AIEEE 2005 Maths Question Paper Mock Test

If a vertex of a triangle is $(1,1)$ and the mid-points of two sides through this vertex are $(-1,2)$ and $(3,2)$, then the centroid of the triangle is:

If the circles $x^2+y^2+2ax+cy+a=0$ and $x^2+y^2-3ax+dy-1=0$ intersect in two distinct points $P$ and $Q$, then the line $5x+by-a=0$ passes through $P$ and $Q$ for:

A circle touches the x-axis and also touches the circle with centre at $(0,3)$ and radius $2$. The locus of the centre of the circle is:

If a circle passes through the point $(a,b)$ and cuts the circle $x^2+y^2=p^2$ orthogonally, then the equation of the locus of its centre is:

An ellipse has $OB$ as semi minor axis, $F$ and $F^{\prime }$ its foci and the angle $\angle FB{F}^{\prime }$ is a right angle. Then the eccentricity of the ellipse is: