A contractor plans to install two slides for the children to play in a park. For the children below the age of \(5\) years, she prefers to have a slide whose top is at a height of \(1.5\ m\), and is inclined at an angle of \(30^o\) to the ground, whereas for elder children, she wants to have a steep slide at a height of \(3\ m\), and inclined at an angle of \(60^o\) to the ground. What should be the length of the slide in each case?
Five cards the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random. (i) What is the probability that the card is the queen? (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?