Let S be the set of all values of θ [-π, π] for which the system of linear equations x+y+√(3) z=0 -x+(tan θ) y+√(7) z=0 x+y+(tan θ) z=0 has non-trivial solution. Then 120/(π) Σ θ s θ is equal to:

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q4628

JEE Main 20238 Apr, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

Let S be the set of all values of

\theta \in[-\pi, \pi]

for which the system of linear equations

x+y+\sqrt{3} z=0

-x+(\tan \theta) y+\sqrt{7} z=0

x+y+(\tan \theta) z=0

has non-trivial solution. Then

\frac{120}{\pi} \sum_\limits{\theta \in \mathrm{s}} \theta

is equal to :