If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :

Suppose A is any 3$$ \times $$ 3 non-singular matrix and ( A $$-$$ 3I) (A $$-$$ 5I) = O where I = I₃ and O = O₃. If $$\alpha $$A + $$\beta $$A^-1 = 4I, then $$\alpha $$ + $$\beta $$ is equal to :

The curve satifying the differeial equation, (x² $$-$$ y²) dx + 2xydy = 0 and passing through the point (1, 1) is :

The number of four letter words that can be formed using the letters of the word BARRACK is :