JEE Advanced Model Paper 9 with solutions for online practice

Let BD = x , EC = y , AH = z
Now , AG × AF = AH × AJ ⇒ 2 × 15 = z × (z + 7) ⇒ z2 + 7z - 30 = 0 ⇒ z = 3
Since, AC = AB ⇒ 16 = 3 + 7 + BJ ⇒ BJ = 6
Now , BJ × BH = BD × BE ⇒ 6 × 13 = x × (16 - y) ..... (i)
Also , CE × CD = CF × CG ⇒ y (16 - x) = 1 × 14 ..... (ii)
On solving equations (i) and (ii) we get
x = 10 - √22 , y = 6 - √22
∴ DE = 16 - x - y = 16 - (10 - √22) - (6 - √22) = 2 √22