HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

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")!)`

Simplify `(("n" + 3)!)/(("n"^2 - 4)("n" + 1)!)`

Simplify `1/("n"!) - 1/(("n" - 1)!) - 1/(("n" - 2)!)`

Simplify n[n! + (n – 1)!] + n²(n – 1)! + (n + 1)!

Simplify `("n" + 2)/("n"!) - (3"n" + 1)/(("n" + 1)!)`

Simplify `1/(("n" - 1)!) + (1 - "n")/(("n" + 1)!)`

Simplify `1/("n"!) - 3/(("n" + 1)!) - ("n"^2 - 4)/(("n" + 2)!)`

Simplify `("n"^2 - 9)/(("n" + 3)!) + 6/(("n" + 2)!) - 1/(("n" + 1)!)`

Select the correct answer from the given alternatives.

In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?