Let a₁, a₂, a₃,......be an A.P. with a₆ = 2. Then the common difference of this A.P., which maximises the product a₁a₄a₅, is :

The negation of the Boolean expression ~ s $$ \vee $$ (~r $$ \wedge $$ s) is equivalent to :

If $${\cos ^{ - 1}}x - {\cos ^{ - 1}}{y \over 2} = \alpha $$,where –1 $$ \le $$ x $$ \le $$ 1, – 2 $$ \le $$ y $$ \le $$ 2, x $$ \le $$ $${y \over 2}$$ , then for all x, y, 4x² – 4xy cos $$\alpha $$ + y² is equal to :

If the tangent to the curve $$y = {x \over {{x^2} - 3}}$$ , $$x \in \rho ,\left( {x \ne \pm \sqrt 3 } \right)$$, at a point ($$\alpha $$, $$\beta $$) $$ \ne $$ (0, 0) on it is parallel to the line 2x + 6y – 11 = 0, then :