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Consider the following statements: I. The smallest element in a max-heap is always at a leaf node II. The second largest element in a max-heap is always a child of the root node III. A max-heap can be constructed from a binary search tree in Θ(n) time IV. A binary search tree can be constructed from a max-heap in Θ(n) time Which of the above statements are TRUE?
A mouse is running at the speed of 15 m/min. After 12 min a cat saw him and started running to catch the mouse at the speed of 16 m/min. How much time will it take to catch the mouse if the cat can boost his speed by 1 m/min in every 5 min?
An operator delete(i) for a binary heap data structure is to be designed to delete the item in the i-th node. Assume that the heap is implemented in an array and i refers to the i-th index of the array. If the heap tree has depth d (number of edges on the path from the root to the farthest leaf), then what is the time complexity to re-fix the heap efficiently after the removal of the element? 
Four horses participated in a race, they started running simultaneously in circular track. They took 45 min, 40 min, 30 min and 20 min respectively to complete one round. They meet at starting point for the first time after how much time?
Tank can be filled by pipe A alone in 90 min and by pipe B alone in 60 min. There is a tap in bottom of tank which can empty the tank in 18 min. In a condition when tank is filled by pipe A and B for 20 min and then close and open the bottom tap. The time taken by tap to empty the tank is ….. min.
Three pipes A, B, C can individually fill a tank in 45 min., 60 min., and 30 min. respectively. If all the three pipes are simultaneously opened in an empty tank, such that pipes A and B are closed after 9 min. and 12 min. respectively, how much time will pipe C take alone to fill the remaining part of the tank?
Five clocks ring simultaneously at 5 pm. They ring at regular intervals of 12 min, 15 min, 20 min, 30 min, and 60 min respectively. The time when all five clocks ring together next is:
There are three athletes A, B and C at a same point. A starts running from a point at a speed of 50 m/min. After 5 minutes, B starts running towards A with a speed of 60 m/min. Determine at what speed C should start running to cross A and B together, if C starts running 5 minutes after B.
A water tanker can be filled by 2 pipes A & B separately in 16 min & 32 min respectively. The outlet of the tanker is partially open and it can empty the full tanker completely in 1 hour 4 min. Pipes A & B were opened simultaneously for 9 min to fill the tanker but the partially open outlet was not closed. After 9 min the pipes A & B were closed and the tanker then went to Mohan's house, 6 km away to deliver water. If the tanker moved at a constant speed of 36 km/hr, approximately what percentage of the tanker was full, when it reached Mohan's house? 
If we implement heap as min-heap, deleting root node (value 1)from the heap. What would be the value of root node after second iteration if leaf node (value 100) is chosen to replace the root at start.