If both the roots of the quadratic equation x² $$-$$ mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :

The logical statement

[ $$ \sim $$ ( $$ \sim $$ p $$ \vee $$ q) $$ \vee $$ (p $$ \wedge $$ r)] $$ \wedge $$ ($$ \sim $$ q $$ \wedge $$ r) is equivalent to :

Let a, b and c be the 7^th, 11^th and 13^th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then $${a \over c}$$ equal to :

The equation of the plane containing the straight line $${x \over 2} = {y \over 3} = {z \over 4}$$ and perpendicular to the plane containing the straight lines $${x \over 3} = {y \over 4} = {z \over 2}$$ and $${x \over 4} = {y \over 2} = {z \over 3}$$ is :