Advertisements
Advertisements
Question
Find n, if (n + 3)! = 110 × (n + 1)!
Advertisements
Solution
(n + 3)! = 110 × (n + 1)!
(n + 3)(n + 2)(n + 1)! = 110(n + 1)!
∴ (n + 3)(n + 2) = 110
∴ n2 + 5n + 6 = 110
∴ n2 + 5n + 6 – 110 = 0
∴ n2 + 5n – 104 = 0
∴ n2 + 13n – 8n – 104 = 0
∴ n(n + 13) – 8(n + 13) = 0
∴ (n + 13)(n – 8) = 0
∴ n + 13 = 0 or n – 8 = 0
∴ n = – 13 or n = 8
But n ∈ N
∴ n ≠ – 13
Hence, n = 8.
APPEARS IN
RELATED QUESTIONS
Evaluate: 8!
Evaluate: 10! – 6!
Evaluate: (10 – 6)!
Compute: `(12!)/(6!)`
Compute: `(12/6)!`
Compute: 3! × 2!
Compute: `(9!)/(3! 6!)`
Compute: `(8!)/(6! - 4!)`
Compute: `(8!)/((6 - 4)!)`
Write in terms of factorial.
5 × 6 × 7 × 8 × 9 × 10
Write in terms of factorial.
3 × 6 × 9 × 12 × 15
Write in terms of factorial.
6 × 7 × 8 × 9
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 + 1)! = 42 × (n – 1)!
Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!
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)!)`
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" + 2)/("n"!) - (3"n" + 1)/(("n" + 1)!)`
Simplify `1/("n"!) - 3/(("n" + 1)!) - ("n"^2 - 4)/(("n" + 2)!)`
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.
Eight white chairs and four black chairs are randomly placed in a row. The probability that no two black chairs are placed adjacently equals.
3. 9. 15. 21 ...... upto 50 factors is equal to ______.
Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn + 1 – Tn = 21, then n is equal to ______.
