A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is

Let f be differentiable for all x. If f(1) = -2 and f'(x) $$ \ge $$ 2 for
x $$ \in \left[ {1,6} \right]$$, then

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?

The normal to the curve
$$x = a\left( {\cos \theta + \theta \sin \theta } \right),y = a\left( {\sin \theta - \theta \cos \theta } \right)$$ at any point
$$\theta\, '$$ is such that