HSC Arts (English Medium) ११ वीं कक्षा - Maharashtra State Board Question Bank Solutions

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?

In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?

Select the correct answer from the given alternatives.

In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate

Select the correct answer from the given alternatives.

Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.

Answer the following:

Find the number of words that can be formed by using all the letters in the word REMAIN If these words are written in dictionary order, what will be the 40^th word?

In the following expansion, find the indicated term:

`(2x^2 + 3/(2x))^8`, 3^rd term.

In the following expansion, find the indicated term.

`(x^2 - 4/(x^3))^11`, 5^th term

In the following expansion, find the indicated term.

`((4x)/5 - 5/(2x))^9`, 7^th term