Six people are seated around a circular table. There are at least two men and two women. There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is :

The expression $\frac{(x+y)-|x-y|}{2}$ is equal to :

Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of four shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes?

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of $$80$$ units, it takes $$100$$ cycles for failure. When the load is halved, it takes $$10000$$ cycles for failure. The load for which the failure will happen in $$5000$$ cycles is ________.