List of practice Questions

The value of the real variable \( x>0 \) that minimizes the function \( f(x) = x^x e^{-x} \) is ________

The general solution of the differential equation \( x^2 y'' - xy' + 5y = 0 \) is _______

The particular integral of the differential equation \[ \frac{d^2y}{dx^2} - \frac{dy}{dx} + 9y = e^{3x} \] is _______

The value of the integral \( \int_C \frac{6z - 5}{z^2 + 4z + 5} \, dz \), where \( C \) is the circle \( |z| = 1 \), is _______

The main advantage of super heterodyne receiver is ________.

The occurrence of double spotting indicates that _________.

Which of the following type of noise becomes of great importance at high frequencies?

As the aperture area of an antenna increases, its gain _________.

The intrinsic impedance of free space is _________.

The standing wave ratio of an open wire transmission line having a characteristic impedance of 600\(\Omega\) and terminated by resistive load of 900\(\Omega\) will be ________.

With some initial change at \(t = 0^+\), a capacitor will act as ________.

Commercial band for FM broadcasting is ________.

Dominant mode of propagation in a rectangular wave guide is ________.

A propagating wave in a lossless medium along z-direction has x and y electric field components both sinusoidal of same amplitude and in phase with each other. The wave is ________.

The skin depth of a wave propagating through aluminium medium of conductivity \(\sigma = 38.2~\text{MS/m}\) is computed at \(1.6~\text{MHz}\) frequency as \(64.4~\mu m\). The skin depth into the same medium at \(6.4~\text{MHz}\) frequency is ________.

A uniform plane wave travels through fresh water characterised by \(\varepsilon_r = 78\). Fresh water is non-magnetic and non-conducting. The wavelength of propagation in fresh water at an operating frequency of \(300~\text{MHz}\) is ________.

An antenna driven by 6 Ampere current radiates 5 kW power into freespace. The radiation resistance of the antenna at 1 GHz frequency is ________.

Shannon’s channel capacity theorem supports the concept and need of ________.

The purpose of a matched filter in a digital communication receiver is to _______.

The ability of a receiver to reproduce the exact replica of the transmitted signal at its output is described through its ________.

Pre-emphasis and De-emphasis are used in ________.

M-ary encoding in Digital communication is done to achieve ________.

Slope overload distortion occurs in ________.

Fastest Logic family is ________.