Let f : R $$ \to $$ R be defined by f(x) = $${x \over {1 + {x^2}}},x \in R$$.   Then the range of f is :

The area (in sq. units) of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is :

Let a₁, a₂, . . . . . ., a₁₀ be a G.P.    If $${{{a_3}} \over {{a_1}}} = 25,$$ then $${{{a_9}} \over {{a_5}}}$$ equals

Let f_k(x) = $${1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ for k = 1, 2, 3, ... Then for all x $$ \in $$ R, the value of f₄(x) $$-$$ f₆(x) is equal to