The area (in sq. units) of the region

{ (x, y) : 0 $$ \le $$ y $$ \le $$ x² + 1, 0 $$ \le $$ y $$ \le $$ x + 1,

$${1 \over 2}$$ $$ \le $$ x $$ \le $$ 2 } is :

A hyperbola having the transverse axis of length $$\sqrt 2 $$ has the same foci as that of the ellipse 3x² + 4y² = 12, then this hyperbola does not pass through which of the following points?

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is :

The lines
$$\overrightarrow r = \left( {\widehat i - \widehat j} \right) + l\left( {2\widehat i + \widehat k} \right)$$ and
$$\overrightarrow r = \left( {2\widehat i - \widehat j} \right) + m\left( {\widehat i + \widehat j + \widehat k} \right)$$