If the relation between the subnormal $SN$ and the subtangent $ST$ at any point $S$ on the curve $by^2 = (x + a)^3$ is $p(SN) = q(ST)^2$,then what is the value of $p/q$?

If the tangent at a point $P$ on the curve $y=4x^4+x$ is perpendicular to the tangent to the same curve at $(0,0)$,then the point $P$ is

If the slope of the tangent to the curve $y = x^3$ at a point is equal to the $y$-coordinate of that point,then the point is:

The line joining the points $(0,3)$ and $(5,-2)$ is a tangent to the curve $y=\frac{c}{x+1}$. Then,$c=$

$f(x)$ is a continuous function on $\mathbb{R}$ and $y=f(x)$ is a curve. If $(\alpha, \beta)$ is a point such that $\beta=f(\alpha)$ and $p\alpha+m\beta+n=0$ $(p \neq 0, m \neq 0)$,then which one of the following is true?

If $\theta$ denotes the acute angle between the curves $y=10-x^2$ and $y=2+x^2$,at a point of the intersection,then $|\tan \theta|$ is equal to