The number of points,having both coordinates as integers,that lie in the interior of the triangle with vertices $(0,0)$,$(0,41)$,and $(41,0)$ is:

If $ad-bc \neq 0$,then the area (in sq. units) of the parallelogram formed by the lines $ax+by+2=0$,$ax+by+5=0$,$cx+dy+3=0$ and $cx+dy+7=0$ is

In a quadrilateral $ABCD$,which is not a trapezium,it is known that $\angle DAB = \angle ABC = 60^{\circ}$. Moreover,$\angle CAB = \angle CBD$. Then,

What is the ratio of the area of $\triangle PQS$ to the area of $\triangle PQR$?

If the points $(a, b)$,$(a', b')$ and $(a - a', b - b')$ are collinear,then:

In a $\triangle ABC$ with $\angle A < \angle B < \angle C$,points $D, E, F$ are on the interior of segments $BC, CA, AB$ respectively. Which of the following triangles cannot be similar to $\triangle ABC$?