For x ∈ (0, π), the equation sin x + 2sin2x −sin3x = 3 has
Infinitely many solutions
Three solutions
One solution
No solution
The correct answer is option D) No solution

The least value of R.H.S is 3 at x = π/2 while the greatest value of L.H.S is 3 at x = π/3.
Hence, L.H.S and R.H.S are not equal at the same value of x. so, no solution
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)