# Electronics and Communication Engg - GATE 2008 Paper Solution

All the four entries of the 2×2 matrix $p=\left[\begin{array}{cc}{p}_{11}& {p}_{12}\\ {p}_{21}& {p}_{22}\end{array}\right]$ are nonzero, and one of its eigenvalues is zero. Which of the following statements is true?

The system of linear equations

4x + 2y = 7
2x + y = 6

has

The equation sin (z) = 10 has

For real values of x, the minimum value of the function f (x) = exp (x) + exp (-x) is

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

Which of the following is a solution to the differential equation $\frac{dx\left(t\right)}{dt}+3x\left(t\right)=0$ ?

In the following graph, the number of trees (P) and the number of cut-sets (Q) are In the following circuit, the switch S is closed at t = 0. The rate of change of current  $\frac{di}{dt}\left(0+\right)$ is given by 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 ?

The impulse response $h\left(t\right)$ of a linear time-invariant continuous time system is described by $h\left(t\right)=exp\left(\alpha t\right)u\left(t\right)+exp\left(\beta t\right)u\left(-t\right)$, where $u\left(t\right)$ denotes the unit step function, and $\alpha$ and $\beta$ are real constants. This system is stable if

The pole-zero plot given below corresponds to a Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

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

Which of the following is true?

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

In the following limiter circuit, an input voltage Vi = 10sin100$\mathrm{\pi }\phantom{\rule{0ex}{0ex}}$t applied. Assume that the diode drop is 0.7V when it is forward biased. The Zener breakdown voltage is 6.8V. The maximum and minimum values of the output voltage respectively are

The drain current of a MOSFET in saturation is given by  ${I}_{\mathit{D}}=K{\left({\mathit{V}}_{\mathit{G}\mathit{S}}\mathit{-}{\mathit{V}}_{\mathit{T}}\right)}^{2}\phantom{\rule{0ex}{0ex}}$ where K is a constant. The magnitude of the transconductance gm is