The given lines are

x − 2y + 3 = 0 … (1)

λx + 3y + 1 = 0 … (2)

4x − λy + 2 = 0 … (3)

It is given that (1), (2) and (3) are concurrent.

∴

⇒ (6 + λ) + 2(2λ – 4) + 3(-λ² – 12) = 0

⇒ 6 + λ + 4λ – 8 – 3λ² – 36 = 0

⇒ 5λ – 3λ² – 38 = 0

⇒ 3λ² – 5λ + 38 = 0

The discriminant of this equation is 25-4 × 3 × 38 = -431

Hence, there is no real value of λ for which the lines x − 2y + 3 = 0, λx + 3y + 1 = 0 and 4x − λy + 2 = 0 are concurrent.