Match of the following columns :

The correct answer is
(a) ......... `" "` (b) ........... `" "` (c)......... `" "` (d) .........

Answer

(a)-(s), (b)-(q), (c)-(p), (d)-(r)

Explanation

Let `AE=x` cm. then, EC=(5.6) cm.
`(AD)/(DB)=(AE)/(EC) rArr (3)/(5)=(x)/(5.6-x)`
`:. 3(5.6-x)=5x rArr 8x= 3xx5.6`
`:. x=(3xx5.6)/(8) =(16.8)/(8) =2.1`
` (b) (AB)/( DE)=(BC)/(EF)rArr (3)/(2)=(6)/(x) rArr 3x=12 rArr x=4`
`(c) (ar(Delta ABC))/(ar (Delta PQR))=(BC^(2))/(QR^(2)) rArr (9)/(16)=(BC^(2))/(QR^(2)) rArr ((3)/(4))^(2) =((BC)/(QR))^(2)`
`rArr (BC)/(QR)=(3)/(4) rArr QR=(4)/(3) xx BC=((4)/(3)xx4.5) cm=6 cm`

(d) `Delta OAB~Delta OCD rArr (OA)/(OD) rArr (2x+4)/(2x-1) =(9x-21)/(3)`
`rArr 6x=12x=18x^(2)-51x+21 rArr 18x^(2)-57 x+9=0`
`rArr 6x^(2)-19x+3=0 rArr x-3x(6x-1)=0 rArr x=3 or x=(1)/(6)`
But, `x=(1)/(6)` makes `(2x-1) lt0` . so we reject it.
`:. x=3`
The correc answer is (a)-(s), (b)-(q), (c)-(p), (d)-(r)