The signal  is ideally sampled at a sampling frequency of 15 Hz. The sampled signal is passed through a filter with impulse response. The filter output is

The bilateral Laplace transform of a function   is

The magnitude and phase of the complex Fourier series coefficients  of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set of purely imaginary numbers         

In the circuit shown, the Norton equivalent resistance (in Ω) across terminals a-b is _______.        

In the bi-stable circuit shown, the ideal op-amp has saturation levels of ± 5 V. The value of  (in kΩ) that gives a hysteresis width of 500 mV is ________.

If C denotes the counter clockwise unit circle, the value of the contour integral  is _______.

The general solution of the differential equation  is

For the signal flow graph shown in the figure, the value of   is

Consider the differential equation  with initial condition x(0) = 1. The response x(t) for t > 0 is

An air-filled rectangular waveguide of internal dimensions a cm × b cm (a>b) has a cut-off frequency of 6 GHz for the dominant  mode. For the same waveguide, if the cut-off frequency of the  mode is 15 GHz, the cut-off frequency of the  mode in GHz is __________.

In The 2-port admittance matrix of the circuit shown is given by         

The value of x for which all the Eigen-values of the matrix given below are real is

Two causal discrete-time signals x[n] and y[n] are related as. If the z-transform of y[n] is , the value of x[2] is _______.

A 1-to-8 de-multiplexer with data input  , address inputs  (with  as the LSB) and  and as the eight de-multiplexed outputs, is to be designed using two 2-to-4 decoders (with enable input  and address inputs  and ) as shown in the figure.  and  are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R, and S terminals should be        

A unity negative feedback system has an open-loop transfer function. The gain K for the system to have a damping ratio of 0.25 is ________.

In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness is 100 nm. The permittivities of the semiconductor and the oxide layer are and respectively. Assuming , the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is ________.

The output of a standard second-order system for a unit step input is given as

 .

The transfer function of the system is

The state variable representation of a system is given as and .

The response y(t) is

The transfer function of a mass-spring-damper system is given by  . The frequency response data for the system are given in the following table.

The unit step response of the system approaches a steady state value of

In a source free region in vacuum, if the electrostatic potential, the value of constant c must be _______.

The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression

The type of the polarization is

Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz and phase shift of π/2 between them (the element at the origin leads in phase). If the maximum radiated E-field at the point P in the x-y plane occurs at an azimuthal angle of 60°, the distance d (in meters) between the antennas is _________.  

Let the signal  outside the interval  where  and  are finite. Furthermore, . The region of convergence (ROC) of the signal’s bilateral Laplace transform F(s) is

By performing cascading and/or summing/differencing operations using transfer function blocks  and, one CANNOT realize a transfer function of the form

If the circuit shown has to function as a clamping circuit, then which one of the following conditions should be satisfied for the sinusoidal signal of period T?        

Input x(t) and output y(t) of an LTI system are related by the differential equation . If the system is neither causal nor stable, the impulse response h(t) of the system is

The diode in the circuit given below has but is ideal otherwise. The current (in mA) in the 4 kΩ resistor is _______.

Let  with , where u(t) is unit step function. If the bilateral Laplace transform of x(t) is  

Then the value of β is __________.

An n-type silicon sample is uniformly illuminated with light which generates  electron-hole pairs per  per second. The minority carrier lifetime in the sample is 1 µs. In the steady state, the hole concentration in the sample is approximately , where x is an integer. The value of x is ___.

A piece of silicon is doped uniformly with phosphorous with a doping concentration of . The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is . The conductivity (in S ) of the silicon sample at 300 K is _______.

A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a length of 1 cm as shown in figure. The donor doping concentration  and the mobility of electrons are  and , respectively. The average time (in µs) taken by the electrons to move from one end of the bar to other end is ________.        

The energy band diagram and the electron density profile n(x) in a semiconductor are shown in the figures. Assume that n(x) =, with α=0.1 V/cm and x expressed in cm. Given , and . The electron current density (in ) at

Let . If  for all  and c = 5, then d should be equal to _______.

In an 8085 microprocessor, which one of the following instructions changes the content of the accumulator?        

The value of the integral  is ___________.  

In the figure shown, the output Y is required to be. The gates G1 and G2 must be, respectively,

A function of Boolean variables X, Y and Z is expressed in terms of the min-terms as

Which one of the product of sums given below is equal to the function F(X, Y, Z)?

A mod-n counter using a synchronous binary up-counter with synchronous clear input is shown in the figure. The value of n is _______

An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is

The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a

In the circuit shown, the initial voltages across the capacitors  and  are 1 V and 3 V, respectively. The switch is closed at time t=0. The total energy dissipated (in Joules) in the resistor R until steady state is reached, is __________.

The electric field of a uniform plane electromagnetic wave is        

 .

The polarization of the wave is

The voltage ( ) across the capacitor (in Volts) in the network shown is ____.

A zero mean white Gaussian noise having power spectral density   is passed through an LTI filter whose impulse response h(t) is shown in the figure. The variance of the filtered noise at t = 4 is                

In the circuit shown, the average value of the voltage  (in Volts) in steady state condition is____.

 is an independent and identically distributed (i.i.d.) random process with equally likely to be +1 or −1.  is another random process obtained as . The autocorrelation function of , denoted by , is

Let  and  be two independent binary random variables. If and , then is equal to

Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is _______.

Consider two real sequences with time-origin marked by the bold value .

Let  and  be 4-point DFTs of  and, respectively.

Another sequence  is derived by taking 4-point inverse DFT of . The value of is ______.

In the circuit shown,  for switch SW in position A and  for SW in position B. Assume that the op-amp is ideal. The value of  is ___________.

Assuming that the op-amp in the circuit shown below is ideal, the output voltage  (in volts) is_______.

For the voltage regulator circuit shown, the input voltage  is 20 V ± 20% and the regulated output voltage is 10 V. Assume the op-amp to be ideal. For a load  drawing 200mA, the maximum power dissipation in  (in Watts) is ________.        

In the ac equivalent circuit shown, the two BJTs are biased in active region and have identical parameters with β >>1. The open circuit small signal voltage gain is approximately _______.        

A sinusoidal signal of amplitude A is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB, the number of levels in the quantizer is _______.

Consider a binary, digital communication system which uses pulses g(t) and -g(t) for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimum probability of bit error?