The number of possible enantiomeric pairs that can be produced during mono-chlorination of $2$-methylbutane is

The eccentricity of the conic $36x^2 + 144y^2 - 36x - 96y - 119 = 0$ is

Two bodies of mass $4 ~kg$ and $5 ~kg$ are moving along east and north directions with velocities $5 ~m/s$ and $3 ~m/s$ respectively. The magnitude of the velocity of the centre of mass of the system is

Active transport of ions by the cell requires

Which of the following does not reduce Benedict's solution?

Let $\overline{a}=2 \hat{i}+\hat{j}-2 \hat{k}$ and $\overline{b}=\hat{i}+\hat{j}$. Let $\overline{c}$ be a vector such that $|\overline{c}-\overline{a}|=3$,$|(\overline{a} \times \overline{b}) \times \overline{c}|=3$,and the angle between $\overline{c}$ and $\overline{a} \times \overline{b}$ is $30^{\circ}$. Then $\overline{a} \cdot \overline{c}$ is equal to