If `k in R_o` then `det{adj(k I_n)}` is equal to (A) `K^(n-1)` (B) `K^((n-1)n)` (C) `K^n` (D) `k`

If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A (2) k^n adj A (3) k^(n-1) adj A (4) k^(n+1) adj A

If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A (2) k^n adj A (3) k^(n-1) adj A (4) k^(n+1) adj A

The value of sum_(r=1)^(n+1)(sum_(k=1)^n "^k C_(r-1)) ( where r ,k ,n in N) is equal to a. 2^(n+1)-2 b. 2^(n+1)-1 c. 2^(n+1) d. none of these

If a + b = k, when a, b gt o and S(k, n) = sum _(r=0)^(n) r^(2) (""^(n) C_(r) ) a^(r) cdot b^(n-r) , then

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)

sum _(k=1)^(n) tan^(-1). 1/(1+k+k^(2)) is equal to

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

Given (1-x^(3))^(n)=sum_(k=0)^(n)a_(k)x^(k)(1-x)^(3n-2k) then the value of 3*a_(k-1)+a_(k) is (a) "^(n)C_(k)*3^(k) (b) "^(n+1)C_(k)*3^(k) (c) "^(n+1)C_(k)*3^(k-1) (d) "^(n)C_(k-1)*3^(k)

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 a,b in R^(+) then find Lim_(nrarroo) sum_(k=1)^(n) ( n)/((k+an)(k+bn)) is equal to