GATE EC 2012 Question Paper (12-Feb-2012) (Shift 2)

For a co-axial cable, inner diameter of outer conductor and diameter of inner conductor are 1 cm and 0.01 cm respectively. If dielectric constant $ϵ{}_r$ of the material filling in cable is 4, characteristic impedance of the co-axial cable is_____$\Omega$

Use ${\mu }_o=4\pi \times 10^{-7}H/m,ϵ{}_o=\frac{{10}^{-9}}{36\pi }F/m$

The radiation pattern of an antenna in spherical co-ordinates is given by

$F\left(\theta \right)={\cos }^2\theta ,0\le \theta \le \pi /2$

The directivity of the antenna is

If x[n] = (1/3)${}^{|n|}$ - (1/2)ⁿ u[n], then the region of convergence (ROC) of its z-transforms in the z-plane will be

In the sum of products function f (X, Y, Z) = ∑ (2, 3, 4, 5) , the prime implicants are

A system with transfer function G(s) shown below is excited by sin(ωt) then the steady state output of the system is zero at

$G\left(S\right)=\frac{\left(S^2+16\right)\left(S+2\right)}{\left(S+1\right)\left(S+3\right)\left(S+5\right)}$