There are 101 towns in a country. Some pairs of towns are connected by one-way roads, and there are exactly 40 roads going into and 40 roads leaving each town. Can you reach each town from any other, driving along at most three roads?⚡aYesbNocMay be

There are 30 towns in a country. Each of them is connected to every other by a single road. What is the maximum number of roads that can be closed in such a way that one can still reach each town from any other?

There are 100 towns in a country. Each of them is connected with every other town by a one-way road. It is possible to change the direction of traffic on one of the roads such that after this operation each town can still be reached from any other.⚡aYesbNocMay be

Consider all scenarios in which we have a city on a flat plane in which all roads are straight lines; the points at which two (or more) roads meet are called junctions; and we have two points A and B that are accessible from each other by road.In this question you have to determine whether the following statement is true or false.Among all possible routes between A and B, the shortest route goes through the fewest number of junctions.The following points may be helpful:Consider using a pen and paper to draw a few maps when thinking about this problem.The statement is about all possible scenarios, not just a particular city map that you may happen to draw. The statement is about all maps imaginable (with the above-mentioned properties). Obviously you cannot draw all possible maps, so you need to reason about this problem.The statement is true if you can convince yourself that it holds in all possible maps for all possible pairs of locations A and B. The statement is false if you can draw a map in which the statement does not hold.You can assume all distances are finite.Is the statement true or false?

State Government wants to connect the state road to the national highway from a town. There are 3 possible locations in the town A,B and C to connect to the National Highway whose locations are given by coordinates (3,8)(3,8),(5,7)(5,7),(6,9)(6,9) . The National Highway connects the 2 points (2,1)(2,1),(10,7)(10,7) and You, being the contractor, have the freedom to select any one of the 3 possible locations in the town.Hint   Always select the shortest path to construct the road.Note: 1 unit = 100 meterWhat is the minimum length of road in meter required to construct to connect to the National Highway?

The road connecting two towns, A and B, goes only uphill or downhill, i.e., there is no stretch of road that is level. Vijay’s car does a constant 40 kmph uphill and 80 kmph downhill. Find the distance between A and B, if it takes exactly nine hours for Vijay to make one round trip from A to B and back.