`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

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)

lim_(x rarr oo)n^(2)(x^((1)/(n))-x^((1)/((n+1)))),x>0, is equal to (a)0(b)e^(x)(c)(log)_(e)x(d) none of these

Lt_(nrarroo)((n!)/n^n)^(1/n)= (A) e^(-2) (B) e^(-1) (C) e^3 (D) e

lim_(nrarroo) (1-x+x.root n e)^(n) is equal to

Let lim_(n rarr oo)(((kn)!)/(n^(kn)))^(1/n)=lambda(k) where k in N

The coefficient of x^k d in the expansion of 1+(1+x)+(1+x_)^2+……+(1+x)^n is (A) ^nC_k (B) ^(n+1)C_k (C) ^(n+1)C_(k+1) (D) none of these

Lt_(nrarroo) sum_(r=1)^(6n) 1/(n+r)= (A) log6 (B) log7 (C) log5 (D) 0

lim_(nrarroo) sum_(r=1)^n 1/n e^(r/n) is (A) 1-e (B) e-1 (C) e (D) e+1

" If "Lt_(nrarroo) ((prod_(k=1)^(n)(1+(k)/(n))))^(1/n)" has the value of equal to "ke^(-1)" where "k in N" ,then the value of "K" is "

If A=[a_(ij)] is a scalar matrix of order n xx n such that a_(ii)=k for all i, then trace of A is equal to nk(b)n+k(c)(n)/(k) (d) none of these