AP EAMCET Engineering 20 Apr 2019 Shift 1 Paper

Consider the system of equations
x+2y+3z=6
x+3y+5z=9
2x+5y+λz=µ
Now from the Cramer's rule,
∆=|

1	2	3
1	3	5
2	5	λ

|
=1(3λ−25)−2(λ−10)+3(5−6)
=λ−8
And,
∆1=|

6	2	3
9	3	5
µ	5	λ

|
=6(3λ−25)−2(9λ−5µ)+3(45−3µ)
=µ−15
And,
∆2=|

1	6	3
1	9	5
2	µ	λ

|
=1(9λ−5µ)−6(λ−10)+3(µ−18)
=3λ−2µ+6
And,
∆3=|

1	2	6
1	3	9
2	5	µ

|
=1(3µ−45)−2(µ−18)+6(5−6)
=µ−15
Now, if λ=8 and µ≠15, then system of linear equation has no solution.
If λ≠8 and µ∈R, then system of linear equation has a unique solution.
If λ=8 and µ=15, then system of linear equation has infinite number of solutions. So, ∆2=3λ−2µ+6 is also zero therefore, the correct option is (2)