GATE EE 2015 Question Paper (07-Feb-2015) (Shift 1)

The maximum value of “$a$ ” such that the matrix ≤ft( {*20c - 3&0& - 2\\ 1& - 1&0\\ 0&a& - 2 } ) has three linear independent real eigenvectors is

A solution of the ordinary differential equation $\frac{d^{2}y}{d{t}^2}+5\frac{dy}{dt}+6y=0$ is such that $y\left(0\right)=2$ and $y\left(1\right)=-\frac{1-3e}{e^3}$. The value of $\frac{dy}{dt}\left(0\right)$ is ______.

The signum function is given by

sgn≤ft( x ) = ≤ft\{ {*20c x/≤ft| x |;x ≠ 0\\ 0;x = 0 } .

The Fourier series expansion of $sgn\left(cos\left(t\right)\right)$ has

Two players, $A$ and $B$, alternately keep rolling a fair dice. The person to get a six first wins the game. Given that player $A$ starts the game, the probability that $A$ wins the game is

An unbalanced DC Wheatstone bridge is shown in the figure. At what value of P will the magnitude of Vₒ be maximum?