If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, then the area of the triangle is maximum when angle between them is:

The maximum value of $f(x)=\dfrac{1}{3(x^2-x+1)}$ is :

The rate of change of area of a circle with respect to its circumference when radius in 6 cm, is

For the function $f(x) = 2x^3 - 3x^2 - 12x + 5$, the difference of maximum and minimum value of $f(x)$ is

The equation of the tangent to the curve $y = \frac{(x - 3)}{(x - 1)(x - 2)}$ at the point, where it cuts x-axis is:

If the interval in which the function f(x) = $\frac{x}{x^2+1}$ is strictly increasing is (-a, a), then a is equal to

If $f(x) = a \log_e|x| + bx^2 + x$ has critical points at $x = -2$ and $x = 1$, then