The correct option is D (4,3)
D=∣∣
∣∣123345444∣∣
∣∣
R3→R3+2R1−2R2
D=∣∣
∣∣123345000∣∣
∣∣=0
For inconsistent system, one of Dx,Dy,Dz should not be equal to 0.
Dx=∣∣
∣∣123μ45δ44∣∣
∣∣=2(2μ−δ−2) ⋯(i)
Dy=∣∣
∣∣1133μ54δ4∣∣
∣∣=−4(−δ+2μ−2) ⋯(ii)
Dz=∣∣
∣∣12134μ44δ∣∣
∣∣=−2(δ−2μ+2) ⋯(iii)
For inconsistent system, we get from (i),(ii) and (iii)
2μ≠δ+2
∴ From the provided options, the system will be inconsistent for μ=4,δ=3.