If the tangent at the point (x₁, y₁) on the curve $$y = {x^3} + 3{x^2} + 5$$ passes through the origin, then (x₁, y₁) does NOT lie on the curve :

The sum of absolute maximum and absolute minimum values of the function $$f(x) = |2{x^2} + 3x - 2| + \sin x\cos x$$ in the interval [0, 1] is :

Let $$\lambda x - 2y = \mu $$ be a tangent to the hyperbola $${a^2}{x^2} - {y^2} = {b^2}$$. Then $${\left( {{\lambda \over a}} \right)^2} - {\left( {{\mu \over b}} \right)^2}$$ is equal to :