If the number of integral terms in the expansion
of (3^1/2 + 5^1/8)ⁿ is exactly 33, then the least value of n is :

The solution curve of the differential equation,

(1 + e^-x)(1 + y²)$${{dy} \over {dx}}$$ = y²,

which passes through the point (0, 1), 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?

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 :