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

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

If (n+2)! =(2550)(n!), find n.

Find n, if (n+2) ! =60xx(n-1)!

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

Find the value of n , if ((2n)! (n - 3)!)/((2n - 3)! n!) = 11

If S_n = n² + 2n , then find first term & common difference?

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that (1*2) C_(2) + (2*3) C_(3) + …+ {(n-1)*n} C_(n) = n(n-1) 2^(n-2) .

Find the derivative of x^n + ax^(n-1) + a^2 x^(n-2) + . . .+ a^(n- 1) x + a^n for some fixed real number a.

If ""^(n)C_(r ): ""^(n)C_(r+1)=1:2 and ""^(n)C_(r+1): ""^(n)C_(r+2)=2:3 , find n and r.