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 masses and radii of the earth and the moon are $M_1, R_1$ and $M_2, R_2$ respectively. Their centres are at a distance $d$ apart. The minimum speed with which a particle of mass $m$ should be projected from a point midway between the two centres so as to escape to infinity is:

Which one of the following halogens liberates oxygen,when passed through hot concentrated $KOH$ solution?

Which one of the following conditions correctly describes the manner of determining the sex?

An organic compound containing $C$ and $H$ has $92.3 \%$ of carbon. Its empirical formula is:

If $A+2 B=\begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix}$ and $2 A-B=\begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix}$,then $\operatorname{Tr}(A)-\operatorname{Tr}(B) = $