A silicon wafer has  of oxide on it and is inserted in a furnace at a temperature above  for further oxidation in dry oxygen. The oxidation rate

The equation sin(z) = 10 has

The recursion relation to solve  using Newton-Raphson method is

A memory-less source emits n symbols each with a probability P. The entropy of the source as a function of n

Which of the following functions would have only odd powers of x in its Taylor series expansion about the point x = 0?

In the following graph, the number of trees (P) and the number of cut-sets (Q) are  

The residue of the function

  at z = 2 is

Consider a Binary Symmetric Channel (BSC) with probability of error being . To transmit a bit, say 1, we transmit a sequence of three 1s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is        

The probability density function (PDF) of a random variable X is as shown below.

The corresponding cumulative distribution function (CDF) has the form

In the Taylor series expansion of  about the point , the coefficient of  is

 is the probability density function for the real random variable X, over the entire x axis. M and N are both positive real numbers. The equation relating M and N is        

Which of the following is a solution to the differential equation ?

Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition . The transfer function  represents a kind of controller. Match the impedances in Group I with the types of controllers in Group II.

Group I

Group II

1. PID controller

2. Lead compensator

3. Lag compensator

The two numbers represented in signed 2’s complement form are

P = 11101101 and Q = 11100110. If Q is subtracted from P, the value obtained in signed 2’s complement form is

All the four entries of the  matrix  are nonzero, and one of its eigenvalues is zero. Which of the following statements is true?

The pole-zero plot given below corresponds to a

The system of linear equations

Has

The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?

An Astable multivibrator circuit using IC 555 timer is shown below. Assume that the circuit is oscillating steadily. The voltage  across the capacitor varies between

A discrete time linear shift-invariant system has an impulse response h[n] with , , , and zero otherwise. The system is given an input sequence x[n] with  and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are, respectively

Consider the Schmidt trigger circuit shown below.

A triangular wave which goes from -12V to 12V is applied to the inverting input of the OPAMP. Assume that the output of the OPAMP swings from +15V to -15V. The voltage at the non-inverting input switches between

A certain system has transfer function, where  is a parameter. Consider the standard negative unity feedback configuration as shown below.  

Which of the following statements is true?

In the following network, the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequency is 10 Hz.

The samples x[n] (n = 0, 1, 2, ………) are given by

The number of open right half plane poles of  is

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2, and P3 with system relations R1, R2, R3, R4. 

In the following network, the switch is closed at t = 0- and the sampling starts from t = 0. The sampling frequency is 10 Hz.

The expression and the region of convergence of the z-transform of the sampled signal are

The drain current of a MOSFET in saturation is given by  where K is a constant. The magnitude of the trans-conductance  is

For the circuit shown in the following figure, transistors  and  are identical NMOS transistors. Assumes that  is in saturation and the output is unloaded. The current  is related to  as

A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltmeters, and ammeters,(all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

(i) -Open,-Closed ;  = 0 A, = 4.5 V,  = 1.5V, = 1 A

(ii) -Closed,-Open ;  = 4 A,= 6 V,  = 6 V,  = 0 A

The z-parameter matrix for this network is         

The measured trans-conductance  of an NMOS transistor operating in the linear region is plotted against the gate voltage  at a constant drain voltage. Which of the following figures represents the expected dependence of on ?

A rectangular waveguide of internal dimensions
(a = 4 cm and b = 3 cm) is to be operated in mode. The minimum operating frequency is

The cross section of a JFET is shown in the following figure. Let  be -2V and let  be the initial pinch-off voltage. If the width W is doubled (with other geometrical parameters and doping levels remaining the same), then the ratio between the mutual trans-conductance of the initial and the modified JFET is

Two identical NMOS transistors  and  are connected as shown below.  is chosen so that both transistors are in saturation. The equivalent  of the pair is defined to be  at constant. The equivalent  of the pair is

A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltmeters, and ammeters,(all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are:

(i) -Open,-Closed ;  = 0 A, = 4.5 V,  = 1.5V, = 1 A

(ii) -Closed,-Open ;  = 4 A,= 6 V,  = 6 V,  = 0 A

The h-parameter matrix for this network is

Consider the matrix . The value of  is

In the following circuit, the comparator output is logic “1” if  and is logic “0” otherwise. The D/A conversion is done as per the relation

volts, where (MSB) ,  and (LSB) are the counter outputs.

The counter starts from the clear state.

The stable reading of the LED displays is

A signal flow graph of a system is given below. The set of equations that correspond to this signal flow graph is

In the following circuit, the comparator output is logic “1” if  and is logic “0” otherwise. The D/A conversion is done as per the relation

volts, where (MSB) ,  and (LSB) are the counter outputs.

The counter starts from the clear state.

The magnitude of the error between  and  at steady state in volts is

For the circuit shown in the following figure,  are inputs to the 4:1 multiplexer. R (MSB) and S are control bits. The output Z can be represented by        

For real value of x, the minimum value of the function  is

For static electric and magnetic fields in an inhomogeneous source-free-medium, which of the following represents the correct form of two of Maxwell’s equations?

Step responses of a set of three second-order under-damped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

The value of the integral of the function  along the straight line segment from the point (0, 0) to the point (1, 2) in the x-y plane is

Consider points P and Q in the x-y plane, with  and . The line integral  along the semicircle with the line segment PQ as its diameter

The impulse response h(t) of a linear time-invariant continuous time system is described by , where u(t) denotes the unit step function, and  and  are real constants. This system is stable if

Group I lists a set of four transfer functions. Group II gives a list of possible step responses y(t). Match the step responses with the corresponding transfer functions.

Group I

Group II

(1)

(2)

(3)

(4)

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = -2 and s = -4, and one simple zero at s = -1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is

The logic function implemented by the following circuit at the terminal OUT is        

Which of the following is NOT associated with a p-n junction?

In the following limiter circuit, an input voltage  is applied. Assume that the diode drop is  when it is forward biased. The Zener breakdown voltage is . The maximum and minimum values of the output voltage respectively are

Consider the following assertions.

S1: For Zener effect to occur, a very abrupt junction is required.

S2: For quantum tunnelling to occur, a very narrow energy barrier is required.

Which of the following is correct?

One end of a loss-less transmission line having the characteristic impedance of  and length of 1cm is short-circuited. At 3GHz, the input impedance at the other end of the transmission line is

Which of the following is true?

For a Hertz dipole antenna, the half power beam width (HPBW) in the E-plane is

The signal x(t) is described by

 .

Two of the angular frequencies at which its Fourier transform becomes zero are

Silicon is doped with boron to a concentration of   atom/. Assume the intrinsic carrier concentration of silicon to be  and the value of  to be 25mV at 300 K. Compared to un-doped silicon, the Fermi level of doped silicon

At 20 GHz, the gain of a parabolic dish antenna of 1 meter diameter and 70% efficiency is

The impulse response h(t) of a linear time-invariant continuous time system is given by

, where u(t) denotes the unit step function.

The frequency response  of this system in terms of angular frequency, is given by 

Which of the following Boolean Expressions correctly represents the relation between P, Q, R and ?        

In the following circuit, the switch S is closed at t=0. The rate of change of current  is given by

The impulse response h(t) of a linear time-invariant continuous time system is given by

, where u(t) denotes the unit step function.

The output of this system, to the sinusoidal input  for all time t, is

The Thevenin’s equivalent impedance  between the nodes P and Q in the following circuit is

The driving point impedance of the following network

Is given by.The component values are

The circuit shown in the figure is used to charge the capacitor C alternately from two current sources as indicated. The Switches  and  are mechanically coupled and connected as follows:        

For         ,        

(n = 0, 1, 2,…)          to  and  to

For        ,        

(n = 0, 1, 2,…)          to  and  to .

Assume that the capacitor has zero initial charge. Given that u(t) is a unit step function, the voltage  across the capacitor is given by

The following series RLC circuit with zero initial conditions is excited by a unit impulse function

For t > 0, the output voltage  is  

The following series RLC circuit with zero initial conditions is excited by a unit impulse function

For t > 0, the voltage across the resistor is

For each of the positive edge-triggered J-K flip flop used in the following figure, the propagation delay is

Which of the following waveforms correctly represents the output at ?

The magnitude of frequency response of an under-damped second order system is 5 at 0 rad/sec and peaks to  at rad/sec. The transfer function of the system is

Noise with double-sided power spectral density of K over all frequencies is passed through a RC low pass filter with 3 dB cut-off frequency of . The noise power at the filter output is

For the circuit shown in the figure, D has a transition from 0 to 1 after CLK changes from 1 to 0. Assume gate delays to be negligible.

Which of the following statements is true?

An 8085 assembly language program is given below.

After execution of line 7 of the program, the status of the CY and Z flags will be

A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant). The magnitude of the reflection coefficient is

An 8085 executes the following instructions

2710        LXI         H, 30A0H

2713         DAD        H

2714        PCHL

All addresses and constants are in Hex. Let PC be the contents of the program counter and HL be the contents of the HL register pair just after executing PCHL.

Which of the following statements is correct?        

Consider the following circuit using an ideal OPAMP. The I-V characteristics of the diode is described by the relation  where,  and V is the voltage across the diode (taken as positive for forward bias). For an input voltage, the output voltage  is        

The OPAMP circuit shown above represents a

In the following transistor circuit, , , and   and all the capacitances are very large.

The value of DC current  is        

In the following transistor circuit, , , and   and all the capacitances are very large.

The mid-band voltage gain of the amplifier is approximately

 is a real-valued periodic sequence with a period N. x[n] and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence is

Consider the amplitude modulated (AM) signal  . For demodulating the signal using envelope detector, the minimum value of  should be

Consider the frequency modulated signal  with carrier frequency of Hz. The modulation index is

The signal  is

Four messages band limited to W, W, 2W and 3W respectively are to be multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth required for transmission of this TDM signal is

A speech signal, band limited to 4 kHz and peak voltage varying between +5V and -5V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

If the bits 0 and 1 are transmitted using bipolar pulses, the minimum bandwidth required for distortion free transmission is

A speech signal, band limited to 4 kHz and peak voltage varying between +5V and -5V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantizer output is

A speech signal, band limited to 4 kHz and peak voltage varying between +5V and -5V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.

The number of quantization levels required to reduced to reduce the quantization noise by a factor of 4 would be