If $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 1 & 2 & 1 \cr 3 & 2 & 6 \cr } } \right]$$ and A$$_{ij}$$ are cofactors of the elements a$$_{ij}$$ of A, then $${a_{11}}{A_{11}} + {a_{12}}{A_{12}} + {a_{13}}{A_{13}}$$ is equal to

The general solution of the differential equation $$x+y \frac{d y}{d x}=\sec \left(x^2+y^2\right)$$ is

$$\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} + 5x - 7} - x} \right) = $$

The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is