If `A=[(2,-4),(1,-1)]` the value of `A^n` is (A) `[(3^n,(-4)^n),(1,(-1)^n)]` (B) `[(3n,-4n),(n,n)]` (C) `[(2+n,5-n),(n,-n)]` (D) none of these

The value of lim_(n->oo)[(2n)/(2n^2-1)cos(n+1)/(2n-1)-n/(1-2n)dot(n(-1)^n)/(n^2+1)]i s 1 (b) -1 (c) 0 (d) none of these

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a). (n !)/((n-1)!(n+1)!) (b). ((2n)!)/((n-1)!(n+1)!) (c). ((2n)!)/((2n-1)!(2n+1)!) (d). none of these

If A= [(3 , -4), (1 , -1) ] , then prove that A^n=[(1+2n , -4n), (n , 1-2n) ] , where n is any positive integer.

Find sum of sum_(r=1)^n r . C (2n,r) (a) n*2^(2n-1) (b) 2^(2n-1) (c) 2^(n-1)+1 (d) None of these

If the value of "^(n)C_(0)+2*^(n)C_(1)+3*^(n)C_(2)+...+(n+1)*^(n)C_(n)=576 , then n is (a) 7 (b) 5 (c) 6 (d) 9

The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (n !)/((n-1)!(n+1)!) b. ((2n)!)/((n-1)!(n+1)!) c. ((2n)!)/((2n-1)!(2n+1)!) d. none of these

if A=[{:(3,-4),(1m,-1):}], then show that A^(n)=[{:(1+2n,-4n),(n,1-2n):}] is true for all natural values of n.

The value of lim_(n to oo) (2n^(2) - 3n + 1)/(5n^(2) + 4n + 2) equals

If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient of x^m is a. ((2n)!)/((m)!(2n-m)!) b. ((2n)!3!3!)/((2n-m)!) c. ((2n)!)/(((2n-m)/3)!((4n+m)/3)!) d. none of these

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)! .