AIEEE 2009 PYQ Mock Test

Three distinct points $A,B$ and $C$ are given such that the ratio of the distance of any one of them from the point $(1,0)$ to the distance from the point $(-1,0)$ is equal to $1/3$. Then the circumcentre of the triangle $ABC$ is at the point:

The remainder left out when $8^{2n}-(62{)}^{2n+1}$ is divided by $9$ is:

The ellipse $x^2+4y^2=4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point $(4,0)$. Then the equation of the ellipse is:

The sum to the infinity of the series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+\dots$ is:

The differential equation which represents the family of curves $y=c_1{e}^{c_{2}x}$, where $c_1$ and $c_2$ are arbitrary constants is: