Let $$x = 2t$$, $$y = {{{t^2}} \over 3}$$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $$SA \bot BA$$, where A is any point on the conic. If k is the ordinate of the centroid of the $$\Delta$$SAB, then $$\mathop {\lim }\limits_{t \to 1} k$$ is equal to :

Let a circle C in complex plane pass through the points $${z_1} = 3 + 4i$$, $${z_2} = 4 + 3i$$ and $${z_3} = 5i$$. If $$z( \ne {z_1})$$ is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then $$arg(z)$$ is equal to :

The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is _____________.

Let $$\theta$$ be the angle between the vectors $$\overrightarrow a $$ and $$\overrightarrow b $$, where $$|\overrightarrow a | = 4,$$ $$|\overrightarrow b | = 3$$ and $$\theta \in \left( {{\pi \over 4},{\pi \over 3}} \right)$$. Then $${\left| {\left( {\overrightarrow a - \overrightarrow b } \right) \times \left( {\overrightarrow a + \overrightarrow b } \right)} \right|^2} + 4{\left( {\overrightarrow a \,.\,\overrightarrow b } \right)^2}$$ is equal to __________.