Sequences and S...

The sum of the value of the digits at the tens place of all the numbers formed with the help of $$3, 4, 5, 6$$ taken all at a time is

The points $$A (2, 9), B (a, 5)$$ and $$C (5, 5) $$ are the vertices of a triangle $$ABC$$ right angled at $$B$$. Find the values of  $$a$$ and hence the area of $$\Delta $$ $$ABC$$.

The area of triangle ABC (in sq. units) is :

Given:   $$\dfrac {20!}{18!}=380$$

Area of the triangle formed by the points P(-1.5, 3), Q(6, -2) and R(-3, 4) is 0.

The numbers 1, 2, ..., 100 are arranged in the squares of an table in the following way: the numbers 1, ... , 10 are in the bottom row in increasing order,  numbers 11, ... ,20 are in the next row in increasing order, and so on. One can choose any number and two of its neighbors in two opposite directions (horizontal, vertical, or diagonal). Then either the number is increased by 2 and its neighbors are decreased by 1, or the number is decreased by 2 and its neighbors are increased by 1. After several such operations the table again contains all the numbers 1, 2, ... , 100. Prove that they are in the original order.

Unit digit in the number $$(12357)^{655}$$ is 

In a class of 80 students it is found that 40 students like Tajmahal and 50 students like Charminar and 18 like both. Then the number of students who do not like neither are.

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

Out of nine cells of a square, one cell is left blank and in the rest of the cells, numbers are written follow some rule. Get the rule and find out the proper option for the blank cell