If the angles $\mathrm{A}, \mathrm{B}$ and C of a triangle are in A.P. and if $\mathrm{a}, \mathrm{b}$ and c denote the length of the sides opposite to $\mathrm{A}, \mathrm{B}$ and C respectively, then the value of $\frac{a}{b} \sin 2 B+\frac{b}{a} \sin 2 A$ is

If the pair of lines $3 x^2-5 x y+\mathrm{p} y^2=0$ and $6 x^2-x y-5 y^2=0$ have one line common, then $\mathrm{p}=$

The number of ways in which 6 boys and 4 girls can be seated around a round table such that 2 special boys and a special girl never sit together is

The differential equation representing the family of parabolas having vertex at the origin and axis along the positive Y -axis is