A person has 2 parents, 4 grandparents, 8 great grand parents, and so on. Find the number of his ancestors during the ten generations preceding his one.

A person has 2 parents, 4 grandparents, 8 great grandparents, and so on, then the number of his ancestors during the ten generations preceeding his own is

Each of two parallel lines has a number of distinct points marked on them. On one line there are 2 points P and Q and on the other there are 8 points. i. Find the number of triangles formed having three of the 10 points as vertices. ii. How many of these triangles include P but exclude Q?

In a certain an algebraical exercise book there and 4 examples on arithmetical progression, 5 examples on permutation and combination, and 6 examples on binomial theorem. Find the number of ways a teacher can select or his pupils at least one but not more than 2 examples from each of these sets.

Pankaj distributes 4 sweets to each student in his class and has 7 sweets left over. Find a rule for the number of sweets he had in terms of the number of students in his class.

The lock of a safe has a dial with holes, sasy ten, in which the numbers 0,1,2,……..9 are inscribed in each hole. The lock can be opened only when a specific code numbersay of six digits is dialled. Suppose the code number is 249916, it means that the can be opened when we first dial 2, then 4 nd so on. Find the maximum number of trials which do not result in opening the lock.

In a four digit number, the digit in thousand’s place in 4 and the digit in the one’s place is twice that in the thousand’s place. The number has no hundreds. The ten’s place digit is the difference between the digit in the thousand’s place and the hundred’s place. Find the number.

Mr. john has x children by his first wife and Ms. Bashu has x+1 children by her first husband. They marry and have children of their own. The whole family has 10 children. Assuming that two children of the same parents do not fight, Find the maximum number of fight that can take place among children.

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in the party, is : 469 (2) 484 (3) 485 (4) 468

Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.(a) How can Arya divide his sandwiches so that each person has an equal share?(b) What part of a sandwich will each boy receive?

In each of the following experiments specify appropriate sample space(i) A boy has a 1 rupee coin, a 2 rupee coin and a 5 rupee coin in his pocket. He takes out two coins out of his pocket, one after the other.(ii) A person is noting down the number of accidents along a busy highway during a year.