HSC Commerce (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Four objects in a set of ten objects are alike. Find the number of ways of arranging them in a circular order.

Find n if `""^6"P"_2 = "n" ""^6"C"_2`

Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3

Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120

Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.

There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.

There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?

Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?

Ten students are to be selected for a project from a class of 30 students. There are 4 students who want to be together either in the project or not in the project. Find the number of possible selections.

A student finds 7 books of his interest, but can borrow only three books. He wants to borrow Chemistry part II book only if Chemistry Part I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.

Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.

There are 8 doctors and 4 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team.

Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.