The slope of the tangent to the curve $x = at^2$, $y = 2at$ at 't' is :

The absolute maximum value of $y = x^3 - 3x + 2$, $0 \leq x \leq 2$, is

The maximum value of the function $f(x)=\sin x(1+\cos x)$ in the internal $[0,\pi]$ is

Angle between tangents to the curve $y = x^2 - 5x + 6$ at the points (2, 0) and (3, 0) 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:

Let $f(x)$ be a function defined by $f(x) = 2x^3 - 24x + 107$. If $\alpha$ and $\beta$ are the maximum and minimum values respectively in the interval $[1,3]$, then $\alpha-\beta$ is equal to:

The function $f(x)=\log_e(\cos x)$ increases on which of the following intervals for $x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$ ?