GATE EC 2015 Question Paper (01-Feb-2015) (Shift 1)

The Newton-Raphson method is used to solve the equation f(x) = x³ – 5x² + 6x – 8 = 0. Taking the initial guess as x = 5, the solution obtained at the end of the first iteration is ________.

A fair die with faces {1, 2, 3, 4, 5, 6} is thrown repeatedly till ‘3’ is observed for the first time. Let X denote the number of times the die is thrown. The expected value of X is ____.

Consider the differential equation

$\frac{d^{2}x\left(t\right)}{d{t}^2}+3\frac{dx\left(t\right)}{dt}+2x\left(t\right)=0.$

Given x(0) = 20 and x(1) = 10/e, where e = 2.718, the value of x(2) is _______.

A vector field D = 2ρ²a${}_{\rho }$ + z a${}_z$ exists inside a cylindrical region enclosed by the surfaces ρ = 1, z = 0 and z = 5. Let S be the surface bounding this cylindrical region. The surface integral of this field on $S\left(\int \int ◯{}_{S}D.ds\right)$ is _______.

In the circuit shown, the current I flowing through the 50 Ω resistor will be zero if the value of capacitor C (in μF) is ______.