The general form of the complementary function of a differential equation is given by where A and B are real constants determined by the initial condition. The corresponding differential equation is__________.

In the context of Bode magnitude plots. . decade is the same as

In the feedback control system shown in the figure below .

R(s), Y(s) and E(s) are the Laplace transforms of r(t), y(t), and e(t), respectively. If the input r(t) is a unit step function, then ________.

Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances , and  (indicated in the figure) are_______.

Let  be the unit vectors along x and y axes, respectively and let A be a positive constant. Which one of the following statements is true for the vector fields

In the circuit below, assume that the long channel NMOS transistor is biased in saturation. The small signal trans-conductance of the transistor is . Neglect body effect, channel length modulation and intrinsic device capacitances. The small signal input impedance  is________.

For the closed loop amplifier circuit shown below, the magnitude of open loop low frequency small signal voltage gain is 40. All the transistors are biased in saturation. The current source  is ideal. Neglect body effect, channel length modulation and intrinsic device capacitances. The closed loop low frequency small signal voltage gain  (rounded off to three decimal places) is________.

For the Boolean function

the essential prime implicants are________

A white Gaussian noise  with zero mean and power spectral density , when applied to a first-order RC low pass filter produces an output . At a particular time , the variance of the random variable  is _________.

A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t). A signal x(0.5 t) is applied to another causal and stable LTI system with impulse response h(0.5t). The resulting output is_________.

For non-degenerately doped n-type silicon, which one of the following plots represents the temperature (𝑇) dependence of free electron concentration (𝑛)

In the circuit shown, the  step-down transformer and the diodes are ideal. The diodes have no voltage drop in forward biased condition. If the input voltage (in Volts) is  and the average value of load voltage  (in Volts) is , the value of  is ________.

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is______.

An amplitude modulator has output (in Volts)

The carrier power normalized to  resistance is 50 Watts. The ratio of the total sideband power to the total power is . The value of  (in Volts, rounded off to two decimal places) is_______.

In a number system of base , the equation  has  as one of its solutions. The value of  is_______.

Let  and  denote the set of real numbers and the three-dimensional vector space over it, respectively. The value of for which the set of vectors

Dose not form a basis of is__________.

In the given circuit, the current  (in mA) is _________.

In the circuit given below, the switch  was kept open for a sufficiently long time and is closed at time . The time constant (in seconds) of the circuit for  is ________.

Suppose  and  are independent and identically distributed random variables that are distributed uniformly in the interval . The probability that  is _________.

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _________.

As shown in the circuit, the initial voltage across the capacitor is , with the switch being open. The switch is then closed at . The total energy dissipated in the ideal Zener diode  after the switch is closed (in , rounded off to three decimal places) is ________.

Consider the Earth to be a perfect sphere of radius R. Then the surface area of the region, enclosed by the N latitude circle, that contains the north pole in its interior is__________.

Consider a unity negative feedback control system with forward path gain  as shown.

The impulse response of the closed-loop system decays faster than  if

A satellite attitude control system, as shown below, has a plant with transfer function  cascaded with a compensator , where K and  are positive real constants.

In order for the closed-loop system to have poles at , the value of  must be ________.

A uniform plane wave with electric field  is travelling in the air (relative permittivity,  and relative permeability,  ) in the  direction ( is a positive constant,  is the unit vector along the  axis). It is incident normally on an ideal electric conductor (conductivity,  ) at . The position of the first null of the total magnetic field in the air (measured from , in metres) is

A 4-bit priority encoder has inputs , and  in descending order of priority. The two-bit output  is generated as , and 11 corresponding to inputs , and , respectively. The Boolean expression of the output bit  is_____.

The propagation delay of the  MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as .

If  is set to 1 then the output  is________.

The sequence of states  of the given synchronous sequential circuit is ________.

Let z be a complex variable. If  and C is the circle in the complex plane with __________.

Consider two continuous time signals x(t) and y(t) as shown below

If X(f) denotes the Fourier transform of x(t), then the Fourier transform of y(t) is__________.

A source transmits a symbol , taken from  with equal probability, over an additive white Gaussian noise channel. The received noisy symbol  is given by , where the noise  is zero mean with variance 4 and is independent of .

Using , the optimum symbol error probability is_______.

A full scale sinusoidal signal is applied to a 10-bit ADC. The fundamental signal component in the ADC output has a normalized power of 1W, and the total noise and distortion normalized power is . The effective number of bits (rounded off to the nearest integer) of the ADC is ________.

The information bit sequence  is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the generator polynomial is . The encoded sequence of bits is ___________.

The opamps in the circuit shown are ideal, but have saturation voltages of .

Assume that the initial inductor current is . The input voltage  is a triangular signal with peak voltages of  and time period of . Which one of the following statements is true?

In the circuit below, the opamp is ideal

If the circuit is to show sustained oscillations, the respective values of  and the corresponding frequency of oscillation are________.

In the circuit shown below, the transistors  and  are biased in saturation. Their small signal transconductances are  and  respectively. Neglect body effect, channel length modulation and intrinsic device capacitances.

Let  be a random process, where amplitude  and phase  are independent of each other, and are uniformly distributed in the intervals  and , respectively.  is fed to an 8 -bit uniform mid-rise type quantizer. Given that the autocorrelation of  is , the signal to quantization noise ratio (in , rounded off to two decimal places) at the output of the quantizer is_________. 

A lossless transmission line with characteristic impedance  is terminated with an unknown load. The magnitude of the reflection co-efficient is . As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in ) is ________.

The relationship between any N-length sequence x[n] and its corresponding N-point discrete Fourier transform X[k] is defined as         

Another sequence y[n] is formed as below

For the sequence x[n]={1,2,1,3}, the value of  Y[0] is __________

For the two port network shown below, the value of the  parameter (in Siemens) is__________.

Consider a MOS capacitor made with p-type silicon. It has an oxide thickness of , a fixed positive oxide charge of  at the oxide-silicon interface, and a metal work function of . Assume that the relative permittivity of the oxide is 4 and the absolute permittivity of free space is . If the flatband voltage is , the work function of the -type silicon (in , rounded off to two decimal places) is________.

In the network shown below, maximum power is to be transferred to the load .

The value of in  is __________.

A non-degenerate n-type semiconductor has  neutral dopant atoms. Its Fermi level is located at  below the conduction band  and the donor energy level  has a degeneracy of 2. Assuming the thermal voltage to be . The difference between  and  (in , rounded off to two decimal places) is __________.

An NMOS transistor operating in the linear region has  of  at  of 0.1 V. Keeping  constant, the  is increased to 1.5 V.        

Given that , the

transconductance at the new operating point
(in , rounded off to two decimal places) is________.

The photocurrent of a PN junction diode solar cell is . The voltage corresponding to its maximum power point is . If the thermal voltage is , the reverse saturation current of the diode (in , rounded off to two decimal places) is______.

A digital communication system transmits through a noiseless bandlimited channel . The received signal  at the output of the receiving filter is given by  where  are the symbols and  is the overall system response to a single symbol. The received signal is sampled at . The Fourier transform of  is . The Nyquist condition that  must satisfy for zero inter symbol interference at the receiver is _______.

A continuous time signal is sampled at a rate of 15 Hz. The sampled signal  when passed through an LTI system with impulse response        

Produces an output The expression for is __________.

For a causal discrete-time LTI system with transfer function

Which of the following statements is/are true?

Let  and  represent density and velocity, respectively, at a point  and time t. Assume  is continuous. Let  be an arbitrary volume in space enclosed by the closed surface  and  be the outward unit normal of  Which of the following equations is/are equivalent to  ?

The free electron concentration profile  in a doped semiconductor at equilibrium is shown in the figure, where the points , and  mark three different positions. Which of the following statements is/are true?

Which of the following statements is/are true for a BJT with respect to its DC current gain  ?

Consider a system S represented in state space as

Which of the state space representations given below has/have the same transfer function as that of S?

Let  be functions of (x, y, z). Suppose that for every given pair of points A and B in space, the line integral evaluates to the same value along any path C that starts at A and ends at B. Then which of the following is/are true? 

Consider the matrix where k is a positive real number. Which of the following vectors is/are eigenvector(s) of this matrix?

The radian frequency value(s) for which the discrete time sinusoidal signal

has a period of 40 is/are__________.