The parabola with directrix $x+2y-1=0$ and focus $(1,0)$ is

If $\vec{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\vec b = \frac{1}{7}(2 \hat{i} + 3 \hat{j} - 6 \hat{k})$,then the value of $(2\vec a - \vec b) \cdot [(\vec a \times \vec b) \times (\vec a + 2\vec b)]$ is

$A$ particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10\, cm$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, N m^2/kg^2$).

$A$ spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ (where $\rho_2 < \rho_1$). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$,i.e.,$F_{viscous} = -kv^2$ (where $k > 0$). Then the terminal speed of the ball is:

The solubility of silver bromide in hypo solution is due to the formation of:

Which of the following secretes interferons?