Syngamy means:

For $k=1, 2, 3$,the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$,$P(B_2)=\frac{1}{3}$,and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn,then the probability that it has come from box $B_2$ is:

$\frac{d}{d x}\left[a \tan ^{-1} x+b \log \left(\frac{x-1}{x+1}\right)\right]=\frac{1}{x^4-1}$
$\Rightarrow a-2 b$ is equal to

Which metal is protected by a layer of its own oxide?

The major product of the following reaction is:

$A$ $Ge$ specimen is doped with $Al$. The concentration of acceptor atoms is $\sim 10^{21} \text{ atoms}/m^3$. Given that the intrinsic concentration of electron-hole pairs is $\sim 10^{19} /m^3$,the concentration of electrons in the specimen is: