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1.How many three digit numbers with distinct digits can be formed such that the product of the digits is the cube of a positive integer?

2.Let A= {x ; x is a prime number and x<30}The number of different rational numbers whose numerator and denominator belong to A is?

3.Find the number of integral solutions to |x||y||z|=15

4.There are 6 boys and 4 girls sitting for a photo session.They were posing for the photograph standing in two rows one behind the other.There were 5 people sitting in the front row and 5 standing in the back row. i)If the boys were divided equally among the front and back rows,in how many ways can the photo session be arranged? ii)In how many ways can the photos be taken such that no two boys and no two girls are standing or sitting together?

5.ABCD is a convex quadrilateral.3,4,5 and 6 points are marked on the sides AB,BC,CD and DA.The number of triangles with vertices on different sides is?

6.The number of triangles that can be formed with 10 points as vertices , n of them being collinear , is 110.What is n?

7.If a , b and c are positive integers such that a+b+c <= 8 then the number of possible values of the ordered triplet (a,b,c) is?

8.The product of “r” consecutive integers is necessarily divisible by a) r b)(r+1)! c)Summation k where k = 1 to (r-1)

9.In an election there are 5 candidates and three members are to be elected, and an elector can vote for any number of candidates not greater than the number to be elected.Then the number of ways in which an elector may vote is?

10.The greatest possible number of points of intersection of 8 straight lines and 4 circles is?

11.In a plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B.Besides, no three lines pass through one point, no line passes through both points A and B,no two are parallel.Then the number of intersection points the lines have is equal to ?

12.The total number of natural numbers of 6 digits that can be made with digits 1,2,3,4 if all digits have to appear in the same number atleast once is?

13.In a club election, number of contestants is one more than the number of maximum candidates for which a voter can vote for.If the total number of ways in which a voter can vote is 62, whta is the number of candidates?

14.All possible two factor products are formed from the numbers 1,2,3,4…200.The number of factors obtained out of the total which are multiples of 5 is?

15.3 apples and 2 bananas have to be distributed among 3 boys and 2 girls, such that each person gets one fruit.In how many different ways can this be done if atleast one girl gets an apple?

16.Find the distinct number of 7 digit numbers the sum of whose digits is even?

17.A man has 7 relatives( 4 ladies and 3 men).His wife also has 7 relatives(3 ladies and 4 men).In how many ways can they invite 3 ladies and 3 men for dinner so that there are 3 of the man’s relatives and 3 of the wife’s relatives?

18.Find the number of numbers between 20000 and 60000 having sum of the digits even?

19.Eight straight lines in a set are parallel to each other and the distance between any two adjacent lines is 1 cm.Another set of 6 straight lines are parallel to each other and the distance between any two adjacent lines is 1 cm. These 6 lines intersect with the 8 lines of first set to form parallelograms.How many of such formed parallellograms will not be rhombuses?

20.10 guests of which 3 are ladies ar eto be seated in a row.The ladies insist on sitting together while 2 of the men refuse to take consecutive seats.In how many ways can the guests be seated?

21.Find the number of non-negative integral solutions of 2x+2y+z=10?

22.How many committees of 11 ppl can be made out of 50 ppl if three persons a , b and c are not to be included together in the committee?

23.If each of the m points on the one straight line be joined to each of the n points on the other staright line, then excluding the points on the given two lines , number of points of intersection of these lines is?