Let`s_k=[[1,k],[0,1]],k∈ N then (s_2)^n (s_x)^-1` (where n in N) is equal to `(s_k)^-1` denotes inverse of matrix `s_k`

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

Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-2k-2sqrt(k)2k-1]a n dB=[0 2k-1sqrt(k)1-2k0 2-sqrt(k)-2sqrt(k)0] . If det (a d jA)+det(a d jB)=10^6,t h e n[k] is equal to. [Note: a d jM denotes the adjoint of a square matix M and [k] denotes the largest integer less than or equal to K ].

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

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

For what value(s) of k the matrix [(4,k),(2,1)] has no inverse?

Let f(n)= sum_(k=1)^(n) k^2 ^"(n )C_k)^ 2 then the value of f(5) equals

lim_(n rarr infty) sum_(k=1)^(n) (n)/(n^(2)+k^(2)x^(2)),x gt 0 is equal to

Let A be an nth-order square matrix and B be its adjoint, then |A B+K I_n| is (where K is a scalar quantity) a. (|A|+K)^(n-2) b. (|A|+K)^n c. (|A|+K)^(n-1) d. none of these

Let A be an nth-order square matrix and B be its adjoint, then |A B+K I_n| is (where K is a scalar quantity) (|A|+K)^(n-2) b. (|A|+K)^n c. (|A|+K)^(n-1) 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