If the entries in a `3xx3` determinant are either 0 or 1, then the greatest value of their determinants is

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability (1)/(2) )

If x , y , z are in A.P. , then the value of the determinant are in A.P. , then the value of the determinant |a+2a+3a+2x a+3a+4a+2y a+4a+5a+2z| is a. 1 b. 0 c. 2a d. a

Let P be a matrix of order 3xx3 such that all the entries in P are from the set {-1,\ 0,\ 1} . Then, the maximum possible value of the determinant of P is ______.

If a determinant of order 3xx3 is formed by using the numbers 1 or -1 then minimum value of determinant is :

Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of the set of all determinants with value -1 . Then

A 3xx3 determinant has entries either 1 or -1 . Let S_(3)= set of all determinants which contain determinants such that product of elements of any row or any column is -1 For example |{:(1,,-1,,1),(1,,1,,-1),(-1,,1,,1):}| is an element of the set S_(3) . Number of elements of the set S_(3)=

A 3xx3 determinant has entries either 1 or -1 . Let S_(3)= set of all determinants which contain determinants such that product of elements of any row or any column is -1 For example |{:(1,,-1,,1),(1,,1,,-1),(-1,,1,,1):}| is an element of the set S_(3) . Number of elements of the set S_(n)=

Let A be the set of all 3 xx 3 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in A is