`sum_(k=1)^m(k^2+1)k=2009xx2010!, then m=` (A) 2009 (B) 2010 (C) 2011 (D) none of these

If sum_(k=1)^(m)(k^(2)+1)k!=1999(2000!), then m is

If a_1,a_2,a_3 are in G.P. having common ratio r such that sum_(k=1)^n a_(2k-1)= sum_(k=1)^na_(2k+2)!=0 then number of possible value of r is (A) 1 (B) 2 (C) 3 (D) none of these

Lt_(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0 , is equal to (A) k/e (B) e/k (C) 1/(ke) (D) none of these

If D_k=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum_(k=1)^n D_k=48 ,then n equals (a)4 (b) 6 (c) 8 (d) none of these

The jump value of the function at the point of the discontinuity of the function f(x)=(1-k^(1/x))/(1+k^(1/x))(k>0) (k=1) is: (A) 4 (B) 2 (C) 3 (D) None of these

Lt_(nrarroo) sum_(r=1)^n (2r)^k/n^(k+1),k!=-1 , is equal to (A) 2^k/(k-1) (B) 2^k/k (C) 1/(k+1) (D) 2^k/(k+1)

If sum_(r=1)^20(r^2+1)r!=k!20 then sum of all divisors of k of the from 7^n, n epsilin N is (A) 7 (B) 58 (C) 350 (D) none of these

If x is real and k=(x^(2)-x+1)/(x^(2)+x+1), then k in[1/3,3] (b) k>=3(c)k<=1/3(d) none of these

If D_k=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum_(k=1)^n D_k=56. then n equals 4 b. 6 c. 8 d. none of these