Find the point on the curve $y=x^{3}-11x+5$ at which the tangent is $y=x-11$.

The length of the subtangent at any point $(x_1, y_1)$ on the curve $y=5^x$ is

The area of the triangle formed by the coordinate axes and the normal to the curve $y = e^{2x} + x^2$ at the point $x = 0$.

If $y = 4x - 6$ is a tangent to the curve $y^2 = ax^4 + b$ at $(3, 6)$,then the values of $a$ and $b$ are:

If $ST$ and $SN$ are the lengths of the subtangent and the subnormal at the point $\theta = \frac{\pi}{2}$ on the curve $x = a(\theta + \sin \theta ), y = a(1 - \cos \theta ), a \neq 0$,then:

If $T$ is the length of the subtangent drawn at any point on the curve $3 y^2 = 4 x^3$ and $N$ is the length of the subnormal at the same point,then $(\beta T)^2 =$