AIEEE 2008 PYQ Mock Test

$AB$ is a vertical pole with $B$ at the ground level and $A$ at the top. A man finds that the angle of elevation of the point $A$ from a certain point $C$ on the ground is $60^{\circ }$. He moves away from the pole along the line $BC$ to a point $D$ such that $CD=7\text{m}$. From $D$, the angle of elevation of the point $A$ is $45^{\circ }$. Then the height of the pole is:

It is given that the events $A$ and $B$ are such that $P(A)=\frac{1}{4}$, $P(B|A)=\frac{1}{2}$ and $P(A|B)=\frac{2}{3}$. Then $P(B)$ is:

A die is thrown. Let $A$ be the event that the number obtained is greater than $3$. Let $B$ be the event that the number obtained is less than $5$. Then $P(A\cup B)$ is:

A focus of an ellipse is at the origin. The directrix is the line $x=4$ and the eccentricity is $1/2$. Then the length of the semi-major axis is:

A parabola has the origin as its focus and the line $x=2$ as the directrix. Then the vertex of the parabola is at: