A road network as shown in the figure connect four cites. In how many ways can you start from any city (say A) and come back to it without travelling on the same road more than once ?

There are five cities A, B, C, D, E on a certain island. Each city is connected to every other city by road. In how many ways can a person starting from city A come back to A after visiting some cities without visiting a city more than once and without taking the same road more than once ? (The order in which he visits the cities also matters. e.g., the routes A rarr B rarr C A and A rarr C rarr B rarr A are different).

How many numbers of 5 digits can be formed with the digit 0,2,5,6,7 without taking any of these digit more than once.

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?

A car is travelling on a road. The maximum velocity the car can attain is 24 ms^-1 and the maximum deceleration is 4 ms^-2. If car starts from rest and comes to rest after travelling 1032m in the shortest time of 56 s, the maximum acceleration that the car can attain is

How many even numbers of four digits can be formed with the digits 0,1,2,3,4,5 and 6 no digit being used more than once?

Every moring, Grishma walks from her house to the bus stop , the placement of the house and bus stop are shown in the diagram to the right. She always travels exactly nine blocks from her house to the bus, but she varies the route she takes every day. (One sample route is shown.) How many days can Grishma walk from her house to the bus stop without repeating the same route?

A bag contains four one-rupee coins, two twenty-five paisa coins, and five ten-paisa coins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag? (Consider coins of the same denominations to be identical.) a. 71 b. 72 c. 73 d. 80

A man has 8children to take them to a zoo. He takes thre of them at a time to the zoo as often as he can without taking the same 3 children together more than once. How many times will he have to go to the zoo? How many times a particular child will to to the zoo?

A small ring of mass m is constrained to slide along a horizontal wire fixed between two rigid supports. The ring is connected to a particle of same mass by an ideal string & the whole system is released from rest as shown in the figure. If the coefficient of friction between ring A and wire is (3)/(5) , the ring will start sliding when the connecting string will make an angle theta with the vertical, then theta will be (particle is free to move and ring can slide only)

A van is standing on a frictionless portion of a horizontal road. To start the engine, the vehicle must be set in motion in theforward direction. How can the persons sitting inside the van do it without coming out and pushing from behind?