GATE EE 2014 Question Paper (01-Mar-2014) (Shift 2)

Given a system of equations

$x+2y+2z=b_1,5x+y+3z=b_2$

Which of the following is true about solutions?

Let $f\left(x\right)=x{e}^{-x}$. The maximum value of the function in the interval ($0,\infty$) is

The solution for the differential equation

$\frac{d^{2}x}{d{t}^2}=-9x$

With initial conditions $x\left(0\right)=1and\frac{dx}{dt}{|}_{t=0}=1$, is

Let $X\left(s\right)=\frac{3s+5}{s^2+10s+21}$ be the Laplace Transform of a signal x(t). Then x(0⁺) is

Let $S$ be the set of points in the complex plane corresponding to the unit circle.$(i.e.,S=\left\{Z:\left|Z\right|=1\right\})$.

Consider the function.$f\left(z\right)=z{z}^{\ast },$ where$z^{\ast }$ denotes the complex conjugate of $z$. The $f\left(z\right)$ maps $S$ to which one the following in the complex plane?