GATE EE 2016 Question Paper (07-Feb-2016) (Shift 2)

Consider the function $f\left(z\right)=z+z^{\ast }$ where is a complex variable and denotes its complex conjugate. Which one of the following is TRUE?

A 3 × 3 matrix is such that, $P^3=P$. Then the eigenvalues of $P$ are

The solution of the differential equation, for $t>0$, $y^{\prime \prime }\left(t\right)+2y^{\prime }\left(t\right)+y\left(t\right)=0$ with initial conditions $y^{\prime }\left(0\right)=1andy\left(0\right)=0$, is $u\left(t\right)$ denotes the unit step functions).

The value of the line integral

_c^ ≤ft( 2xy^2dx + 2x^2 y dy + dz )

along a path joining the origin and the point (1,1,1) is

Let f(x) be a real, periodic function satisfying f(-x) = -f(x). The general form of its Fourier series representation would be