If $\frac{e^x + 2}{(e^x - 1)(2e^x - 3)} = -\frac{3}{e^x - 1} + \frac{B}{2e^x - 3}$,then $B = $

If the point $P(\alpha, \beta, \gamma)$ lies on the plane $2x+y+z=1$ and $[\alpha \ \beta \ \gamma] \begin{bmatrix} 1 & 9 & 1 \\ 8 & 2 & 1 \\ 7 & 3 & 1 \end{bmatrix} = [0 \ 0 \ 0]$,then $\alpha^2+\beta^2+\gamma^2=$

$\int_{-2}^2 |[x]| \, dx$ is equal to

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then

If $A$ and $B$ are two independent events such that $P(B)=\frac{2}{7}$ and $P(A \cup B^c)=0.8$, then $P(A)$ is equal to:

The chlorination of ethane is an example of which of the following types of reactions?