The volume of the tetrahedron formed by the coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is $3$. Then the volume of the parallelepiped formed by the coterminous edges $\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}$ is

If the radius of a nucleus with mass number $125$ is $1.5 \text{ fermi}$,then the radius of a nucleus with mass number $64$ is: (in $\text{ fermi}$)

Let $\vec{V} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{W} = \hat{i} + 3\hat{k}$. If $\vec{U}$ is a unit vector,then the maximum value of the scalar triple product $[\vec{U} \, \vec{V} \, \vec{W}]$ is:

The eccentricity of the conic $\frac{5}{r}=2+3 \cos \theta+4 \sin \theta$ is

The process of the isolation of a metal by dissolving the ore in a suitable chemical reagent followed by precipitation of the metal by a more electropositive metal is called:

Two workers $A$ and $B$ are engaged to do a piece of work. Working alone,$A$ takes $8 \text{ h}$ more to complete the work than if both worked together. On the other hand,working alone,$B$ would need $4 \frac{1}{2} \text{ h}$ more to complete the work than if both worked together. How much time would they take to complete the job working together (in $\text{ h}$)?