A continuous-time function x(t) is periodic with period T. The function is sample uniformly with a sampling period  In which one of the following cases is the sampled signal periodic?

A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low pass filter with a cut-off frequency of 23 Hz. The fundamental frequency (in Hz) of the output is____________

A sequence x|n] is specified as        

for n≥2.

The initial conditions are x|0| = 1, x[1] = 1, and x[n] = 0 for n < 0. The value of x[12] is_____________

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor(C) elements, connected all in series or all in parallel, is excited with a source of the form where

The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?

Consider a discrete memory-less source with alphabetand respective probabilities of occurrence  the entropy of the source (in bits) is____________

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number of zeros, the decoder decides in favor of a 1. Assuming a binary symmetric channel with crossover probability p = 0.1, the average probability of error is______________

In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor R is________.

The open-loop transfer function of a unity-feedback control system is

The value of K at the breakaway point of the feedback control system’s root-locus plot is______.

Consider the oscillator circuit shown in the figure. The function of the network (shown in dotted lines) consisting of the 100kΩ resistor in series with the two diodes connected back-to-back is to:        

In the following integral, the contour C encloses the points 2πj and -2πj.

The value of the integral is_________

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation

X: The system is stable ...            

Y: The system is unstable ...

Z: The test breaks down ...          

P: ... when all elements are positive

Q: ... when any one element is zero

R: ... when there is a change in sign of coefficient

The transfer function of a linear time invariant system is given by

The number of zeros in the right half of the s-plane is_______________

Consider a two-port network with the transmission matrix: If the network is reciprocal, then

Let , (where I denotes the identity matrix) and M ≠ I,  and . Then, for any natural number k,  equals:

Identify the circuit below.        

What is the voltage  in the following circuit?

The functionality implemented by the circuit below is        

Consider the following statements for a metal oxide semiconductor field effect transistor (MOSFET).

P: As channel length reduces, OFF-state current increases.

Q: As channel length reduces, output resistance increases.

R. As channel length reduces, threshold voltage remains constant.

S: As channel length reduces, ON current increases.

Which of the above Statements are INCORRECT?

Consider the sequence where u[n] denotes the unit-step sequence and 0 < |a| < |b| < 1. The region of convergence (ROC) of the z-transform of x[n] is

Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-to source
voltage of 1.8 V. Assume that, , the threshold voltage is0.3V, and the channel length modulation parameter is 0.09 . In the saturation region, the drain conductance (in micro Siemens) is_____________

The open-loop transfer function of a unity-feedback control system is given by.

For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is_____.

Which one of the following is an eigen function of the class of all continuous-time, linear,

time-invariant systems (u(t) denotes the unit-step function)?

Consider the signal

Ifis the discrete-time Fourier transform of then is equal to______________

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of ,  and , respectively. The value of  required to ensure that the electric flux density   at radius 10 m is______________

Two lossless X-band horn antennas are separated by a distance of 200λ. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are 0.15 and 0.18, respectively. The maximum directivities of the transmitting and receiving antennas (over the isotropic antenna) are 18 dB and 22 dB, respectively. Assuming that the input power in the lossless transmission line connected to the antenna is 2 W, and that the antennas are perfectly aligned and polarization matched, the power (in mW) delivered to the load at the receiver is______________        

The far-zone power density radiated by a helical antenna is approximated as:

The radiated power density is symmetrical with respect to ∅ and exists only in the upper hemisphere: is a constant. The power radiated by the antenna (in watts) and the maximum directivity of the antenna, respectively, are

The current density in a medium is given by

The total current and the average current density flowing through the portion of a spherical surfaceare given, respectively, by

Consider a silicon p-n junction with a uniform acceptor doping concentration of  on the p-side and a uniform donor doping concentration of  on the n-side. No external voltage is applied to the diode. Given: kT/q = 26 mV,  = 1.5 x  , = , = 8.85 ×  and q = 1.6 × . The charge per unit junction area (nC ) in the depletion region on the p-side is__________

The Laplace transform of the causal periodic square wave of period T shown in the figure below is

A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time responses for t ≥ 0:

X: Impulse                 

Y: Unit step         

Z: Ramp         

An AC voltage source V = 10 sin(t) volts is applied to the following network. Assume that ,  and , and that the diode is ideal.

RMS current  (in mA) through the diode is______________.

The propagation constant of a lossy transmission line is (2 + j5)  and its characteristic impedance is (50+ jo)Ω at ω = rad . The values of the line constants L, C, R, G are, respectively,        

A small percentage of impurity is added to an intrinsic semiconductor at 300 K. Which one of the following statements is true for the energy band diagram shown in the following figure?        

The figure below shows the doping distribution in a p-type semiconductor in log scale.

The magnitude of the electric field (in kV/cm) in the semiconductor due to non uniform doping is________

In an 8085 system, a PUSH operation requires more clock cycles than a POP operation.

Which one of the following options is the correct reason for this?

Consider a silicon sample at T = 300 K, with a uniform donor density , illuminated uniformly such that the optical generation rate is  throughout the sample. The incident radiation is turned off at t = 0. Assume low-level injection to be valid and ignore surface effects. The carrier lifetimes are  and .        

The hole concentration at t=0 and the hole concentration at t = 0.3μs, respectively, are

Given the following statements about a function f:
, select the right option:

P: If f(x) is continuous at then it is also differentiable at  

Q: If f(x) is continuous at then it may not be differentiable at  

R: If f(x) is differentiable at then it is also continuous at

A closed-loop control system is stable if the Nyquist plot of the corresponding open loop transfer function

The output of the combinational circuit given below is

Which one of the following is a property of the solutions to the Laplace equation: f = 0?

Consider the plot of f(x) versus x as shown below.        

Suppose 

Which one of the following is a graph of F(x)?

The integral dxdy, where D denotes the disc: , evaluates to_______________

The region specified by

in cylindrical coordinates has volume of__________

The electric field of a uniform plane wave travelling along the negative z direction is given by the following equation:

This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation:

The polarization of the incident wave, the polarization of the antenna and losses due to the polarization mismatch are, respectively,

The second moment of a Poisson-distributed random variable is 2. The mean of the random variable is ___________        

An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = S(t) + n(t), where n(t) is additive white Gaussian noise with power spectral density . The received signal is passed through a filter with impulse response h(t). Let and  denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter , which of the following holds?

An antenna pointing in a certain direction has a noise temperature of 50 K. The ambient temperature is 290 K. The antenna is connected to a pre-amplifier that has a noise figure of 2 dB and an available gain of 40 dB over an effective bandwidth of 12MHz. The effective input noise temperature  for the amplifier and the noise power at the output of the preamplifier, respectively, are

Consider the constant current source shown in the figure below. Let's β represent the current gain of the transistor. The load current  through  is         

The following signal  of peak voltage 8 V is applied to the non-inverting terminal of an ideal op-amp. The transistor has  and .        

The number of times the LED glows is________________

An ideal op-amp has voltage sources connected to the non-inverting input and connected to the inverting input as shown in the figure below . The voltages ,.... are 1, - 1/2, 1/3, -1/4, 1/5, -1/6,.... volt, respectively. As N approaches infinity, the output voltage (in volt) is_________.

A PIN photodiode of responsivity 0.8A/W is connected to the inverting input of an ideal op-amp as shown in the figure,  Load resistor  If 10μW of power is incident on the photodiode, then the value of the photocurrent (in μA) through the load is_______________.        

A super-heterodyne receiver operates in the frequency range of 58 MHz - 68 MHz. The intermediate frequency and local oscillator frequency are chosen Such that It is required that the image frequencies fall outside the 58 MHz - 68 MHz band. The minimum required  (in MHz) is______________

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal s(t) = 5cos 1600πt + 20cos 1800πt + 5cos 2000πt. The value of the modulation index is________________

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) required for a roll-off factor of 0.25 is_________.