The least value of the expression $$2\,\,{\log _{10}}\,x\, - \,{\log _x}(0.01)$$ for x > 1, is

For what values of $$m,$$ does the system of equations $$$\matrix{ {3x + my = m} \cr {2x - 5y = 20} \cr } $$$

has solution satisfying the conditions $$x > 0,\,y > 0.$$

If $$\,({x^2} + px + 1)\,$$ is a factor of $$(a{x^3} + bx + c)$$, then

A straight line $$L$$ is perpendicular to the line $$5x - y = 1.$$ The area of the triangle formed by the line $$L$$ and the coordinate axes is $$5$$. Find the equation of the Line $$L$$.