Permutations an...

A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is agraph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any other point through a sequence of edges. The number of edges "e" in the graph must satisfy the condition

In the following questions, the numbers are arranged in a particular order or pattern. Choose the missing number from the given alternatives.3, 9, 17, 27, _ , 

There are $$6$$ boxes numbered $$1, 2 ....... 6$$. Each box is to be filled up either with a red or a green ball in such a way that at least $$1$$ box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

Rajdhani Express going from Bombay to Delhi stops at five inter-mediate stations, $$10$$ passengers enter the train during the journey with $$10$$ different ticket of two classes. The number of different sets of tickets they may have is

Seven girls are to dance in a circle. In how many different ways can they stand on the circumference of the circle?

Find the area of the triangle whose vertices are $$(3,2), \ (-2, -3)$$ and $$(2,3)$$.

Observe the given multiples of 37.
$${37\times3=111}$$
$${37\times 6 =222}$$
$${37\times9=333}$$
$${37\times12=444}$$-------------------------------
Find the product of $${37\times27}$$

The area of the triangle whose vertices are $$A(1,1), B(7, 3)$$ and $$C(12, 2)$$ is

Find the area of the triangle formed by joining the midpoints of the sides of the triangle whose vertices are $$(2,2)$$, $$(4,4)$$ and $$(2,6)$$.

Consider the points $$A( a, b + c)$$, $$B(b, c + a)$$, and $$C(c, a +b)$$ be the vertices of $$\bigtriangleup$$ABC. The area of $$\bigtriangleup$$ABC is: