GATE EC 2014 Question Paper (15-Feb-2014) (Shift 2)

The system of linear equations

$\left(\begin{array}{ccc}2& 1& 3\\ 3& 0& 1\\ 1& 2& 5\end{array}\right)\left(\begin{array}{c}a\\ b\\ c\end{array}\right)=\left(\begin{array}{c}5\\ -4\\ 14\end{array}\right)$ has

The real part of an analytic function f(z) where z = x + iy is given by e${}^{-y}$ cos (x). The imaginary part of f(z) is

The maximum value of the determinant among all 2 × 2 real symmetric matrices with trace 24 is _______.

If $\vec{r}=x{\hat{a}}_x+y{\hat{a}}_y+z{\hat{a}}_z$ and $\left|\vec{r}\right|=r$, then div (r²∇ (In r)) = ______

A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of the current is half the value at resonance. If the values of L, C and R are 1 H, 1 F, and 1 Ω, respectively, the operating angular frequency (in rad/s) is _______