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

If A be any n xx n matrix and k any scalar, then detkA is equal to -

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

n lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is a. sum_(k=1)^(n-1)k b. n(n-1) c. n^2 d. none of these

If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (a)always -1 if n is even (b) always 1 if n is odd (c) always 1 (d) none of these

A and B are square matrices and A is non-singular matrix, then (A^(-1) BA)^n,n in I' ,is equal to (A) A^-nB^nA^n (B) A^nB^nA^-n (C) A^-1B^nA (D) A^-nBA^n

Let n(A) = m, n(B) = n, then the total number of relations between A and B is K^(mn) , find K.

Let f(n ,k) denote the number of ways in which k identical balls can be colored with n colors so that there is at least one ball of each color. Then f(n ,2n) must be equal to a. ""^(2n) C_n b. ""^(2n-1)C_(n+1) c. ""^(2n-1)C_n d. none of these

Let vecalpha=a hat i+b hat j+c hat k , vecbeta=b hat i+c hat j+a hat ka n d vecgamma=c hat i+a hat j+b hat k are three coplanar vectors with a!=b ,a n d vec v= hat i+ hat j+ hat kdot Then v is perpendicular to vecalpha b. vecbeta c. vecgamma d. none of these

The centre of the circle given by vec r.( hat i+2 hat j+2 hat k)=15a n d| vec r.( hat j+2 hat k)|=4 is a. (0,1,2) b. (1,3,4) c. (-1,3,4) d. none of these

The number of value of k for which [x^2-(k-2)x+k^2]xx""[x^2+k x+(2k-1)] is a perfect square is a. 2 b. 1 c. 0 d. none of these