Permutations an...

Six points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points of intersection is equal to

A parallellogram is cut by two sets of m lines parallel to its sides. The number of parallelograms thus formed is

The greatest possible number of points of intersection of 8 straight lines and 4 circle is

Out of 10 points in a plane 6 are in a straight line. The number of triangles formed by joining these points are

How many numbers lying between 10 and 1000 can be formed from the digits 1,2,3,4,5,6,7,8,9 (repetition is allowed)

If ⁵⁶P_r+6 : ⁵⁴P_r+3 = 30800 : 1, then r =

The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is

In a certain test there are n questions. In the test 2^{n - i} students gave wrong answers to at least i questions, where i = 1,2,......n.If the total number of wrong answers given is 2047 , then n is equal to

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is