Which of the following has the highest octane number?

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Four objects,each of mass $m$,are placed gently at the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be:

Let $A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$ and $10B = \begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{bmatrix}$. If $B$ is the inverse of matrix $A$,then $\alpha$ is:

Which one of the following equations represents the Freundlich adsorption isotherm?

Which of the following could act as a propellant for rockets?

$\sum_{k=1}^{2n+1} (-1)^{k-1} k^2$ is equal to