JEE Main201912 Apr 2019Evening ShiftMathematicsDeterminantsActual
If [ x ] denotes the greatest integer ≤ x , then the system of linear equations [ s i n θ ] x + [ - c o s θ ] y = 0 , [ c o t θ ] x + y = 0
Options
- Ahas a unique solution if θ ∈ π 2 , 2 π 3 ∪ π , 7 π 6
- Bhave infinitely many solution if θ ∈ π 2 , 2 π 3 ∪ π , 7 π 6
- Chas a unique if θ ∈ π 2 , 2 π 3 and have infinitely many solutions if θ ∈ π , 7 π 6
- Dhave infinitely many solutions if θ ∈ π 2 , 2 π 3 and has a unique solution if θ ∈ π , 7 π 6
Correct answer
D. have infinitely many solutions if θ ∈ π 2 , 2 π 3 and has a unique solution if θ ∈ π , 7 π 6
Step-by-step solution
sin ⁡ θ x + - cos ⁡ θ y = 0   and cos ⁡ θ x + y = 0   for infinite many solution sin ⁡ θ - cos ⁡ θ cot ⁡ θ   1 = 0 i.e. sin θ =   - cos θ     c o t θ       . . . i when θ ∈ π 2 ,   2 π 3 then s i n θ ∈ 0 ,   1 2   ⇒   sin θ = 0 and - cos θ ∈ 0 ,   1 2   ⇒   - cos θ = 0 and cot θ ∈ -