HSC Commerce (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Write in terms of factorial:
5 × 10 × 15 × 20 × 25

Evaluate: `("n"!)/("r"!("n" - "r"!)` For n = 8, r = 6

Evaluate: `("n"!)/("r"!("n" - "r"!)` For n = 12, r = 12

Find n, if `"n"/(8!) = 3/(6!) + 1/(4!)`

Find n, if `"n"/(6!) = 4/(8!) + 3/(6!)`

Find n, if `1/("n"!) = 1/(4!) - 4/(5!)`

Find n, if (n + 1)! = 42 × (n – 1)!

Find n, if (n + 3)! = 110 × (n + 1)!

Find n if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5:3

Find n if: `("n"!)/(3!("n" - 5)!) : ("n"!)/(5!("n" - 7)!)` = 10:3

Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!

Find n, if: `((15 - "n")!)/((13 - "n")!)` = 12

Find n, if: `((2"n")!)/(7!(2"n" - 7)!) : ("n"!)/(4!("n" - 4)!)` = 24:1

Show that
`("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!`

Show that: `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`

Find the value of: `(8! + 5(4!))/(4! - 12)`

Find the value of: `(5(26!) + (27!))/(4(27!) - 8(26!)`

Show that: `((2"n")!)/("n"!)` = 2ⁿ(2n – 1)(2n –  3)....5.3.1

Two dice are thrown together. What is the probability that sum of the numbers on two dice is 5 or number on the second die is greater than or equal to the number on the first die?

A card is drawn from a pack of 52 cards. What is the probability that, card is either red or black?