Home
Class 12
MATHS
If a(1),a(2),a(3) "and" b(1),b(2),b(3) i...

If `a_(1),a_(2),a_(3) "and" b_(1),b_(2),b_(3) in` R and are such that `a_(i)b_(j)ne "for" 1lt=I,jlt=3`,
`|{:((1-a_(1)^(3)b_(1)^(3))/(1-a_(1b_(1))),(1-a_(1)^(3)b_(2)^(3))/(1-a_(1b_(2))),(1-a_(1)^(3)b_(3)^(3))/(1-a_(1b_(3)))),((1-a_(2)^(3)b_(1)^(3))/(1-a_(2)b_(1)),(1-a_(2)^(3)b_(2)^(3))/(1-a_(2)b_(2)),(1-a_(2)^(3)b_(3)^(3))/(1-a_(2)b_(3))),((1-a_(3)^(3)b_(1)^(3))/(1-a_(3)b_(1)),(1-a_(3)^(3)b_(2)^(3))/(1-a_(3)b_(2)),(1-a_(3)^(3)b_(3)^(3))/(1-a_(3)b_(3))):}|gt` 0 provided either
`a_(1)lta_(2)lta_(3)" "and b_(1)ltb_(2)ltb_(3) " "or a_(1)gta_(2)gta_(3) " "and"b_(1)gtb_(2)gtb_(3).`

A

depends on `a_(i),i`=1,2,3,4

B

depends on `b_(i)`,i=1,2,3,4

C

dependes on `c_(i)`,i=1,2,3,4

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Similar Questions

Explore conceptually related problems

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)|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),a_(2),a_(3)"....." are in GP with first term a and common rario r, then (a_(1)a_(2))/(a_(1)^(2)-a_(2)^(2))+(a_(2)a_(3))/(a_(2)^(2)-a_(3)^(2))+(a_(3)a_(4))/(a_(3)^(2)-a_(4)^(2))+"....."+(a_(n-1)a_(n))/(a_(n-1)^(2)-a_(n)^(2)) is equal to

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 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

(1+x)^(10)=a_(0)+a_(1)x+a_(2)x^(2)+……..+a_(10)x^(10) then the value of (a_(0)-a_(2)+a_(4)-a_(6)+a_(8)-a_(10))^(2)+(a_(1)-a_(3)+a_(5)-a_(7)+a_(9))^(2) is ……

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

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.

If a_(1),a_(2),a_(3),"........",a_(n) are in AP with a_(1)=0 , prove that (a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1)) .

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)