If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$,then $P(\bar{A})+P(\bar{B})$ is equal to:

The major product in the following reaction is:

The major product of the following reaction is :

$A$ solid cube having certain fixed melting and boiling points takes heat from some source. The variation of temperature $\theta$ of the cube with the heat supplied $Q$ is shown in the adjoining graph. The portion $BC$ of the graph represents the conversion of

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix $A$ and $|A| = 4$,then $\alpha$ is equal to:

$(\vec{a} \times \vec{b}) \times [(\vec{b} \times \vec{c}) \times (\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a})]$ is