A system with transfer function H(z) has impulse response h[n] defined as h[2] = 1, h[3] = –1 and h[k] = 0 otherwise. Consider the following statements.

S1: H (z) is a low-pass filter.

S2: H (z) is an FIR filter.

Which of the following is correct?

An LTI system having transfer function  and input  is in steady state. The output is sampled at a rate rad/s to obtain the final output {y(t)}. Which of the following is true?

The Fourier series of a real periodic function has only

P. cosine terms if it is even

Q. Sine terms if it even

R. cosine terms if it is odd

S. sine terms if it is odd

Which of the above statements are correct?

Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of  is

A communication channel with AWGN operating at a signal to noise ratio SNR >> 1 and bandwidth B has capacity . If the SNR is doubled keeping B constant, the resulting capacity is given by

A function is given by .

Which of the following is true?

In the circuit shown, what value of  maximizes the power delivered to?

If  then  is given by

The order of the differential equation  is

A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

The Taylor series expansion of  at  is given by

Match each differential equation in Group I to its family of solution curves from Group II           

Consider two independent random variables X and Y with identical distributions. The variables X and Y take values 0, 1 and 2 with probabilities ,  and  respectively. What is the conditional probability?

A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean of X as 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true?        

The feedback configuration and the pole-zero locations of  are shown below. The root locus for negative value of k, i.e. for , has breakaways / break-in points and angle of departure at pole P (with respect to the positive real axis) equal to

The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. Which of the following compensators has such a magnitude plot?

The Eigen values of the following matrix are

In the following Astable multi-vibrator circuit, which properties of  depend on ?

Consider a system whose input x and output y are related by the equation

,

Where h(t) is shown in the graph

Which of the following four properties are possessed by the system?

BIBO: Bounded input gives a bounded output.

Causal: The system is causal

LP: The system is low pass

LTI: The system is linear and time-invariant.        

The ROC of Z-transform of the discrete time sequence  is

Consider the following two statements about the internal conditions in an n-channel MOSFET operating in the active region.

: The inversion charge decreases from source to drain

: The channel potential increases from source to drain

Which of the following is correct?

Consider the CMOS circuit shown,

Where the gate voltage  of the n-MOSFET is increased from zero, while the gate voltage of the p-MOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the trans-conductance parameter and the (W/L), is.

For small increase in  beyond 1 V, which of the following gives the correct description of the region of operation of each MOSFET?        

Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?

Consider the CMOS circuit shown,

Where the gate voltage  of the n-MOSFET is increased from zero, while the gate voltage of the p-MOSFET is kept constant at 3 V. Assume that, for both transistors, the magnitude of the threshold voltage is 1 V and the product of the trans-conductance parameter and the (W/L), is.

Estimate the output voltage  for .

[Hint: Use the approximate current-voltage equation for each MOSFET,]

Consider the system  with  and  where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y-axis. The other wire is in the x-y plane and parallel to the x-axis. Which components of the resulting magnetic field are non-zero at the origin?

If a vector filed  is related to another vector filed  through, which of the following is true? Note: C and  refer to any closed contour and any surface whose boundary is C.

A magnetic field in air is measured to be

What current distribution leads to this field?

[Hint: The algebra is trivial in cylindrical coordinates.]

The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer functions has these properties?

A fully charged mobile phone with a 12 V battery is good for a 10 minute talk-time. Assume that, during the talk-time, the battery delivers a constant current of 2 A and its voltage drops linearly from 12 V to 10 V as shown in the figure. How much energy does the battery deliver during this talk-time?

In the interconnection of ideal sources shown in the figure, it is known that the 60 V source is absorbing power. Which of the following can be the value of the current source I?

The full forms of the abbreviations TTL and CMOS in reference to logic families are

Consider a silicon p-n junction at room temperature having the following parameters:

Doping on the n-side

Depletion width on the n-side

Depletion width on the p-side

Intrinsic carrier concentration

Thermal voltage = 26 mV

Permittivity of free space

Dielectric constant of silicon = 12

The built-in-potential of the junction

In the circuit below, the diode is ideal. The voltage V is given by

Consider a silicon p-n junction at room temperature having the following parameters:

Doping on the n-side

Depletion width on the n-side

Depletion width on the p-side

Intrinsic carrier concentration

Thermal voltage = 26 mV

Permittivity of free space

Dielectric constant of silicon = 12

The peak electric field in the device is

A transmission line terminates in two branches, each of length , as shown. The branches are terminated by  loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance  as seen by the source.

In an n-type silicon crystal at room temperature, which of the following can have a concentration of?

The ratio of the mobility to the diffusion coefficient in a semiconductor has the units

If X =1 in the logic equation , then

What are the minimum number of 2-to-1 multiplexers required to generate a 2-input AND gate and a 2-input Ex-OR gate?

Two products are sold from a vending machine, which has two push buttons and . When a button is pressed, the price of the corresponding product is displayed in a 7-segment display.

If no buttons are pressed, ‘0’ is displayed, signifying ‘Rs. 0’.

If only  is pressed, ‘2’ is displayed, signifying ‘Rs. 2’.

If only  is pressed, ‘5’ is displayed, signifying ‘Rs. 5’.

If both  and  are pressed, ‘E’ is displayed, signifying ‘Error’.

The names of the segments in the 7-segment display, and the glow of the display for ‘0’, ‘2’, ‘5’ and ‘E’, are shown below.

Consider

(i) Push button pressed /not pressed is equivalent to logic 1/0 respectively,

(ii) A segment glowing / not glowing in the display is equivalent to logic 1/0 respectively

If the segments a to g are considered as functions of  and , then which of the following is correct?        

Two products are sold from a vending machine, which has two push buttons and . When a button is pressed, the price of the corresponding product is displayed in a 7-segment display.

If no buttons are pressed, ‘0’ is displayed, signifying ‘Rs. 0’.

If only  is pressed, ‘2’ is displayed, signifying ‘Rs. 2’.

If only  is pressed, ‘5’ is displayed, signifying ‘Rs. 5’.

If both  and  are pressed, ‘E’ is displayed, signifying ‘Error’.

The names of the segments in the 7-segment display, and the glow of the display for ‘0’, ‘2’, ‘5’ and ‘E’, are shown below.

Consider

(i) Push button pressed /not pressed is equivalent to logic 1/0 respectively,

(ii) A segment glowing / not glowing in the display is equivalent to logic 1/0 respectively

What are the minimum numbers of NOT gates and 2-input OR gates required to design the logic of the driver for this 7-segment display?

If the transfer function of the following network is, the value of the load resistance  is

The switch in the circuit shown was on position ‘a’ for a long time, and is moved to position ‘b’ at time t=0. The current i(t) for t>0 is given by         

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown.

Which of the following statements is true?

The time domain behaviour of an RL circuit is represented by         

For an initial current of , the steady state value of the current is given by

An AC source of RMS voltage 20 V with internal impedance  feeds a load of impedance  in the figure below. The reactive power consumed by the load is

The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed-loop system in the feedback configuration shown.

The gain and phase margins of G(s) for closed loop stability are

Refer to the NAND and NOR latches shown in the figure. The inputs 1 for both the latches are first made (0, 1) and then, after a few seconds, made (1, 1). The corresponding stable outputs  are        

A white noise process X(t) with two-sided power spectral density  W/Hz is input to a filter whose magnitude squared response is shown below.

The power of the output process Y(t) is given by

What are the counting states  for the counter shown in the figure below?

If the power spectral density of a stationary random process is a sinc-squared function of frequency, the shape of its autocorrelation is

In microprocessor, the service routine for a certain interrupt starts from a fixed location of memory which cannot be externally set, but the interrupt can be delayed or rejected. Such an interrupt is

If the signal to quantization noise ratio required in uniformly quantizing the signal is 43.5 dB, the step size of the quantization is approximately

If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the negative values are uniformly quantized with a step size of 0.1 V, the resulting signal to quantization noise ratio is approximately

In the circuit shown below, the op-amp is ideal, the transistor has  and . Decide whether the feedback in the circuit is positive or negative and determine the voltage V at the output of the op-amp.

A small signal source is applied  to a transistor amplifier as shown below. The transistor has  and.  Which expression best approximate?

The 4-point Discrete Fourier Transform (DFT) of a discrete time sequence {1, 0, 2, 3} is

For a message signal  and carrier of frequency, which of the following represents a single side-band (SSB) signal?

A message signal given by

Is amplitude-modulated with a carrier of frequency  to generate

What is the power efficiency achieved by this modulation scheme?