Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives :

Let $$a \in \left( {0,{\pi \over 2}} \right)$$ be fixed. If the integral

$$\int {{{\tan x + \tan \alpha } \over {\tan x - \tan \alpha }}} dx$$ = A(x) cos 2$$\alpha $$ + B(x) sin 2$$\alpha $$ + C, where C is a

constant of integration, then the functions A(x) and B(x) are respectively :

The general solution of the differential equation (y² – x³)dx – xydy = 0 (x $$ \ne $$ 0) is : (where c is a constant of integration)

The equation of common tangent to the curves y² = 16x and xy = –4, is :