Electronics & Communication Engineering (EC) 2017 [Session 2]

The rank of the matrix \[ \begin{bmatrix} 1 & -1 & 0 & 0 & 0 \\ 0 & 0 & 1 & -1 & 0 \\ 0 & 1 & -1 & 0 & 0 \\ -1 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & -1 \end{bmatrix} \] is ______.

The general solution of the differential equation \[ \frac{d^2 y}{dx^2} + 2 \frac{dy}{dx} - 5y = 0 \] in terms of arbitrary constants \(K_1\) and \(K_2\) is

The smaller angle (in degrees) between the planes \(x + y + z = 1\) and \(2x - y + 2z = 0\) is ______.

The residues of a function \[ f(z) = \frac{1}{(z-4)(z+1)^3} \] are

In the circuit shown, V is a sinusoidal voltage source. The current I is in phase with voltage V. The ratio \[ \frac{\text{amplitude of voltage across the capacitor}}{\text{amplitude of voltage across the resistor}} \] is ______.

A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value 10 Ω, 5 Ω, 2 Ω are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is ______.