The greatest possible number of points of intersection of 8 straight lines and $4$ circles is $104$.

Solve:$\dfrac{2}{2}+\dfrac{3}{3}+\dfrac{4}{4}+$...... + upto $1000$ terms= ?

There are 6 equally spaced points A, B, C, D, E and F marked on a circle with radius R. How many convex pentagons of distinctly different areas can be drawn using these points advertises?

From 0 to 9 , four digited numbers can be formed such that
the digits  are in ascending order is

A point $(a, b)$ is called a good point if both $a$ and $b$ are integers. Number of good points on the curve $xy$ $=$ $225$ 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

Total number of ways of selecting two numbers from the set ${1,2,3,...90}$ so that their sum is divisible by $3$ is

If the letter of word $MOTHER$ are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word $MOTHER$

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:

The sides of a quadrilateral are all positive integers and three of them are $5, 10, 20.$ How many possible value are there for the fourth side?

In Hyderabad there are 5 routes to Begumpet from Kukatpally and 9 routes to Dilsukhnagar from Begumpet In how many ways can a person travel from Kukatpally to Dilsukhnagar via Begumpet?

Rajdhani Express going from Bombay to Delhi stops at five intermediate 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

There are 8 teams in a certain league and each team plays each of the other teams exactly once. If each game is played by 2 teams, what is the total number of games played? 

The number of $n$ digit numbers which consists of the digits $1$ & $2$ only if each digits is to be used atleast once, is equal to $510$  then $n$ is equal to

In a test there were n questions. In the test $\displaystyle 2^{n-i}$ students gave wrong answers to i questions where $\displaystyle i=1,2,3...,n$. If the total number of wrong answers given is 2047 then n is

The number of ways in which three numbers in A.P. can be seleced from the set of first n natural number if n is odd is

A college offers $7$ courses in the morning and $5$ courses in the evening. Find the number of ways a student can select exactly one course either in the morning or in the evening.

If $^nC _3=^nC _{13}$, then $^{20}C _n$ is.

The number of rectangles that can be obtained by joining four of the twelve vertices of a $12$ sided regular polygon is

The 30 members of a club decided to playa badminton singles tournament. Every time a member loses a game he is out of tournament. There is no ties. What is the minimum number of matches that must be played to determine the winner?

Each  section of soccer stadium has 44 rows with 22 sets in first row, 23 in the second row, 24 in the third row, and so on. How many seats are there in row 44.

The number of all three digit even number such that if $3$ is one of the digits, then next digit is $5$, is 

In an election, the number of candidates is one more than the number of members to be elected. A voter can cast any number of the vote but not more than the candidates to be elected. If a voter can cast his vote in $30$ ways, then the number of the candidates is