AIEEE 2004 (Maths) Mock Test

A point on the parabola $y^2=18x$ at which the ordinate increases at twice the rate of the abscissa is

A function $y=f(x)$ has a second order derivative $f^{\prime \prime }(x)=6(x-1).$ If its graph passes through the point $(2,1)$ and at that point the tangent to the graph is $y=3x-5,$ then the function is

The normal to the curve $x=a(1+\cos \theta ),y=a\sin \theta$ at '$\theta$ ' always passes through the fixed point

If $2a+3b+6c=0,$ then at least one root of the equation $a{x}^2+bx+c=0$ lies in the interval

${\lim }_{n\to \infty }{\sum }_{r=1}^n\frac{1}{n}{e}^{\frac{r}{n}}$ is