If $$\theta$$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then cos $$\theta$$ = _______

The ratio of boys to girls in a class is 7 to 3. Among the options below, an acceptable value for the total number of students in the class is :

There are multiple routes to reach from node 1 to node 2, as shown in the network. The cost of travel on an edge between two nodes is given in rupees. Nodes ‘a’, ‘b’, ‘c’, ‘d’, ‘e’, and ‘f’ are toll booths. The toll price at toll booths marked ‘a’ and ‘e’ is Rs.200, and is Rs.100 for the other toll booths. Which is the cheapest route from node 1 to node 2?

Ten freiends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friends had to pay Rs 150 more. The cost of the gift was Rs. ___________.