The elevation of boiling point of 0.10 m aqueous CrCl₃.xNH₃ solution is two times that of 0.05 m aqueous CaCl₂ solution. The value of x is ______.

[Assume 100% ionisation of the complex and CaCl₂, coordination number of Cr as 6, and that all NH₃ molecules are present inside the coordination sphere]

A spherical balloon of radius 3 cm containing helium gas has
a pressure of 48 $$ \times $$ 10^–3 bar. At the same temperature, the pressure, of a spherical balloon of radius 12 cm containing the
same amount of gas will be ________ $$ \times $$ 10^–6 bar.

The region represented by
{z = x + iy $$ \in $$ C : |z| – Re(z) $$ \le $$ 1} is also given by the
inequality : {z = x + iy $$ \in $$ C : |z| – Re(z) $$ \le $$ 1}

The general solution of the differential equation

$$\sqrt {1 + {x^2} + {y^2} + {x^2}{y^2}} $$ + xy$${{dy} \over {dx}}$$ = 0 is :

(where C is a constant of integration)