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

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 y^r=(n !^(n+r-1)C_(r-1))/(r^n),w h e r en=k r(k is contstant), then ("lim")_(rvecoo)y is equal to (a)(k-1)(log)_e(1+k)-k (b)(k+1)(log)_e(1-k)+k (c)(k+1)(log)_e(1-k)-k (d)(k-1)(log)_e(1-k)+k

"^(n-1)C_r=(k^2-8)^(n)C_(r+1) then k is

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

D_ (k) = | 2 ^ (k-1) (1) / (k (k + 1)) sin k theta xyz2 ^ (n) -1 (n) / (n + 1) (sin ((n +) 1) / (2) theta (sin n) / (2) theta) / (sin theta) / 2, thensum_ (k = 1) (n) D_ (k)

sum_(k =1)^(n) k(1 + 1/n)^(k -1) =