The number of 4-digit numbers that can be made with the digits 1,2, 3, 4 and 5 in which at least two digits are identical, is
The number of words that can be made by rearranging the letters of the word APURBA so that vowels and consonants alternate is
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The number of words that can be made by writing down the letters of the word CALCULATE such that each word starts and ends with a consonant, is
The number of numbers of 9 different non-zero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is
In the decimal system of numeration the number of 6-digit numbers in which the digit in any place is greater than the- digit to the left of it is
The number of 5 digit numbers in which no two consecutive digits are identical is
The number of 6-digit numbers in which the sum of the digits is divisible by 5 is
The sum of all the numbers of four different digits that can be made by using the digits 0, 1, 2 and 3 is
A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not lake the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is
ABCD is a convex quadrilateral, 3, 4, 5 and 6 points are marked on the sides AB, BC, CD and DA respectively. The number of triangles with vertices on different sides is
There are 10 points in a plane of which no three points are collinear and 4 points are concyclic. The number of different circles that can be drawn through at least 3 points of these points is
In a polygon the number of diagonals is 54. The number of sides of the polygon is
In a polygon no three diagonals are concurrent, if the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is
n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is
The number of triangles that can be formed with 10 points as vertices, n of them being collinear, is 110. Then n is
There are three coplanar parallel lines. If any p points are taken on each of the lines, the maximum number of triangles with vertices at these points is
Two teams are to play a series of 5 matches between them. A match ends in a win or loss or draw for a term. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain n people, where n is
A bag contains 3 black, 4 white and 2 red balls, all the balls being different. The number of selections of at most 6 balls cotaining balls of all the colours is
In an examination of 9 papers a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is
The number of 5-digit numbers that can be made using the digits 1 and 2 and in which at least one digit is different, is
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