Perimeter of a triangle with integral sides is $17$ units. Number of such triangles is:

A cone is made from a circular sector of radius $2$ units. If total surface area of cone (including base) is $\pi \mathrm{sq}.\mathrm{unit}$, find the area of sector ( in $\mathrm{sq}.\mathrm{unit}$ )

At end $A$ of a chord $AB$ of a circle, tangent is drawn, a point $D$ is taken on tangent such that $\angle ABE=\angle ABD,$ where $E$ is some point on the circumference, if $BE=3$ units and $BD=6$ units. Find $AB$.

Two perpendicular chords $AB$ and $CD$ of a circle intersect at $O,$ (inside the circle) $AB$ is bisected at $O.$ If $AO=4$ units and $OD=6$ units. Find circumradius of $\Delta ACO$.

In the given figure. Find radius of smaller circle.

A frustum is made by joining edges of following figure. The volume of the frustum thus formed will be:
$\left(\pi =\frac{22}{7}\right)$