If the system of equations 2x+5y= 7,6x+λy= 28 is inconsistent, then

The correct answer is Option (4) → $λ=15$

Given equations:

$2x + 5y = 7 \quad ...(1)$

$6x + \lambda y = 28 \quad ...(2)$

For inconsistency, the ratio of coefficients of $x$ and $y$ must be equal, but the ratio of constants must be different.

$\frac{2}{6} = \frac{5}{\lambda} \ne \frac{7}{28}$

From $\frac{2}{6} = \frac{5}{\lambda}$ ⇒ $\lambda = \frac{5 \times 6}{2} = 15$

Final Answer:

$\lambda = 15$