Monthly Archives: August 2017

Answer to STEP I 2008 Q.13

Three married couples sit down at a round table at which there are six chairs. All of the possible seating arrangements of the six people are equally likely.

(i) Show that the probability that each husband sits next to his wife is 2/15

(ii) Find the probability that exactly two husbands sit next to their wives.

(iii) Find the probability that no husband sits next to his wife. Continue reading

Answer to STEP III 2007 Q.9

III/2007/9 – Two small beads, A and B, each of mass m, are threaded on a smooth horizontal circular hoop of radius a and centre O. The angle θ is the acute angle determined by 2 θ = AOB.

The beads are connected by a light straight spring. The energy stored in the spring is
mk^2a^2(\theta - \alpha)^2
where k and α are constants satisfying k > 0 and \frac{\pi}{4} < \alpha < \frac{\pi}{2}
The spring is held in compression with θ = β and then released. Find the period of oscillations in the two cases that arise according to the value of θ and state the value of β for which oscillations do not occur. Continue reading