The area of the region

A = {(x, y) : 0 $$ \le $$ y $$ \le $$x |x| + 1  and  $$-$$1 $$ \le $$ x $$ \le $$1} in sq. units, is :

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is :

If both the roots of the quadratic equation x² $$-$$ mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :

The logical statement

[ $$ \sim $$ ( $$ \sim $$ p $$ \vee $$ q) $$ \vee $$ (p $$ \wedge $$ r)] $$ \wedge $$ ($$ \sim $$ q $$ \wedge $$ r) is equivalent to :