AIEEE 2012 PYQ Mock Test

Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y,Z)$ that can be formed such that $Y\subseteq X,Z\subseteq X$ and $Y\cap Z$ is empty, is:

An ellipse is drawn by taking a diameter of the circle $(x-1{)}^2+y^2=1$ as its semi-minor axis and a diameter of the circle $x^2+(y-2{)}^2=4$ as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is:

Consider the function $f(x)=|x-2|+|x-5|,x\in \mathbb{R}$.Statement 1: $f^{\prime }(4)=0$ Statement 2: $f$ is continuous in $[2,5]$, differentiable in $(2,5)$ and $f(2)=f(5)$.

A line is drawn through the point $(1,2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle $OPQ$, where $O$ is the origin. If the area of the triangle $OPQ$ is least, then the slope of the line $PQ$ is:

Let $ABCD$ be a parallelogram such that $\overrightarrow{AB}=\vec{q}$, $\overrightarrow{AD}=\vec{p}$ and $\angle BAD$ be an acute angle. If $\vec{r}$ is the vector that coincides with the altitude directed from the vertex $B$ to the side $AD$, then $\vec{r}$ is given by: