Simplify:
find the value of n
`(n)/(2)-(3n)/(4)+(5n)/(6)=21`

(i) If (n!)/(2.(n-2)!): (n!)/(4!.(n-4)!) = 2:1 , find the valye of n. (ii) If ((2n)!)/(3!(2n-3)!): (n!)/(2!(n-2)!) = 44:3 , then find the value of n.

Find the value of 'n' if (n+4) ! = 56 (n+2) ! .

Solve the linear equations. n/2 - (3 n)/4 + (5 n)/6 = 21

Find the value of n if: (i) (n+2)! = 12n! (ii) (n+2)! = 60(n-1)! (iii) (n+3)! = 2550 (n+1)! (iv) (n-2)! = 132. (n-4)! .

Find the values of m and n if : 4^(2m)=(root(3)(16))^(-(6)/(n))=(sqrt(8))^(2)

Find the value of n : (2^(3)xx5^(n+1)xx10^(2)xx5^(n-1))/(125xx5^(n-2)xx2^(7))=(25)/(4)

find the value of n, given : (4^(n-2)xx2^(n-5)xx6xx2^(n+3))/(3xx6^(2))=(4)/(18)

Find the value of n such that "(i) "^(n)P_(5) =42 xx ""^(n)P_(3), n gt 4 " (ii) "(""^(n)P_(4))/(" "^(n-1)P_(4))=(5)/(3), n gt 4.

The value of lim_(n to oo)((n!)/(n^(n)))^((2n^(4)+1)/(5n^(5)+1)) is equal

Simplify: (6m-n)(6m+n)