यदि `ab_(1) = a_(1)b` हो , तो सिद्ध कीजिए कि बिन्दु `(a, b), (a_(1), b_(1))` और `(a-a_(1), b-b_(1))` संरेखीय बिन्दु हैं ।

If a_(1)<(28)^(1/3)-3

Prove that the points (a,b),(a_(1),b_(1)) and (a-a_(1),b-b_(1)) are collinear if ab_(1)=a_(1)b

If a_(1) lt ( 28)^((1)/( 3)) - 3 lt b_(1) , then (a_(1) b_(1)) ( a_(1) , b_(1)) is

If a_(1) lt ( 257)^(1//4) -4 lt b _(1) , then (a_(1) , b_(1) ) ( a_(1) , b_(1)) is

The value of the determinant Delta = |(1 + a_(1) b_(1),1 + a_(1) b_(2),1 + a_(1) b_(3)),(1 + a_(2) b_(1),1 + a_(2) b_(2),1 + a_(2) b_(3)),(1 + a_(3) b_(1) ,1 + a_(3) b_(2),1 + a_(3) b_(3))| , is

The value of the determinant Delta = |(1 + a_(1) b_(1),1 + a_(1) b_(2),1 + a_(1) b_(3)),(1 + a_(2) b_(1),1 + a_(2) b_(2),1 + a_(2) b_(3)),(1 + a_(3) b_(1) ,1 + a_(3) b_(2),1 + a_(3) b_(3))| , is

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

Let a_(1), a_(2), cdots and b_(1), b_(2) cdots be arithmetic progression such that a_(1) = 25, b_(1) = 75 and a_(100) + b_(100) = 100 , then the sum of first hundred terms of the progression a_(1) + b_(1), a_(2) + b_(2), cdots is