and . The system is

Addressing of a  memory is realized using a single decoder. The minimum number of AND gates required for the decoder is

The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are  and , respectively.

If all the inputs  and  are applied simultaneously and held constant, the maximum propagation delay of the circuit is

For a unit step input , a discrete-time LTI system produces an output signal

Let  be the output of the system for an input . The value of  is ________.

If the vectors  and  and  are linearly dependent, the value of  is ________.

In the circuit shown in the figure, the transistors  and  are operating in saturation. The channel length modulation coefficients of both the transistors are non-zero. The transconductance of the MOSFETs  and  are  and  respectively, and the internal resistance of the MOSFETs  and  are  and , respectively.

Ignoring the body effect, the AC small signal voltage gain  of the circuit is

A real  non-singular matrix  with repeated eigen value is given as

where  is a real positive number. The value of  (rounded off to one decimal place) is ________.

An antenna with a directive gain of  is radiating a total power of . The amplitude of the electric field in free space at a distance of  from the antenna in the direction of  gain (rounded off to three decimal places) is _______

For an n-channel silicon MOSFET with  gate oxide thickness, the substrate sensitivity  is found to be  at a substrate voltage , where  is the threshold voltage of the MOSFET. Assume that,  , where   is the separation between the Fermi energy level  and the intrinsic level  in the bulk. Parameters given are

Electron charge  

Vacuum permittivity   

Relative permittivity of silicon   

Relative permittivity of oxide   

The doping concentration of the substrate is        

For the transistor  in the circuit shown in the figure,  and , where  is the mobility of electron,  is the oxide capacitance per unit area,  is the width and  is the length.

The channel length modulation coefficient is ignored. If the gate-to-source voltage  is  to keep the transistor at the edge of saturation, then the threshold voltage of the transistor (rounded off to one decimal place) is _______ V.

Consider the signals  and , where  is the unit step sequence. Let  and  be the discrete time Fourier transform of  and , respectively. The value of the integral

(rounded off to one decimal place) is ___________.

Consider the circuit shown in the figure.

The current I flowing through the 7Ω resistor between P and Q (rounded off to one decimal place) is ________ A.

Consider the circuit shown in the figure.

The value of  (rounded off to one decimal place) is ________ V.

The impedance matching network shown in the figure is to match a lossless line having characteristic impedance  with a load impedance . A quarter-wave line having a characteristic impedance  is connected to . Two stubs having characteristic impedance of  each are connected to this quarter-wave line. One is a short-circuited (S.C.) sub of length  connected across  and the other one is an open-circuited (O.C.) stub of length  connected across RS.

The impedance matching is achieved when the real part of  is

The content of the registers are ,  and . The following machine instructions are executed,        

PUSH

PUSH

PUSH

After execution, the content of registers   are

An symmetrical periodic pulse train  of  amplitude with on-time  and off-time  is applied to the circuit shown in the figure. The diode  is ideal.

The difference between the maximum voltage and minimum voltage of the output waveform  (in integer) is __________ V.

A bar of silicon is doped with boron concentration of  and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of he bar at the rate of . If the recombination lifetime is  s intrinsic carrier concentration of silicon is  and assuming  ionization of boron, then the approximate product of steady state electron and hole concentration due to this light exposure is

The energy band diagram of a p-type semiconductor bar of length  under equilibrium condition (i.e, the Fermi energy level  is constant) is shown in the figure. The valence band  is sloped since doping is non-uniform along the bar. The difference between the energy levels of the valence band at the two edges of the bar is .

If the charge of an electron is , then the magnitude of the electric field developed inside this semiconductor bar is

The switch in the circuit in the figure is in position  for a long time and then moved to position  at time .

The value of  at is

A silicon  junction is shown in the figure. The doping in the P region is  and doping in the N region is . The parameters given are

Built-in voltage

Electron charge

Vacuum permittivity

Relative permittivity of silicon

The magnitude of reverse bias voltage that would completely deplete one of the two regions ( or ) prior to the other (rounded off to one decimal place) is __________ V.

In the circuit shown in the figure, the switch is closed at time , while the capacitor is initially charged to  (i.e.,  ).

The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is _______.

The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time .

Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is____________A.

The complete Nyquist plot of the open-loop transfer function  of a feedback control system is shown in the figure.        

If  has one zero in the right-half of the splane, the number of poles that the closed-loop system will have in the right-half of the s-plane is

Consider two 16-point sequence  and . Let the linear convolution of  and  be denoted by , while  denotes the 16 -point inverse discrete Fourier transform (IDFT) of the product of the 16-point DFTs of  and . The value(s) of  for which  is/are

Consider a rectangular coordinate system  with unit vectors  and . A plane wave traveling in the region  with electric field vector  is incident normally on the plane at , where  is the phase constant. The region  is in free space and the region  is filled with a lossless medium (permittivity , permeability , where  and  ). The value of the reflection coefficient is________.

The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is . The propagation delay of all the flip-flops is assumed to be zero. The clock (Clk) frequency provided to the circuit is .

Starting from the initial value of the flip-flop outputs  with , the minimum number of triggering clock edges after which the flip-flop outputs  becomes 100 (in integer) is _________.

The refractive indices of the core and cladding of an optical fibre are 1.50 and 1.48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fibre to achieve the total internal reflection, (rounded off to two decimal places) is ________degree.

The vector function  is defined over a circular arc  shown in the figure.

The line integral of  is

Consider the vector field

in a rectangular coordinate system  with unit vectors , and . If the field  is irrotational (conservative), then the constant  (in integer) is ________.

For a vector field  in a cylindrical coordinate system  with unit vectors  and , the net flux of  leaving the closed surface of the cylinder  (rounded off to two decimal places) is ________.

For the circuit with an ideal Op-Amp shown in the figure,  is fixed.        

If  Volt for  Volt and  Volt for  Volt, where  is measured across  connected at the output of this Op-Amp, the value of  is

Consider the circuit with an ideal Op-Amp shown in the figure.

Assuming  and , the condition at which  equals to zero is

The autocorrelation function  of a wide-sense stationary random process  is shown in the figure.

The average power of X(t) is __________.

A circuit with an ideal Op-Amp is shown in the figure. A pulse  of  duration is applied to the input. The capacitors are initially uncharged.

The output voltage  of this circuit at (in integer) is ________ V.

Consider a carrier signal which is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of . If the carrier and one of the sidebands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is_________

Consider a superheterodyne receiver tuned to . If the local oscillator feeds a  signal to the mixer, the image frequency (in integer) is ________ kHz.

A  sinusoidal message signal having amplitude  is fed to a delta modulator (DM) operating at a sampling rate of . The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is __________ V.

A sinusoidal message signal having root mean square value of  and frequency of 1kHz is fed to a phase modulator with phase deviation constant . If the carrier signal is , the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is _________ .

A speech signal, band limited to , is sampled at 1.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range  to , are subsequently quantized in an 8-bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is , the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is __________ .

A message signal having peak-to-peak value of , root mean square value of  and bandwidth of  is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of , Assuming that the quantization error is uniformly distributed, the maximum signal to quantization noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is _________

Consider a polar non-return to zero (NRZ) waveform using  and  for representing binary ' 1 ' and ' 0 ' respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance . If the a priori probability of transmission of a binary ' 1 ' is 0.4, the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is _______V.