(I) All sides of a parallelogram are of different length. This statement is incorrect because a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. (II) All sides of a rhombus are equal. This statement is correct. A rhombus is a flat shape with 4 equal straight sides and its diagonals are perpendicular to each other. (III) Rectangle is not a parallelogram. This statement is incorrect because a rectangle is considered a special case of a parallelogram because a parallelogram is a quadrilateral with 2 pairs of opposite, equal and parallel sides. A rectangle is a quadrilateral with 2 pairs of opposite, equal and parallel sides, but also forms right angles between adjacent sides. (IV) A parallelogram has no obtuse angle. This statement is incorrect because as adjacent angles of a parallelogram are supplementary and opposite angles are equal, if one angle is obtuse, adjacent angle would be acute and opposite angle would be obtuse. Hence, a parallelogram can have no more than two obtuse angles. Option (2) is correct.
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