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

Write in terms of factorial.

6 × 7 × 8 × 9

Write in terms of factorial.

5 × 10 × 15 × 20

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

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

Evaluate `("n"!)/("r"!("n" - "r")!)` for n = 15, r = 10

Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 15, r = 8

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

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

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

Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 7)!)` = 1 : 6

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!)`

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

Simplify `((2"n" + 2)!)/((2"n")!)`