If for x $$ \ge $$ 0, y = y(x) is the solution of the differential equation
(x + 1)dy = ((x + 1)² + y – 3)dx, y(2) = 0, then y(3) is equal to _______.

If e₁ and e₂ are the eccentricities of the ellipse, $${{{x^2}} \over {18}} + {{{y^2}} \over 4} = 1$$ and the hyperbola, $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ respectively and (e₁, e₂) is a point on the ellipse, 15x² + 3y² = k, then k is equal to :

Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm^–2
between A and B where the area of cross section
are 40 cm² and 20 cm², respectively. Find the
rate of flow of water through the tube.
(density of water = 1000 kgm^–3)

An electric dipole of moment
$$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} $$ C.m is
at the origin (0, 0, 0). The electric field due to this dipole at
$$\overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k$$ (note that $$\overrightarrow r .\overrightarrow p = 0$$ ) is parallel to :