Among $K$,$Mg$,$Au$,and $Cu$,the one which is extracted by heating its ore in air is

If the acute angle between the lines $ax^2+2hxy+by^2=0$ is $\frac{\pi}{4}$,then $4h^2=$

$A$ body of mass $m_1 = 4 \ kg$ moves at $5 \hat{i} \ m/s$ and another body of mass $m_2 = 2 \ kg$ moves at $10 \hat{i} \ m/s$. The kinetic energy of the centre of mass is

The compound prepared by a substitution reaction of benzene is

The half-life of a radioactive nucleus is $50 \ days$. The time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and the time $t_1$ when $\frac{1}{3}$ of it has decayed is ......... $days$.

If $\tanh ^{-1} x = a \log \left(\frac{1+x}{1-x}\right)$,$|x| < 1$,then $a$ is equal to