If $\cos (x-y), \cos x, \cos (x+y)$ are three distinct numbers which are in harmonic progression and $\cos x \neq \cos y$,then $1+\cos y$ is equal to

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:

Which one of the following is a slime mould?

$A$ heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $3: 1$. The ratio of radii of the fragments is

In Van der Waals equation of state for a non-ideal gas,the term that accounts for intermolecular forces is

Which of the following pair of ores cannot be converted into corresponding metals by pyrometallurgy?