Let `{D_(1),D_(2),D_(3),cdots, D_(n)}` be the set of third order determinants that can be made with the distinct non-zero real numbers `a_(1),a_(2), cdots,a_(9).` Then ,

Let {D_(1),D_(2),D_(3)...,D_(n)} be the set of third order determinant that can be made with the distinct non-zero real numbers a_(1),a_(2),...a_(q) Then sum_(i=1)^(n)D_(i)=1 b.sum_(i=1)^(n)D_(i)=0cD_(i)-D_(j),quad AA i,j d.none of these

Let {D_1, D_2, D_3 ,D_n} be the set of third order determinant that can be made with the distinct non-zero real numbers a_1, a_2, a_qdot Then sum_(i=1)^n D_i=1 b. sum_(i=1)^n D_i=0 c. D_i-D_j ,AAi ,j d. none of these

Let {D_1, D_2, D_3 ,D_n} be the set of third order determinant that can be made with the distinct non-zero real numbers a_1, a_2, a_qdot Then sum_(i=1)^n D_i=1 b. sum_(i=1)^n D_i=0 c. D_i-D_j ,AAi ,j d. none of these

Let {D_1, D_2, D_3 ,D_n} be the set of third order determinant that can be made with the distinct non-zero real numbers a_1, a_2, a_qdot Then a. sum_(i=1)^n D_i=1 b. sum_(i=1)^n D_i=0 c. D_i-D_j ,AAi ,j d. none of these

Let {D_1, D_2, D_3 ,D_n} be the set of third order determinant that can be made with the distinct non-zero real numbers a_1, a_2, a_qdot Then sum_(i=1)^n D_i=1 b. sum_(i=1)^n D_i=0 c. D_i-D_j ,AAi ,j d. none of these

Let a_(1),a_(2),a_(100) be non-zero real numbers such that a_(1)+a_(2)++a_(100)=0. Then

Let a_(1)=0 and a_(1),a_(2),a_(3),...,a_(n) be real numbers such that |a_(i)|=|a_(i-1)+1| for all i then the A.M.of the numbers a_(1),a_(2),a_(3),...,a_(n) has the value A where

Let theta=(a_(1),a_(2),a_(3),...,a_(n)) be a given arrangement of n distinct objects a_(1),a_(2),a_(3),…,a_(n) . A derangement of theta is an arrangment of these n objects in which none of the objects occupies its original position. Let D_(n) be the number of derangements of the permutations theta . The relation between D_(n) and D_(n-1) is given by