If $$A = \left[ {\matrix{ {\cos \theta } & { - \sin \theta } \cr {\sin \theta } & {\cos \theta } \cr } } \right]$$, then the matrix A^–50 when $$\theta $$ = $$\pi \over 12$$, is equal to :

For any $$\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)$$, the expression

$$3{(\cos \theta - \sin \theta )^4}$$$$ + 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta $$

equals :

The system of linear equations
x + y + z = 2
2x + 3y + 2z = 5
2x + 3y + (a² – 1) z = a + 1 then

The maximum volume (in cu.m) of the right circular cone having slant height 3 m is :