If (n+1)! = 12 [(n-1)!], find n.

If (n+2)! = 60 [(n-1)!], find n.

If "^(2n)C_3 : ^nC_2= 12: 1 , find n .

If A = [[1 ,1],[1,1]] and det (A^(n) - 1) = 1 -lambda ^(n), n in N, then the value of lambda is

If a_(1)=1,a_(n+1)=(1)/(n+1)a_(n),a ge1 , then prove by induction that a_(n+1)=(1)/((n+1)!)n in N .

If 1/(9!)+1/(10!) =n/(11!) , find n.

The number of functions f: {1,2, 3,... n}-> {2016, 2017} , where ne N, which satisfy thecondition f1)+f(2)+ ...+ f(n) is an odd number are a. 2^n b. n*2^(n-1) c. 2^(n-1) d. n!

If "^(n-1)C_r : ^nC_r : ^(n+1)C_r= 6:9: 13 , find n and r.

Let f : WrarrW , be defined as f (n) = n – 1 , if n is odd and f (n) = n + 1 , if n is even. Show that f is invertible. Find the inverse of f . Here, W is the set of all whole numbers.

The sum of n terms of two arithmetic series are in the ratio of (7n + 1)/(4n + 27) . Find the ratio of their 12th terms.

If A = [[1,1,1],[1,1,1],[1,1,1]] , prove that A^n = [[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)]], n in N