Which of the following elements constitutes a major impurity in pig iron?

$\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=$

$A$ weightless thread can bear a tension up to $3.7\,kg-wt$. $A$ stone of mass $500\,g$ is tied to it and revolved in a circular path of radius $4\,m$ in a vertical plane. If $g = 10\,ms^{-2}$,then the maximum angular velocity of the stone will be ......... $rad\,s^{-1}$

If $\cos x = \tan y$,$\cot y = \tan z$ and $\cot z = \tan x$,then $\sin x$ equals to

$A$ segment of wire vibrates with a fundamental frequency of $450 ~Hz$ under a tension of $9 ~kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 ~Hz$ is

The point on the line $4x - y - 2 = 0$ which is equidistant from the points $(-5, 6)$ and $(3, 2)$ is