UPSC 2013 CDS 2 Math Paper

Remember:
The diagonals of a rhombus and a square are perpendicular to each other, but in a square, the diagonals are equal also.
So, if the diagonals of a parallelogram ABCD are perpendicular, then ABCD may be a rhombus.
Hence, statement 1 is correct
In statement 2, it is given that if the diagonals of a quadrilateral ABCD are equal and perpendicular, then ABCD is a square. This statement is wrong as the other possible figure can also be drawn, i.e.,