Let be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are

Match the application to appropriate numerical method.

Application 

P1: Numerical integration

P2: Solution to a transcendental equation

P3: Solution to a system of linear equations

P4: Solution to a differential equation

Numerical Method

M1: Newton-Raphson Method

M2: Runge-Kutta Method

M3: Simpson’s 1/3-rule

M4: Gauss Elimination Method

A binary random variable X takes the value of 1 with probability 1/3. X is input to a cascade of 2 independent identical binary symmetric channels (BSCs) each with crossover probability 1/2. The output of BSCs are the random variables  and  as shown in the figure.

The value of in bits is __________.        

In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?

If WL is the Word Line and BL the Bit Line, an SRAM cell is shown in

Which ONE of the following is a linear non-homogeneous differential equation, where x and y are the independent and dependent variables respectively?

Consider the following block diagram in the figure.

The transfer function   is

An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is

An analog voltage in the range 0 to 8 V is divided in 16 equal intervals for conversion to 4-bit digital output. The maximum quantization error (in V) is _________.

A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is

Consider an air filled rectangular waveguide with a cross-section of 5 cm × 3 cm. For this waveguide, the cut-off frequency (in MHz) of  mode is _________.

For an all-pass system , where  , for all ω. If Re(a) ≠ 0, , then b equals

Let  

The quantities p, q, r are real numbers. Consider  

If the zero of H(z) lies on the unit circle, then r = _____.

Consider the multiplexer-based logic circuit shown in the figure.

Which one of the following Boolean functions is realized by the circuit?

Which one of the following statements is NOT true for a square matrix A?

The z-transform of the sequence x[n] is given by , with the region of convergence  . Then, x[n] is ________.

In the circuit shown, W and Y are MSBs of the control inputs. The output F is given by        

If X and Y are inputs and the Difference (D = X – Y) and the Borrow (B) are the outputs, which one of the following diagrams implements a half-subtractor?

In MOSFET fabrication, the channel length is defined during the process of

The slope of the vs.  curve of an n-channel MOSFET in linear regime is  at  = 0.1 V. For the same device, neglecting channel length modulation, the slope of the vs. curve (in ) under saturation regime is approximately _________        

For the MOSFET  shown in the figure, assume W/L = 2, ,  and . The transistor  switches from saturation region to linear region when  (in Volts) is__________.

An ideal MOS capacitor has boron doping-concentration of in the substrate. When a gate voltage is applied, a depletion region of width 0.5 µm is formed with a surface (channel) potential of 0.2 V. Given that  and the relative permittivity of silicon and silicon dioxide are 12 and 4, respectively, the peak electric field (in V/µm) in the oxide region is ________________.

The steady state error of the system shown in the figure for a unit step input is _________.

The state equation of a second-order linear system is given by  

  and

For  and for  

 When  , x(t) is

Given the vector

,

where  denote unit vectors along xy directions, respectively. The magnitude of curl of A is ________.

A region shown below contains a perfect conducting half-space and air. The surface current  on the surface of the perfect conductor is  amperes per meter. The tangential  field in the air just above the perfect conductor is

The input , where u(t) is the unit step function, is applied to a system with transfer function  .If the initial value of output is -2, then the value of the steady state is ___________.

The donor and accepter impurities in an abrupt junction silicon diode are  and , respectively. Assume that the intrinsic carrier concentration in silicon  at 300 K,   and the permittivity of silicon . The built-in potential and the depletion width of the diode under thermal equilibrium conditions, respectively, are

The maximum value of the function   occurs at x=______.

Let h(t) denote the impulse response of a causal system with transfer function .

Consider the following three statements.

S1: The system is stable.

S2:   is independent of t for t>0.

S3: A non-causal system with the same transfer function is stable.

For the above system,

The figure shows a half-wave rectifier. The diode D is ideal. The average steady-state current (in Amperes) through the diode is approximately ____________.

In the figure shown, the value of the current I (in Amperes) is__________.        

For the Y-network shown in the figure, the value of R1 (in Ω) in the equivalent ∆-network is ____.

If , then

The maximum value of  in the interval  is ______.

A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to

At T = 300 K, the hole mobility of a semiconductor  and. The hole diffusion constant  in  is ________.

In the following figure, the transmitter Tx sends a wideband modulated RF signal via a coaxial cable to the receiver Rx. The output impedance  of Tx, the characteristic impedance of the cable and the input impedance of Rx are all real.

Which one of the following statements is TRUE about the distortion of the received signal due to impedance mismatch?

A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage, the resistance R, the capacitance C, and the current i(t) is given below:        

 .

Which one of the following represents the current i(t)?

The desirable characteristics of a trans-conductance amplifier are

Consider the building block called ‘Network N’ shown in the figure. Let C = 100 µF and R= 10kΩ.

Two such blocks are connected in cascade, as shown in the figure.

The transfer function   of the cascaded network is

The circuit shown in the figure is a        

Let X(t) be a wide sense stationary (WSS) random process with power spectral density . If Y(t) is the process defined as Y(t)=X(2t-1), the power spectral density  is

In the circuit shown in the figure, the value of node voltage  is         

Let , , and  be independent and identically distributed random variables with the uniform distribution on [0,1]. The probability  is _________.

In the circuit shown in the figure, the angular frequency ω (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b′ is purely resistive, is _________.        

Assume that a plane wave in air with an electric field   incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z>0. The angle of transmission in the dielectric slab is ________ degrees.

A real band-limited random process X(t) has two-sided power spectral density

Where f is the frequency expressed in Hz. The signal X(t) modulates a carrier and the resultant signal is passed through an ideal band-pass filter of
unity gain with centre frequency of 8 kHz and band-width of 2 kHz. The output power (in Watts) is _______.

Assuming that the Op-amp in the circuit shown is ideal,  is given by        

In the circuit shown, the PNP transistor has  and β = 50. Assume that . For  to be 5 V, the value of  (in kΩ) is _______.

In the circuit shown, the silicon BJT has β = 50. Assume  and 0.2V. Which one of the following statements is correct?        

A modulated signal is, where the baseband signal m(t) has frequency components less than 5 kHz only. The minimum required rate (in kHz) at which y(t) should be sampled to recover m(t) is _______.

The phase response of a pass-band waveform at the receiver is given by  

Where  is the centre frequency, and α and β are positive constants. The actual signal propagation delay from the transmitter to receiver is        

Consider an FM signal

.

The maximum deviation of the instantaneous frequency from the carrier frequency  is

In a PCM system, the signal  V is sampled at the Nyquist rate. The samples are processed by a uniform quantizer with step size 0.75 V. The minimum data rate of the PCM system in bits per second is _____.