For the system of linear equations:

$$x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k \in R$$,

consider the following statements :

(A) The system has unique solution if $$k \ne 2,k \ne - 2$$.

(B) The system has unique solution if k = $$-$$2

(C) The system has unique solution if k = 2

(D) The system has no solution if k = 2

(E) The system has infinite number of solutions if k $$ \ne $$ $$-$$2.

Which of the following statements are correct?

The system of linear equations
3x - 2y - kz = 10
2x - 4y - 2z = 6
x+2y - z = 5m
is inconsistent if :

Let $$\theta = {\pi \over 5}$$ and $$A = \left[ {\matrix{ {\cos \theta } & {\sin \theta } \cr { - \sin \theta } & {\cos \theta } \cr } } \right]$$.

If B = A + A⁴ , then det (B) :

Let m and M be respectively the minimum and maximum values of

$$\left| {\matrix{ {{{\cos }^2}x} & {1 + {{\sin }^2}x} & {\sin 2x} \cr {1 + {{\cos }^2}x} & {{{\sin }^2}x} & {\sin 2x} \cr {{{\cos }^2}x} & {{{\sin }^2}x} & {1 + \sin 2x} \cr } } \right|$$

Then the ordered pair (m, M) is equal to :