If `a_(1)`, `a_(2)`, `a_(3)`, `5`, `4`, `a_(6)`, `a_(7)`, `a_(8)`, `a_(9)` are in `H.P.` and the value of the determinant `|{:(a_(1),a_(2),a_(3)),(5,4,a_(6)),(a_(7),a_(8),a_(9)):}|` is `D` then the value of `21 D//10` is

Answer

2

Explanation

We have `D=|{:(a_(1),,a_(2),,a_(3)),(5,,4,,a_(6)),(a_(7),,a_(8),,a_(9)):}|`
Since `a_(n)=(20)/(n): d=(1)/(20)`
`" Hence " D= |{:(20,,(20)/(2),,(20)/(3)),((20)/(4),,(20)/(5),,(20)/(6)),((20)/(7),,(20)/(8),,(20)/(9)):}|=((20)^(3))/(4xx7) |{:(1,,(1)/(2),,(1)/(3)),(1,,(4)/(5),,(2)/(3)),(1,,(7)/(8),,(7)/(9)):}|`
`R_(1) to R_(1)-R_(2) " and " R_(2) to R_(2)-R_(3)`
`=((20)^(3))/(4xx7) |{:(0,,(-3)/(10),,(-1)/(3)),(0,,(-3)/(40),,(-1)/(9)),(1,,(7)/(8),,(7)/(9)):}|=(50)/(21)`
`rArr [D] =2`