GATE IN 2014 Question Paper (02-Feb-2014) (Shift 2)

A scalar-valued function is defined as f (x) = x${}^T$ Ax + b${}^T$ x + c , where A is a symmetric positive definite matrix with dimension n × n ; b and x are vectors of dimension n × 1. The minimum value of f (x) will occur when x equals

The iteration step in order to solve for the cube roots of a given number Nusing the Newton- Raphson’s method is

For the matrix A satisfying the equation given below, the eigen values are

$[A]\left[\begin{array}{ccc}1& 2& 3\\ 7& 8& 9\\ 4& 5& 6\end{array}\right]=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$

In the circuit shown in the figure, initially the capacitor is uncharged. The switch ‘S’ is closed at 𝑡 = 0. Two milliseconds after the switch is closed, the current through the capacitor (in mA) is ___________.

A capacitor ‘C’ is to be connected across the terminals ‘A’ and ‘B’ as shown in the figure so that the power factor of the parallel combination becomes unity. The value of the capacitance required in μF is___________.