Let f : [0,1] $$ \to $$ R be such that f(xy) = f(x).f(y), for all x, y $$ \in $$ [0, 1], and f(0) $$ \ne $$ 0. If y = y(x) satiesfies the differential equation, $${{dy} \over {dx}}$$ = f(x) with y(0) = 1, then y$$\left( {{1 \over 4}} \right)$$ + y$$\left( {{3 \over 4}} \right)$$ is equal to :

The coefficient of t⁴ in the expansion of $${\left( {{{1 - {t^6}} \over {1 - t}}} \right)^3}$$ is :

Let z₀ be a root of the quadratic equation, x² + x + 1 = 0, If z = 3 + 6iz$$_0^{81}$$ $$-$$ 3iz$$_0^{93}$$, then arg z is equal to :

If the system of linear equations
x $$-$$ 4y + 7z = g
       3y $$-$$ 5z = h
$$-$$2x + 5y $$-$$ 9z = k
is consistent, then :