A square, of each side 2, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30^o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :

For two 3 × 3 matrices A and B, let A + B = 2B^T and 3A + 2B = I₃, where B^T is the transpose of B and I₃ is 3 × 3 identity matrix. Then :

The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60^o. If the area of the quadrilateral is $$4\sqrt 3 $$, then the perimeter of the quadrilateral is :

If the vector $$\overrightarrow b = 3\widehat j + 4\widehat k$$ is written as the sum of a vector $$\overrightarrow {{b_1}} ,$$ paralel to $$\overrightarrow a = \widehat i + \widehat j$$ and a vector $$\overrightarrow {{b_2}} ,$$ perpendicular to $$\overrightarrow a ,$$ then $$\overrightarrow {{b_1}} \times \overrightarrow {{b_2}} $$ is equal to :