The number of diagonal matrix, `A` or order`n` which `A^3=A` is a. is a a. 1 b. 0 c. `2^n` d. `3^n`

If d is the determinant of a square matrix A of order n , then the determinant of its adjoint is d^n (b) d^(n-1) (c) d^(n+1) (d) d

The number of possible outcomes in a throw of n ordinary dice in which at least one of the die shows and odd number is a. 6^n-1 b. 3^n-1 c. 6^n-3^n d. none of these

Let A be a set of n(geq3) distance elements. The number of triplets (x ,y ,z) of the A elements in which at least two coordinates is equal to a. ^n P_3 b. n^3-^n P_3 c. 3n^2-2n d. 3n^2-(n-1)

For a non singular matrix A of order n the rank of A is (A) less than n (B) equal to n (C) greater than n (D) none of these

If D_1 and D_2 are diagonal matices of order 3xx3 then (A) D_1^n is a diagonal matrix (B) D_1D_2=D_2D_1 (C) D_1^2+D_2^2 is diagonal matrix (D) D_1D_2 is a diagonal matix

(lim)_(n->oo)(n !)/((n+1)!+n !) is equal to a. 1 b . 0 c. 2 d. 1/2

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

The total number of ways of selecting two numbers from the set {1,2, 3, 4, ........3n} so that their sum is divisible by 3 is equal to a. (2n^2-n)/2 b. (3n^2-n)/2 c. 2n^2-n d. 3n^2-n

Suppose A is a complex number and n in N , such that A^n=(A+1)^n=1, then the least value of n is 3 b. 6 c. 9 d. 12