Two parallel chords of a circle of radius 2 are at a distance √3+1 apart. If the chords subtend at the centre, angles of πk and 2πk, where k>0, then the value of [k] is [Note: [k] denotes the largest integer less than or equal to k].

Solution:
2cos(π/2k) + 2cos(πk) = √3 + 1
or, cos(π/2k) + cos(πk) = (√3 + 1)/2
Let πk = θ
cos(θ/2) + cos θ = (√3 + 1)/2
2cos²(θ/2) - 1 + cos θ = (√3 + 1)/2
cos²(θ/2) + cos θ = (√3 + 3)/2
cos²θ/2 = t
or, t² + t - (√3 + 3)/2 = 0
or, t = (-1 ± √(1 + 4(√3 + 3)/2))/2 = (-1 ± √(1 + 2√3 + 6))/2 = (-1 ± (2√3 + 1))/4 = √3/2 or -√3/2 - 1
∵ t ∈ [-1, 1]
or, t = cos²(θ/2) = √3/2
or, θ/2 = π/6
∴ k = 3
Hence, B is the correct option.