If `|a_(1)|gt|a_(2)|+|a_(3)|,|b_(2)|gt|b_(1)|+|b_(3)|` and
`|c_(2)|gt|c_(1)|+|c_(2)|` then show that `|{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|ne0.`

If a_(1),b_(1),c_(1),a_(2),b_(2),c_(2) "and" a_(3),b_(3),c_(3) are three digit even natural numbers and Delta=|{:(c_(1),a_(1),b_(1)),(c_(2),a_(2),b_(2)),(c_(3),a_(3),b_(3)):}| , then Delta is

if (1+ax+bx^(2))^(4)=a_(0) +a_(1)x+a_(2)x^(2)+…..+a_(8)x^(8), where a,b,a_(0) ,a_(1)…….,a_(8) in R such that a_(0)+a_(1) +a_(2) ne 0 and |{:(a_(0),,a_(1),,a_(2)),(a_(1),,a_(2),,a_(0)),(a_(2),,a_(0),,a_(1)):}|=0 then the value of 5.(a)/(b) " is " "____"

Statement -1 Consider the determinant Delta=|{:(a_(1)+b_(1)x^(2),a_(1)x^(2)+b_(1),c_(1)),(a_(2)+b_(2)x^(2),a_(2)x^(2)+b_(2),c_(2)),(a_(3)+b_(3)x^(2),a_(3)x^(2)+b_(3),c_(3)):}|=0, where a_(i),b_(i),c_(i) in R (i=1,2,3) and x in R Stement -2 If |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| =0, then Delta =0

If a_1,a_2,a_3….a_r are in G.P then show that |{:(a_(r+1),a_(r+5),a_(r+9)),(a_(r+7),a_(r+11),a_(r+15)),(a_(r+11),a_(r+7),a_(r+21)):}| is independent of r

bar(a)=a_(1)hati+a_(2)hatj+a_(3)hatk,bar(b)=b_(1)hati+b_(2)hatj+b_(3)hatk,bar( c )=c_(1)hati+c_(2)hatj+c_(3)hatk are three non zero vectors. The unit vector bar( c ) is perpendicular to bar(a) and bar(b) . The angle between bar(a) and bar(b) is (pi)/(6) then, |{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| = .............

The number of functions from f:{a_(1),a_(2),...,a_(10)} rarr {b_(1),b_(2),...,b_(5)} is

Answer each question by selecting the proper alternative from those given below each question so as to make the statement true: The solution of the pair of linear equations a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 by corss-multiplication method is given by .................. x=(b_(2)c_(1)-b_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(1)c_(2)-a_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)) x=(b_(1)c_(2)-b_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(1)c_(2)-a_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)) x=(b_(2)c_(1)-b_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(2)c_(1)-a_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1)) x=(b_(1)c_(2)-b_(2)c_(1))/(a_(1)b_(2)-a_(2)b_(1)), y=(a_(2)c_(1)-a_(1)c_(2))/(a_(1)b_(2)-a_(2)b_(1))

If Delta=|{:(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33)):}| and C_(ij)=(-1)^(i+j) M_(ij), "where " M_(ij) is a determinant obtained by deleting ith row and jth column then then |{:(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33)):}|=Delta^(2). If |{:(1,x,x^(2)),(x,x^(2),1),(x^(2),1,x):}| =5 and Delta =|{:(x^(3)-1,0,x-x^(4)),(0,x-x^(4),x^(3)-1),(x-x^(4),x^(3)-1,0):}| then sum of digits of Delta^(2) is

the value of the determinant |{:((a_(1)-b_(1))^(2),,(a_(1)-b_(2))^(2),,(a_(1)-b_(3))^(2),,(a_(1)-b_(4))^(2)),((a_(2)-b_(1))^(2),,(a_(2)-b_(2))^(2) ,,(a_(2)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(3)-b_(1))^(2),,(a_(3)-b_(2))^(2),,(a_(3)-b_(3))^(2),,(a_(3)-b_(4))^(2)),((a_(4)-b_(1))^(2),,(a_(4)-b_(2))^(2),,(a_(4)-b_(3))^(2),,(a_(4)-b_(4))^(2)):}| is

If A_(1),A_(2),A_(3),………………,A_(n),a_(1),a_(2),a_(3),……a_(n),a,b,c epsilonR show that the roots of the equation (A_(1)^(2))/(x-a_(1))+(A_(2)^(2))/(x-a_(2))+(A_(3)^(2))/(x-a_(3))+…+(A_(n)^(2))/(x-a_(n)) =ab^(2)+c^(2) x+ac are real.